SAINT LOUIS, MISSOURI – April 2, 2018

In our last S.A.F.E.R. Simulation post, we explored the growing importance of Verification and Validation (V&V) as the use of simulation software becomes more wide spread among not just FEA specialists but also the non-FEA expert design engineer. The emphasis on increased V&V has driven a need for improved Simulation Governance to provide managerial oversight of all the methods, standards, best practices, processes, and software to ensure the reliable use of simulation technologies by expert and novice alike.

In this final post of our current series we will profile the stress analysis software product StressCheck and the applications for which it is used in A&D engineering. StressCheck incorporates the latest advances in numerical simulation technologies that provide intrinsic, automatic capabilities for solution verification through the use of hierarchic finite element spaces, and a hierarchic modeling framework to evaluate the effect of simplifying modeling assumptions in the predictions. We will detail what that actually means for engineering users and how StressCheck enables the practice of Simulation Governance by engineering managers to make simulation Simple, Accurate, Fast, Efficient, and Reliable – S.A.F.E.R. – for experts and non-experts alike.

What is StressCheck?

StressCheck live results extraction showing the convergence of maximum stress on a small blend in an imported legacy FEA bulkhead mesh.

StressCheck is an engineering structural analysis software tool developed from its inception by Engineering Software Research & Development (ESRD) to exploit the most recent advances in numerical simulation that support Verification and Validation procedures to enable the practice of Simulation Governance. While StressCheck is based on the finite element method, StressCheck implements a different mathematical foundation than legacy-generation FEA software. StressCheck is based on hierarchic finite element spaces capable of producing a sequence of converging solutions of verifiable computational accuracy. This approach not only has a great effect on improving the quality of analysis results but also in reforming the time-consuming and error-prone steps of FEA pre-processing, solving, and post-processing as they have been performed for decades.

The origins of StressCheck extend from R&D work performed by ESRD in support of military aircraft programs of the U.S, Department of Defense. The motivation behind the development of StressCheck was to help structural engineers tackle some of the most elusive analysis problems encountered by A&D OEM suppliers and their contracting agencies in the design, manufacture, test, and sustainment of both new and aging aircraft. Historically, many of these problem types required highly experienced analysts using expert-only software tools. Yet even then, the results produced were dependent on the same expert to assess their own validity of output.

During the development of StressCheck, ESRD realized that many aerospace contractors were frustrated with the complexity, time, and uncertainty of stress analysis performed using the results of legacy finite element modeling software. As a consequence, it was not uncommon that engineering groups relied upon or even preferred to use design curves, handbooks, empirical methods, look-up tables, previous design calculations, and closed-form solutions. The time to create, debug, and then tune elaborately constructed and intricately meshed finite element models was just too exorbitant, especially early in the design cycle where changes to geometry and loads were frequent.

StressCheck was developed to address these deficiencies. Since its introduction it has now been used by every leading U.S. aircraft contractor along with many of their supply chain and sustainment partners.

What are the applications for StressCheck in the A&D industry?

StressCheck is ideally suited for engineering analysis problems in solid mechanics which require a high-fidelity solution of a known computational accuracy that is independent of the user’s expertise or the model’s mesh. In the aviation, aerospace, and defense industries these application problem classes include: structural strength analysis, detail stress analysis, buckling analysis, global/local workflows, fastened and bonded joint analysis, composite laminates, multi-body contact, engineered residual stresses, structural repairs, and fatigue and fracture mechanics in support of durability and damage tolerance (DaDT). To explore examples of these applications visit our Applications showcase area and click on any of the featured tiles.

StressCheck is not intended to be a replacement for general purpose finite element codes used for internal loads modeling of large aero-structures or complete aircraft. In these global loads models an artisan-like approach of building up a digital structure using an assortment of 2D frame and shell element types, typically of mixed element formulations with incompatible theories, may be sufficient when accuracy beyond that of approximate relative load distributions is unimportant. Most of the strength, stress, and fatigue analyses performed by aerospace structures groups occurs downstream of the global loads modeling. Historically, these analyses workflows required a series of models, each progressively adding in more structural details that had previously been approximated in often crude fashion or ignored all together.

Multi-scale, global-local including multi-body contact analysis of wing rib structure in StressCheck.

Using StressCheck it is now feasible to employ FEA with analysis problems which require modeling large spans of an aero-structure that has widely varying geometric dimensions with numerous joints, fasteners, cutouts, material types and stress concentrations. Before with traditional FEA methods it was often impossible to use solid elements throughout a multi-scale model using geometry directly from CAD data. So much time and often tricks were required to simplify, defeature, approximate, and repair the design topology that engineering managers were reluctant to approve the use of FEA for some analysis types.

Because of its inherent robustness and reliability, StressCheck is also ideal as the solver engine powering a new generation of Simulation Apps which help to democratize the power of simulation. Smart Sim Apps based on StressCheck can help to simplify, standardize, automate, and optimize recurring analysis workflows such that non-expert engineers may employ FEA-based analysis tools with even greater confidence than expert analysts can using legacy software tools.

How is StressCheck’s numerical simulation technology different from that used by legacy or traditional FEA softwares?

In a previous S.A.F.E.R. Simulation post we exposed the limitations of finite element modeling as it has been practiced to date. Most of these constraints are attributable to decisions made early in the development of the first generation of FEA software years before high performance computing was available on the engineers desktop. Unfortunately, those limitations became so entrenched in the thinking, expectations, and practices of CAE solution providers such that each new generation of FEA software was still polluted by these artifacts. To learn how this occurred and what makes StressCheck’s numerical simulation technology so different, we encourage you to view the 3.5-minute StressCheck Differentiators video:

What are the key differences and advantages of StressCheck for users?

StressCheck has numerous intrinsic features that support hierarchic modeling, live dynamic results processing, automatic reporting of approximation errors & more.

The most visible difference to the new user is that StressCheck employs a much smaller, simpler, and smarter library of elements. There are only five element types to approximate the solution of a problem of elasticity, whether it is planar, axi-symmetric, or three-dimensional. This compares to the many dozens of element types of legacy FEA software which often require a wizard to know which one to select, where to use or not to use them and more importantly, how to understand their idiosyncrasies and interpret their often erratic behavior.

The second big difference for users is that StressCheck elements map to geometry without the need for simplification or defeaturing. The available higher-order mapping means that the elements are far more robust with respect to size, aspect ratio, and distortion. As such, a relatively coarse mesh created just to follow geometry may be used across variant-scale topologies. There is no loss of resolution or a need for intermediate highly simplified “stick & frame” or “plate & beam” models.

StressCheck meshes are much easier to create, check, and change as the elements and their mesh no longer have to be the principal focus and concern of the analyst’s attention. StressCheck models aren’t fragile nor do they break as easily, and thus have to be recreated, with changes to design geometry, boundary conditions, or analysis types (e.g., linear, nonlinear, buckling). For example, a linear analysis result is the starting point for a subsequent nonlinear analysis, so the analyst simply switches solver tabs to obtain a nonlinear solution. Because of the use of hierarchic spaces during the solution execution, each run is a subset of the previous run, making it possible to perform error estimation of any result of interest, anywhere in the model after a sequence of solutions is obtained.

So, what’s the bottom line? High-fidelity solutions can be obtained from low-density meshes while preserving an explicit automatic measurement of solution quality.  No guesswork is required to determine if the FEA result can be trusted.

Detailed stress concentrations represented on “low-density” StressCheck meshes.

The errors of idealization are separated from those due to discretization/approximation (e.g. do I have ‘enough’ mesh? DOF? Element curvature?). Sources of inaccuracies and errors are immediately identifiable not because an expert catches it, but because the software is intelligent enough to report them. For each analysis users are provided with a dashboard of convergence curves that show the error in any one of a number of engineering quantities such as stress, strain, and energy norm.

Because solutions are continuous, a-priori knowledge or educated guesses of where stress concentrations may occur are no longer needed. Any engineering data of interest can dynamically be extracted at any location within the continuous domain and at any time without loss of precision due to interpolation or other post-processing manipulation necessitated from having nodal results only, characteristic of legacy FEA codes. Proof of solution convergence is also provided for any function at any location regardless of the element mesh and nodal location. As a consequence, the post-processing of fixed solutions common in legacy FEA becomes in StressCheck dynamic instantaneous extraction of live results:

What is the benefit to engineering groups and value to A&D programs from the use of StressCheck?

StressCheck automatically increases the approximation of stresses on a fixed mesh, making solution verification simple, accurate, fast, efficient & reliable.

With the use of StressCheck, the results of FEA-based structural analysis are far less dependent on the user expertise, modeling approximations, or mesh details. High-fidelity stress analysis of complex 3D solid model geometries, with numerous joints and fastener connections typical of aero-structures may be obtained in less time, with reduced complexity and greater confidence.

As a result, the stress analysis function becomes an inherently more reliable and repeatable competency for the engineering organization. FEA-based structural analysis performed with StressCheck is not an error-prone process where every different combination of user, software, elements, and mesh risks generating different answers all to the dismay of engineering leads and program managers.

By using industry application-focused, advanced numerical simulation software like StressCheck it is now possible to simplify, standardize, and automate some recurring analysis tasks to become more robust for less experienced engineers to conduct. New engineers are productive sooner with access to safer analysis tools that are intelligent enough to capture institutional methods and incorporate best practices. The role and value of the expert engineering analyst evolves to a higher level by creating improved methods and custom tools such as automated global local workflow templates and Sim Apps, respectively.

As presented in the first post of this series, the business drivers to produce higher performing damage tolerant aero-structures are requiring a near hyper-level of engineering productivity, precision, and confidence from the use of simulation technologies earlier in the design cycle. This is also true in the later stages as digital simulation replaces more physical prototyping and flight testing to facilitate concurrency of engineering and build.

Status-quo methodologies dependent on expert-only software that risk adding more time, risk, and uncertainty to the project plan is no longer satisfactory to meet these demands. Next generation simulation technologies implemented in software like StressCheck can help to encapsulate complexity, contain cost, improve reliability, mitigate risk, accelerate maturity, and support better governance of the engineering simulation function.

With StressCheck engineering simulation is Simple, Accurate, Fast, Efficient, and Reliable.

Coming Up Next…

We will discuss why StressCheck is an ideal numerical simulation tool for both benchmarking and digital engineering handbook development (i.e. StressCheck CAE handbooks).  In addition, we will provide examples of how StressCheck CAE handbooks are a robust form of Smart Sim Apps that serve to encapsulate both tribal knowledge and state-of-the-art simulation best practices.

To receive future S.A.F.E.R. Simulation posts…

In this “S.A.F.E.R. Simulation” post we will share the key takeaways for engineers and their managers from a recent ESRD webinar on “Durability and Damage Tolerance Analysis Best Practices in the A&D Industry”. We’ll identify the factors that restrain the wider adoption of computational numerical simulation methodologies, and in particular finite element analysis (FEA) software, when used for detail stress analysis in support of critical engineering tasks such as fatigue life prediction. We hope to lift the fog that exists over the limitations of legacy FEA methods that are encountered by even the most expert simulation analysts. These same challenges make durability & damage tolerance (DaDT) calculations impractical if not risky for the occasional and especially new engineering user to perform.

Why DaDT is becoming ever more important with aging aircraft fleets….

The C130 Hercules transport aircraft depends heavily on reliable DaDT predictions to stay in service

There are numerous fixed wing and rotorcraft platforms that have far exceeded their initial program estimates for years in service. Keeping these aircraft flying safely with ever increasing performance requirements has fueled the need for more reliable and robust computational tools in fatigue life and fracture crack growth calculations to support the DaDT engineering function within repair, maintenance, and sustainment organizations. Aerospace and Defense (A&D) conferences like the Aircraft Airworthiness and Sustainment (AA&S) and Aircraft Structural Integrity Program (ASIP) have become increasingly important in their role to share best practices and new technologies which can improve aircraft life and reduce cost by expanding maintenance intervals. These conferences have revealed the need for new simulation technologies, and software tools based upon them, which improve the fidelity, accuracy, thoroughness, and speed of engineering analysis with improved confidence, reliability, and robustness of results and processes that is independent of the user or model.

To illustrate this growing demand, a strength engineer performing a “typical” stress analysis at the design stage is often delighted with answers within, say, 5% of actual or expected values. But when performing DaDT engineering simulations, being “close” with stress intensity factor (SIF), beta or other fracture mechanics computations is not good enough. For example, as the below figure demonstrates, being off by as little as 5% in SIF predictions can result in a 350% difference in crack growth cycles. The impact of getting this type of prediction wrong can be catastrophic for engineers practicing in the A&D industry (and beyond).

The sensitivity in DaDT life predictions is driven by unknown risks in the input data (e.g. SIF’s)

The application and value of FEA-based tools for numerical simulation is well established in the commercial and military aviation industry. The structural design, loads, strength and stress groups routinely use finite element models to generate internal loads of entire aero structures. FEA tools are then used to perform detail stress analysis to calculate margins of safety on components that are resistant to engineering handbooks, design curves, closed form solutions, and empirical data.

However, in many organizations there is still a preference for quick hand-whipped stress analysis with ample margins of safety when the alternative is constructing complete 3D virtual prototypes with no detail lacking, or to perform more testing on physical prototypes.

Fast high-Fidelity FEA of large aircraft assemblies is still problematic…

Modeling of large multi-scale spanning geometries for capturing SIF’s is unfeasible in most FEA codes

The wider-spread use of FEA tools in fatigue and fracture domains for DaDT calculations is another matter. Over ESRD’s twenty plus years of working within the aerospace community, as well as attending industry conferences like ASIP and AA&S, we have observed a reluctance to turn to the FEA tool kit in the calculation of important DaDT engineering data such as SIF’s. This is surprising as ever-increasing demands on airframe performance and life expectancy are requiring a larger volume of higher-fidelity structural analyses be conducted with improved levels of certainty and confidence. This is occurring at a time where budgetary constraints translates into fewer engineers available to perform analysis work that has become more complex, all with less time for advanced training and fewer resources to rely upon in methods and tools support groups.

In interviewing engineers and their managers who are responsible for DaDT work, we have heard these reservations about the generic use of FEA:

“It takes too long to import and clean up the geometry then build a high-resolution mesh around a high-risk or damaged component.”

“Solving crack propagation problems on my desktop computer takes too long as it is, then I have to go thru many cycles to debug and tune a model to get a result that is believable.”

“The quality of my solutions are a subjective exercise at best, based on my years of experience in handling similar types of analysis problems.”

“My team managers have more faith in historical analysis methods and it’s hard to convince them to let us loose on a digital model.”

All of the above issues were indeed valid at one time. It is not surprising that an organizational dependency arose on using closed-form solutions and empirically-based handbook tables to predict SIF’s. That was true even for design geometries and load cases that had little resemblance to their textbook surrogates.  Yet, not every analysis can be reduced to well-known cases like a simple plate with a thru-crack. It can be risky to force fit an existing curve or table to meet the needs of an analysis which is clearly well out of its original scope. An example is the use of compounding beta factors to account for variances in geometry and loads which can be precarious to apply and prone to error.

Despite these challenges, many DaDT engineers, rather than changing the legacy processes of their organizations, rely on historical methods no matter however approximate they are.  When these simpler methods failed, they would as a last resort – clearly not the first choice – turn to FEA for modelling complex 3D geometries with a wide variety of loadings, material types, residual stresses, crack shapes, and other complicating features.

Another inconvenient truth…

Despite their longevity in the industry, even legacy FEA methods and software struggle with these more complex classes of problems in DaDT, even when employed by simulation experts.  Obtaining consistently accurate and numerically verifiable solutions with traditional finite element methods has unfortunately added more complexity, time, risk, and cost that was prohibitive for many organizations to endure, especially when they were seeking speed, confidence, and safety.  Only a few highly experienced and well-trained DaDT specialists could perform the work due largely to endless sources of approximations, idealizations, decisions, judgement calls and errors in modelling, analysis, and results interpretation. There was little time available to think about numerical verification, much less understand it was not the same as results validation.

The reason for this state of simulation in DaDT is often obscured by a fog of complexity hiding underneath the hood of legacy FEA codes. The foundational finite element theory, methods, and technology base implemented by nearly all commercial FEA software products has remained largely unchanged over decades. That is not to say there have not been substantial improvements in aspects of FEA such as model creation for faster preprocessing, high performance computing for faster analysis, and improved visualization for post-processing. Yet, these only masked underlying limitations that made FEM an art for the expert masters rather than a reliable numerical computational science for the engineering masses.

These limitations are well known to users of simulation software – as evidenced by the size of the element library – but are less so recognized by their managers who often think this is just the way it has to be. In our next S.A.F.E.R. Simulation post we plan to discuss how these limitations in legacy FEA throttle the wider use and economic value of numerical simulation across the A&D industry. Nowhere is this timelier than in the supply and service chains which have increasing authority for design and analysis, and now new accountability for lifecycle maintenance and program sustainment that requires deeper expertise in DaDT.

Fixing the Holes…

Example 3D crack life calculation using FEA-based methods (ESRD’s Crack Propagation Analysis Tool)

For the last decade ESRD has been at the forefront of advancements in numerical simulation that makes the performance of finite element analysis less a craft of modelling traps, tips, and tricks when practiced by experts, and more S.A.F.E.R. methodology when used by the non-expert. With these advancements it is now possible for DaDT engineers to conduct analyses using more transparent models with greater accuracy, producing faster simulations in more efficient workflow processes which require less re-meshing and debugging, and generating more reliable results from inherently more robust methods independent of the level of expertise of the user or complexity of the engineering problem.

In a future S.A.F.E.R. post on the use of FEA in DaDT we will dive deeper into what makes this now possible in practice. Until then, in the most recent ESRD webinar on DaDT we demonstrated several example fatigue life and crack propagation problems which illustrated that conventional expectations of being “close enough” are no longer “good enough”.  To view this webinar click here. If your corporate firewall prohibits live access please send us an email to webinars@esrd.com and we can provide a link to download.

What do you think…

Related links and conversations…

• ESRD’s DaDT and Fracture Mechanics Application Highlights (via ESRD.com)
  • Learn about the types of DaDT and fracture mechanics applications for which ESRD is best suited, and how A&D engineers solving legacy aircraft problems can benefit from our simulation technology.
• Seven Questions to Ask CAE Vendors of Structural Analysis and Simulation Software (via Engineering.com)
  • Engineering.com Editor Shawn Wasserman highlights what questions are driving simulation technology and development, and what factors should determine the best tool for a simulation (such as DaDT).
• NAFEMS World Congress 2017 Tackles the Big Issues in Simulation and Analysis (via Digital Engineering)
  • DE’s Jamie Gooch describes the events and presentations given at the most recent NAFEMS World Congress, including how ESRD’s Chairman Dr. Barna Szabó warned against democratization of simulation without Simulation Governance.

To receive future S.A.F.E.R. Simulation posts…

SAINT LOUIS, MISSOURI – May 7, 2018

ESRD President and CEO Dr. Ricardo Actis

Finite element modeling originated in the aerospace industry over 60 years ago. Owing to the level of expertise and experience required, it has remained a practice of analysts. There are many reasons for this, among them getting the right mesh for a problem and getting the mesh right is always near the top of why it takes both an expert and much time to get a solution. Not to mention the expertise required to navigate the minefield of multi-purpose finite element software tools in selecting the “right” elements from an ever-expanding element library, and selecting the “right” value of tuning parameters to overcome various deficiencies in implementations.

Yet, looking at this more closely, the focus should not be the level of experience or modeling skills of the user, but the level of intelligence in the software. Nearly all of the most popular legacy FEA software products were designed to support the practice of finite element modeling and as such none of them have the capability to provide a simple Q/A dashboard to advise the non-expert user if they have a good solution.

Splice joint stress contours generated by ESRD’s Multi-Fastener Analysis Tool (MFAT) Sim App

How then can the vision for expanding the use of numerical simulation by persons who do not have expertise in finite element analysis (FEA) be safely realized? The solution lies in the establishment of Simulation Governance through the development and dissemination of expert-designed Engineering Simulation Apps to ensure the level of reliability and consistency needed for widespread adoption.

The Key Ingredient for FEA-Based Simulation Apps

FEA-based Simulation Apps for the standardization and automation of recurring analysis tasks and process workflows for use by persons who do not have expertise in FEA must be designed by expert analysts to fit into existing analysis processes, capturing institutional knowledge and best practices to produce consistent results by tested and approved analysis procedures. Only by meeting the technical requirements of Simulation Governance can simulation apps have the reliability and robustness needed to support engineering decision-making processes!

Simulation Governance must be understood as a managerial function that provides a framework for the exercise of command and control over all aspects of numerical simulation through the establishment of processes for the systematic improvement of the tools of engineering decision-making over time. This includes the proper formulation of idealizations, the selection and adoption of the best available simulation technology, the management of experimental data, verification of input data and verification of the numerical solution.

Establishing the Proper Framework

Double lap joint inputs for ESRD’s Single Fastener Analysis Tool (SFAT) Smart Sim App.

In the creation of FEA-based Simulation Apps for the application of established design rules, data verification and solution verification are essential. The goal is to ensure that the data are used properly and the numerical errors in the quantities of interest are reasonably small: they must have built-in safeguards to prevent use outside of the range of parameters for which they were designed; they must incorporate automatic procedures for solution verification; and must be deployed with a detailed description of all assumptions incorporated in the mathematical model and a clear definition of the range and scope of application.

To ensure their proper use, Simulation Apps must incorporate estimation of relative errors in the quantities of interest, an essential technical requirement of Simulation Governance. They should not be deployed without objective measures of the approximation errors for all the reported results. The success of the vision of Democratization of Simulation depends on it!

Previous S.A.F.E.R. Simulation Posts…

• S.A.F.E.R. Numerical Simulation for Structural Analysis in the Aerospace Industry Part 1: Trends in A&D Driving Simulation
• S.A.F.E.R. Numerical Simulation for Structural Analysis in the Aerospace Industry Part 2: Challenges with Legacy FEA
• S.A.F.E.R. Numerical Simulation for Structural Analysis in the Aerospace Industry Part 3: FEM is not Numerical Simulation
• S.A.F.E.R. Numerical Simulation for Structural Analysis in the Aerospace Industry Part 4: Simulation Governance
• S.A.F.E.R. Numerical Simulation for Structural Analysis in the Aerospace Industry Part 5: An Introduction to StressCheck for High-Fidelity Aero-structure Analysis

To receive future S.A.F.E.R. Simulation posts…

Selecting the simplest model for an analysis is not always trivial for engineers. A Hierarchic Modeling framework eases this burden by providing support for investigating model form errors.

In our previous SAFER Simulation articles, we have explored the concepts of Numerical Simulation, Challenges of Legacy FEA, Finite Element Modeling, Simulation Governance and High-Fidelity Aerostructure Analysis. We worked to establish a lexicon and foundational basis for how ESRD’s technological framework fits into solving the increasingly complex applications facing today’s engineering community.

In this SAFER Simulation article, we explore the concept of Hierarchic Modeling, some practical applications of Hierarchic Modeling, and the importance of implementing a Hierarchic Modeling framework in CAE software tools to support the practice of Simulation Governance.

What Is Hierarchic Modeling?

“Hierarchic models for plates and shells” by Drs. Ricardo Actis, Barna Szabó and Christoph Schwab. Comput. Methods Appl. Mech. Engrg. 172 (1999) 79-107.

The concept of Hierarchic Modeling is not new, it was introduced in the 1990s, and together with hierarchic finite element spaces and hierarchic basis functions it was implemented in StressCheck Professional. From the introduction to the 1999 Computer methods in applied mechanics and engineering technical paper “Hierarchic models of laminated plates and shells” by Drs. Actis, Szabó and Schwab:

The notion of hierarchic models differs from the notions of hierarchic finite element spaces and hierarchic basis functions. Hierarchic models provide means for systematic control of modeling errors whereas hierarchic finite element spaces provide means for controlling discretization errors. The basis functions employed to span hierarchic finite element spaces may or may not be hierarchic. Brief explanations follow:

Hierarchic models are a sequence of mathematical models, the exact solutions of which constitute a converging sequence of functions in the norm or norms appropriate for the formulation and the objectives of analysis. Of interest is the exact solution of the highest model, which is the limit of the converging sequence of solutions. In the case of elastic beams, plates and shells the highest model is the fully three-dimensional model of linear elasticity, although even the fully three-dimensional elastic model can be viewed as only the first in a sequence of hierarchic models that account for nonlinear effects, such as geometric, material and contact nonlinearities.

Hierarchic Modeling makes it possible to identify the simplest model that accounts for all features that influence the quantities of interest given the expected accuracy. This is related to the problem-solving principle, known as Occam’s razor, that when presented with competing models to solve a problem, one should select the model with the fewest assumptions, subject to the constraint of required accuracy.

Not all CAE software tools are capable of supporting Hierarchic Modeling in practice, especially for complex applications for which many modeling assumptions are to be examined.

What Do CAE Software Tools Need to Support Hierarchic Modeling?

As previously discussion in our S.A.F.E.R. Simulation blog article on Numerical Simulation, to enable support for a Hierarchic Modeling framework, and by extension the practice of Simulation Governance, CAE software tools must meet three basic requirements:

1. The model definition must be independent from the approximation.
2. Simple procedures must be available for assessing the influence of modeling assumptions (in support of model validation).
3. Simple procedures must be available for objective assessment of the errors of approximation (in support of solution verification).

The above requirements, and how meeting these requirements are supported in practice, are explained in greater detail in our Brief History of FEA page and its narrated video. The first implementation of model hierarchies in a CAE software tool, as explained in the video, was released in 1991 (ESRD’s StressCheck Professional).

An implementation framework meeting these three requirements enables the practice of Simulation Governance, providing the basis for the creation and deployment of engineering Sim Apps. Democratization of Simulation for standardization and automation of new technologies, such as Sim Apps, can be done with proper safeguards provided that the software tools used for the creation and deployment meet these technical requirements.

Why Should Engineers Care About Hierarchic Modeling?

“On the role of hierarchic spaces and models in verification and validation” by Drs. Barna Szabó and Ricardo Actis. Comput. Methods Appl. Mech. Engrg. 198 (2009) 1273-1280.

Legacy CAE tools used for Finite Element Modeling were not designed to support Hierarchic Modeling. This is because the concept of Hierarchic Modeling was established many years after the infrastructure of legacy FEA tools was created. Their main limitation is that the model definition and the approximation are not treated separately. Different orders of model complexity cannot be objectively compared by engineering analysts, therefore there is no basis for establishing  confidence in the modeling assumptions.

From 2009’s Computer methods in applied mechanics and engineering technical paper “On the role of hierarchic spaces and models in verification and validation” by Drs. Actis and Szabó:

…It is also necessary for the computer implementation
to support hierarchic sequences of models, allowing investigation of the sensitivities of the data of interest and the data measured in validation experiments to the various assumptions incorporated in the model…There is a strong predisposition in the engineering community to view each model class as a separate entity. It is much more useful however to view any mathematical model as a special case of a more comprehensive model, rather than a member of a conventionally defined model class.

For example, the usual beam, plate and shell models are special cases of a model based on the three-dimensional linear theory of elasticity, which in turn is a special case of large families of models based on the equations of continuum mechanics that account for a variety of hyperelastic, elastic-plastic and other material laws, large deformation, contact, etc. This is the hierarchic view of mathematical models.

Comparison of maximum von Mises stress convergence for different hierarchic fastened connection models.

To aid finding the simplest model, sensitivity studies via virtual experimentation are recommended. For example, modeling fastened joints may or may not require full multi-body contact effects if the data of interest are sufficiently far from the region of load transfer; bearing load applications, distributed normal springs or partial contact via “plugs” may be sufficient. By extension, if a structural support is to be approximated by distributed springs, the spring coefficients should be defined parametrically so that sensitivity studies are easy to perform.

The following examples and practical applications illustrate how a Hierarchic Modeling framework leads to increased control over and confidence in the engineering decision-making process.

Applications of Hierarchic Modeling In Engineering Practice

We will focus on two practical applications common to many aerospace engineers: fastened (bolted) joint analysis, and the influences of nonlinear effects such as plasticity. Both engineering applications require high-fidelity analyses to represent the data of interest, and are typically sensitive to the modeling assumptions.

Fastened Joint Analysis

ESRD recently provided a webinar titled “Hierarchic Approaches to Modeling Fastened Connections”, which incorporated the main points from the above discussion. The webinar can be viewed below in its entirety.

Through StressCheck Professional‘s Hierarchic Modeling framework, different modeling assumptions are tested for several classes of fastened joints and connections, including lap joints, splice joints and fittings, and in many cases a simpler model was found that represented the data of interest within a sufficient tolerance:

Some of the fastened joint modeling assumptions explored included the following:

• In-plane only vs out-of-plane bending effects on load transfer and detailed stresses
• 2D structural shear connections vs 3D detailed multi-body contact
• 2D bearing loading vs 3D bearing loading vs 3D multi-body contact
• Compression-only normal springs vs multi-body contact
• Fused fasteners vs multi-body contact
• Linear elastic vs. elastic-plastic materials

Without a Hierarchic Modeling framework, exploring these modeling assumptions would be unfeasible in engineering practice, and create a “simulation bottleneck” for engineering analysts.

Linear vs Nonlinear Effects

In some aerospace engineering applications, it may be necessary to investigate the influence of nonlinearities, such as plasticity and/or large deformations, in the results of interest.  For that reason a linear solution (i.e. small strain, small deformation and linear elastic material coefficients) must be viewed as the first in a hierarchy of models that includes nonlinear constitutive  relations, finite deformation and mechanical contact.

In a Hierarchic Modeling framework, engineering analysts should not need to change the discretization (i.e. mesh, element types and mapping) when transitioning from a linear to nonlinear model analysis for example; the switch should be seamless and simple, allowing the order of the model to increase on demand.

The following demo videos examine two case studies in nonlinear effects, in which the Hierarchic Modeling framework of StressCheck Professional was used to assess the influence of simplifying modeling assumptions without changing the discretization.

Geometric Nonlinearities

In the first case study, a linear vs. geometric nonlinear (large strain/large displacement) analysis for a 3D helical spring was performed:

Performing a geometric nonlinear analysis for the helical spring, in which equilibrium is satisfied in the deformed configuration, required no interaction with the model inputs or discretization parameters. The engineering analyst simply starts from a converged linear solution as the first step in the geometric nonlinear iterations.

The model hierarchies were then compared in live results processing with minimal effort, allowing the engineering analyst to quickly assess how accounting for large displacements/rotations affects the outcome of the results.

Material Nonlinearities

In the second case study, elastic-plastic materials are assigned to a detailed 3D eyebolt geometry, allowing plasticity to develop as the eyebolt is overloaded in tension:

To incorporate plasticity into the model, it was only required to update the material properties from linear to elastic-plastic; no other change in model inputs was required. Then, after a converged linear solution was available, a material nonlinear analysis was seamlessly initiated.

As in the previous case study, both models were available for assessment in live results processing, allowing the engineering analyst to determine whether material nonlinear effects are significant at the given load level (i.e. is the plasticity extensive) or the plastic zone is fully confined by elastic material.

Summary

As demonstrated in the above examples, and articulated in the technical paper excerpts, support for a seamless transition between model orders and theories is made possible by the implementation of a Hierarchic Modeling framework. To implement Hierarchic Modeling, CAE software tools must also allow separation of model definition from the discretization (in legacy FEA software, the definition of the model and the numerical approximation are combined, necessitating large element libraries). Without this clear separation, it is not feasible to reliably perform verification and validation in engineering practice.

Additionally, engineering analysts should expect modern FEA and CAE tools to support “what if” and sensitivity studies, such that modeling assumptions can be easily assessed and the simplest model used with confidence. As more and more engineering organizations look to democratize simulation, and virtual experimentation is increasingly used, it is essential to have numerical simulation tools that treat model definition separately from the approximation.

Finally, through the use of hierarchic finite element spaces and mathematical models it is possible to control approximation errors separately from modeling errors, while providing objective measures of solution quality for every result, anywhere in the model, in support of the increasing simulation demands on engineers.

How We Can Help…

Verifying the accuracy of FEA solutions is straightforward when employing the following Key Quality Checks.

In a recent ESRD webinar, we asked a simple but powerful question: if you routinely perform Numerical Simulation via finite element analysis (FEA), how do you verify the accuracy of your engineering simulations? During this webinar, we reviewed ‘The Four Key Quality Checks’ that should be performed for any detailed stress analysis as part of the solution verification process:

• Global Error: how fast is the estimated relative error in the energy norm reduced as the degrees of freedom (DOF) are increased? And, is the associated convergence rate indicative of a smooth solution?
• Deformed Shape: based on the boundary conditions and material properties, does the overall model deformation at a reasonable scale make sense? Are there any unreasonable displacements and/or rotations?
• Stress Fringes Continuity: are the unaveraged, unblended stress fringes smooth or are there noticeable “jumps” across element boundaries? Note: stress averaging should ALWAYS be off when performing detailed stress analysis. Significant stress jumps across element boundaries is an indication that the error of approximation is still high.
• Peak Stress Convergence: is the peak (most tensile or compressive) stress in your region of interest converging to a limit as the DOF are increased? OR is the peak stress diverging?

When the stress gradients are also of interest, there is an additional Key Quality Check that should be performed:

• Stress Gradient Overlays: when stress distributions are extracted across or through a feature containing the peak stress, are these gradients relatively unchanged with increasing DOF? Or are the stress distribution overlays dissimilar in shape?

In this S.A.F.E.R. Simulation blog, we’ll explore each of the above Key Quality Checks as well as additional best practices for verifying the accuracy of FEA solutions. To help us drive the conversation in a practical manner, we selected a widely available and well understood benchmark problem to model, solve and perform each Key Quality Check using ESRD’s flagship FEA software, StressCheck Professional.

Note: the following Key Quality Checks for FEA Solution Verification focus on results processing for linear and nonlinear detailed stress analyses applications. Webinars containing solution verification best practices have been previously presented for fracture mechanics applications, global-local analysis (co-hosted by Altair), and fastened connection and bolted joint analysis.

Benchmark Problem: Tension Bar of Circular Cross Section with Semi-Circular Groove

Benchmark problem for Key Quality Checks for FEA Solution Verification.

The benchmark problem for the following discussion focuses on accurately computing a very common stress concentration factor, the classical solution(s) of which may be found in myriad engineering handbook publications and used often by many practicing structural engineers: tension bar of circular cross section with a semi-circular groove.

Since the available literature supports numerous classical solutions, we will limit our coverage to three (3) of the most popular classical stress concentration factor approximation sources: Peterson, Shigley and Roark.

Classical Source #1: ‘Peterson’s Stress Concentration Factors’ (Pilkey)

Our first classical source comes from Section 2.5.2 and Chart 2.19 (‘Stress concentration factors K_tn for a tension bar of circular cross section with a U-shaped groove’) in ‘Peterson’s Stress Concentration Factors’, 2^nd Edition, by Walter D. Pilkey:

Courtesy ‘Stress Concentration Factors’, 2nd Edition (Pilkey).

Courtesy ‘Stress Concentration Factors’, 2nd Edition (Pilkey).

The curve marked ‘Semicircular’ will be used for the classical stress concentration factor approximation.

Note: as is documented in Section 2.5.2 above, Chart 2.19 is computed from the Neuber 3D case K_tn curve (Chart 2.18, see below) for a nominal Poisson’s ratio of 0.3:

Courtesy ‘Stress Concentration Factors’, 2nd Edition (Pilkey).

Pilkey notes in Section 1.4 (‘Stress Concentration as a Three-Dimensional Problem’) that the Poisson’s ratio will have an effect on the K_tn for cases such as the above.

Classical Source #2: ‘Shigley’s Mechanical Engineering Design’ (Budnyas & Nisbett)

Our second classical source comes from Figure A-15-13, Table A-15, in ‘Shigley’s Mechanical Engineering Design’, 9^th edition, by Richard G. Budnyas & J. Keith Nisbett:

Courtesy ‘Shigley’s Mechanical Engineering Design’, 9th edition (Budnyas & Nisbett).

Classical Source #3: ‘Roark’s Formulas for Stress and Strain’ (Young & Budynas)

Our third source comes from the equation in Table 17.1, ’15. U-notch in a circular shaft’, ‘Roark’s Formulas for Stress and Strain’, 7^th Edition, by Warren C. Young and Richard D. Budynas:

Courtesy Roark’s ‘Formulas for Stress and Strain’, 7th Edition (Young & Budynas).

We will use the equation for the semi-circular notch (h/r = 1) for the classical stress concentration factor approximation.

Classical Stress Concentration Factor Comparison:

For this benchmark case study, the dimensions and axial tension force were defined as following (in US Customary units):

• D = 9″
• d = 6″
• h = 1.5″
• r = 1.5″
• P = 10,000 lbf
• σ_nom = 4*P/π/d² = 354 psi
• r/d = 0.25
• D/d = 1.5
• h/r = 1.0

These values result in the following classical solutions for the stress concentration factor:

The above classical solutions are noted by the authors as approximations of the stress concentration factor, given the configuration of geometric and axial loading parameter values; the exact solution can be obtained by solving the 3D elasticity problem. An approximation to the solution of the elasticity problem can be obtained using the finite element method (e.g. via StressCheck Professional or another FEA implementation).

A reasonable goal of our benchmark case study is to determine which (if any) of the classical solutions best approximates this particular configuration.

Modeling Process: CAD + Automesh + BC’s + Material Properties

The solid geometry for the benchmark case study was constructed in StressCheck Professional using 3D solid modeling techniques, an automesh of 3665 curved tetrahedral elements was generated, and boundary conditions (axial loads, rigid body constraints) were applied:

Curved Tetrahedral Automesh (courtesy StressCheck Professional)

The linear elastic material properties selected for the benchmark case study are representative of a 2014-T6 aluminum extrusion (i.e. E = 10.9 Msi, v = 0.397).

Solution Process: Linear P-extension + Fixed Mesh

The model was analyzed in StressCheck Professional’s Linear solver via an hierarchic p-extension process, in which the orders of all elements on the fixed mesh were uniformly increased from 2^nd order (p=2) to 8^th order (p=8) for a total of seven (7) runs.

Note: before executing the solution, the mesh was converted to geometric (blended) mapping, which ensured the optimal representation of the geometric boundaries. This conversion was required for the solution order to exceed p=5, as by default StressCheck Professional’s tetrahedral elements are curved using 2^nd order functions (Isopar).

Since StressCheck Professional automatically stores all completed runs of increasing DOF for results processing, we can determine the minimum DOF for which the benchmark case study was well approximated for each Key Quality Check.

Note: it is not necessary to always increase the order of all elements to 8^th order, unless the mesh is a) generated manually and is a minimum mesh of high-aspect ratio elements, or b) a solution of exceedingly low discretization error in the data of interest is the goal (our reason). Many times a sufficiently refined mesh at a lower order (p<6) will achieve an acceptable discretization error for most practical engineering applications.

Results Extraction: Do We Pass Each Key Quality Check?

After the solution process completed, the estimated relative error in the energy norm (EREEN) was automatically reported as 0.01%, indicating no significant discretization errors but telling us very little about our data of interest, the stress concentration factor.

Then, how do we determine if we have an accurate enough FEA solution to approximate the stress concentration factor for the benchmark case study? Let’s go through each Key Quality Check to determine if our discretization is sufficient.

Key Quality Check #1: Global Error

Key Quality Check #1: Global Error (courtesy StressCheck Professional)

Studying how the global error (% Error column), as represented by EREEN, decreases with increasing DOF is our first ‘Key Quality Check’. This value is a measure of how well we are approximating the exact solution of the 3D elasticity problem in energy norm.

Additionally, a Convergence Rate of >1.0 is also a good indicator of the overall smoothness of the solution. Note: in problems with mathematical singularities, such as the simulation of cracks in fracture mechanics applications, the convergence rate is typically <1.0.

VERDICT: Pass

Key Quality Check #2: Deformed Shape

Key Quality Check #2: Deformed Shape (courtesy StressCheck Professional)

Since the benchmark case study was loaded axially under self-equilibrating loads of P=10,000 lbf, rigid body constraints were applied to three nodes at the leftmost side to cancel the six rigid body modes in 3D elasticity.

The deformed shape for the highest DOF run indicates the model is behaving as expected at a 2,000:1 deformed scale (red outlines are the undeformed configuration).

VERDICT: Pass

Key Quality Check #3: Stress Fringes Continuity

Key Quality Check #3: Stress Fringes Continuity (courtesy StressCheck Professional)

When assessing the stress fringes for quality, it is important to ensure that there are no significant “jumps” across element boundaries (edges/faces) in regions where the stresses are expected to be smooth, continuous and unperturbed. This assessment requires that the stresses be plotted without any averaging or blending features enabled.

The 1^st principal stress (S1) fringe continuity for the highest DOF run is quite smooth across element boundaries, with no significant “jumps” detected in the region of interest (root of the notch). The maximum 1^st principal stress value (S1_max) is computed as 619.3 psi.

However, we will need to verify that this value has converged to a limit (e.g. independent of DOF) before it is compared with the benchmark case study’s theoretical K_tn and σ_max.

VERDICT: Pass

Key Quality Check #4: Peak Stress Convergence

Key Quality Check #4: Peak Stress Convergence (courtesy StressCheck Professional)

For this benchmark case study, our data of interest was the peak stress at the root of the circumferential groove. Since StressCheck Professional automatically keeps all solutions for ‘deep dive’ results processing, it is very simple and easy to ‘check the stress’.

Selecting the StressCheck model’s curve which encircles the root of the groove, an extraction of maximum 1^st principal stress (S1_max) vs. each run of increasing DOF was performed. Even though we have a fairly refined mesh in the groove, note the large differences between the first three runs (p=2 to 4) and the final four runs (p=5 to 8). For this reason, it is simply not enough to have a “good mesh” or smooth stress fringes that pass the “eyeball norm”; the peak stress values must be rigorously proven to be independent of mesh and DOF.

It can be observed from the table that convergence in S1_max was achieved by the 4th or 5th run, with a converged value of S1_max = 619.3 psi. Here is a summary of how the classical stress concentration factor approximations K_tn rate for this particular configuration:

% Relative Difference = 100*(σ_{max –} S1_max)/S1_max

It appears that Peterson’s classical stress concentration factor approximation is most appropriate, with a relative difference of 1.75% when compared to the estimated exact solution from the numerical simulation.

Note: the S1_max convergence table confirms that it was not necessary to continue increasing the DOF by p-extension past the 5th run (p=6 in this particular case); we could have stopped the p-extension process once the error in the S1_max was sufficiently small for our purposes.

VERDICT: Pass

A Note on the Poisson’s Ratio Effect

Recalling the derivation of the Peterson K_tn, the value use in the benchmark case study assumed a v=0.3 for its approximation, while a v=0.397 as was used in StressCheck Professional. This highlights the importance of understanding the derivation and limitations of classical solutions.

If we “eyeball” Chart 2.18 for r/d = 0.25 and a v~0.4, we get a K_tn of ~1.78 (vs. K_tn~1.81 for v=0.3). We then multiply the Peterson K_tn by 1.78/1.81 to get an ‘adjusted’ Peterson K_tn ~1.75 for v=0.397. This results in a σ_max = 619.67, a difference of 0.06%.

That being said, it is always up to the engineer and management to determine an acceptable classical solution error in practical engineering applications.

Key Quality Check #5: Stress Gradient Overlays

Key Quality Check #5: Stress Gradient Overlays (courtesy StressCheck Professional)

As an additional Key Quality Check, we should ensure that the stresses nearby the location of peak stress are also well-represented and do not change much with increasing DOF. In StressCheck Professional we can dynamically extract the stresses across or through any feature, for any resolution and available solution, and overlay these stress gradients on the same chart for an assessment of quality.

The stress gradient extraction was performed across the groove for the final three runs (p=6 to 8), and the automatic stress gradient overlay showed that there was practically no difference between the point-wise values. Again, this proves that the 5th run (p=6) was sufficient for representing both the peak stress and the groove stress gradient.

Note: as for the stress fringe continuity check (Key Quality Check #3), it is important to perform this extraction without averaging features enabled.

VERDICT: Pass

In Summary…

Example of the democratization of classical engineering handbook methods via FEA-based digital engineering applications.

Solutions of typical structural details in 2D and 3D elasticity obtained by classical methods are approximations obtained using various techniques developed in the pre-computer age. This benchmark case study shows that in order to rank results obtained by classical methods, they have to be compared with the corresponding values obtained from the exact solution of the problem of elasticity. Alternatively, when the exact solution is not available, classical methods can be compared with the results from an approximate solution of the same problem of elasticity obtained by FEA.

It was also shown that strict solution verification procedures are required to provide evidence that the approximation error in the quantities of interests are much smaller than the difference observed among the results obtained by classical solutions, an essential technical requirement of Simulation Governance and any benchmarking-by-FEA process.

Finally, this example also highlights another important point: Classical engineering handbooks and design manuals are examples of democratization practiced in the pre-computer age. With the maturing of numerical simulation technology it is now possible to remove the manifold limitations of classical engineering solutions and provide parametric solutions for the problems engineers actually need to solve. This is the main goal of democratization.

There is a fundamentally important prerequisite, however: The exceptionally rare talents of engineer-scientists who populated conventional handbooks have to be democratized, that is, digitally mapped into the world of modern-day analysis.

The time has come for democratization to be reinvented.

This joint ESRD/Rev-Sim webinar will explore Sim-Gov compliant Sim Apps for democratization of simulation.

On July 29, 2019 a joint webinar on the the importance of Simulation Governance in FEA-based Sim App development & deployment, titled “Democratization of Simulation Governance-Compliant Sim Apps”, was provided by ESRD’s Brent Lancaster and Rev-Sim‘s Malcolm Panthaki.

In this timely webinar, we discussed why it is essential that Sim Apps implement Numerical Simulation technologies which enable the practice of Simulation Governance in order for the vision of democratization of simulations to be realized, as well as why it is important for engineering managers to get on the Simulation Governance train sooner rather than later. Strategies were explored for democratizing engineering simulations via Sim Apps which are: 1) based on the latest Numerical Simulation technologies, 2) available in Commercial Off the Shelf (COTS) form, and most importantly 3) Simulation Governance-compliant.

Live demos of ESRD’s CAE Handbook and Multi-Fastener Analysis Tool (MFAT) were provided in order to prove that COTS, FEA-based, Simulation Governance-compliant Sim Apps are not just “vaporwares” but plug-and-play software solutions!

View Webinar Recording

Click the button below to view the 4 part, 55-minute webinar recording (scroll to the bottom of the webinar landing page to find the videos):

View Webinar Slides

Click the button below to view the webinar slides (PowerPoint Show):

Acknowledgments

As always, many thanks to our attendees for their interest and feedback! And, of course, thanks to the Rev-Sim leadership for their time and contributions. We hope to collaborate on another webinar in the future!

By Dr. Barna Szabó, ESRD Co-Founder & Chairman

All major engineering organizations use numerical simulation in support of decisions pertaining to design and design certification. The question of how well numerical simulation is managed is being addressed by the various stakeholders with increasing urgency. It is now generally recognized that numerical simulation, properly managed, can be a major corporate asset but poorly managed, or not managed at all, can become a major corporate liability.

What Is Simulation Governance?

By its definition in Wikipedia: “Simulation governance is a managerial function concerned with assurance of reliability of information generated by numerical simulation. The term was introduced in 2011 [1] and specific technical requirements were addressed from the perspective of mechanical design in 2012 [2]. Its strategic importance was addressed in 2017 [3] [4]. At the 2017 NAFEMS World Congress in Stockholm simulation governance was identified as the first of eight “big issues” in numerical simulation.

Simulation governance is concerned with (a) selection and adoption of the best available simulation technology, (b) formulation of mathematical models, (c) management of experimental data, (d) data and solution verification procedures, and (e) revision of mathematical models in the light of new information collected from physical experiments and field observations [5].”

Why Is Simulation Governance Important?

To appreciate the fundamental importance of simulation governance, please consider the following scenarios.

Scenario #1

A senior executive (SE) of a Fortune 500 corporation, in charge of a multi-billion dollar program, came to suspect that something was very wrong with the way finite element modeling was being done. There were large discrepancies between the outcomes of physical tests and the outcomes predicted by engineer-analysts. This made it necessary to do more testing than originally planned, resulting in substantial delays and cost overruns.

Getting reliable and timely correlation between predicted and realized test results was particularly important because new materials were being introduced for which design rules had to be developed, yet the discrepancies between predicted and realized outcomes were substantial, to say the least.

The SE invited outside consultants to address his concerns. He also invited five senior engineers to the first meeting. These engineers were responsible for finite element modeling in one way or another. Each of them had impeccable academic credentials and decades of experience.

The consultants explained the difference between finite element modeling and numerical simulation. They conveyed (in as diplomatic a way as they could) that the erroneous predictions were caused by the now obsolete practice of finite element modeling which can produce reasonable results in structural calculations but is not suited for strength calculations.

The engineers were visibly upset by the suggestion that the method they have been using for years is now obsolete. Their strong opposition to any substantive change in current practices became obvious. What do you think the SE should do?

Scenario #2

Your corporation grew over time by acquisition. Each acquisition brought with it a corporate culture, engineering manuals, software, Excel-based calculations and the like. Just to see what would happen, you gave a problem to three engineer-analysts and you got three different answers. What do you think you should do?

Scenario #3

You feel overwhelmed by the number of software products used by your engineering staff. You would like to streamline the workflows and initiate a vendor-reduction program. Your senior engineers agree with your goals but do not agree on what streamlining means and what criteria should be used in the vendor-reduction program. What will you do?

Scenario #4

A flight-critical component of a rotorcraft is to be tested in a fatigue experiment. A finite element model predicted that the probability is 90% that failure will occur between 100 and 250 thousand cycles. The failure occurred at 80 thousand cycles. If you were the engineer in charge of the design, what would you do?

Scenario #5

Your organization decided to introduce a new type of composite material for which design rules are not yet available. You were assigned to set up a program for the development of design rules. Your senior analysts proposed three different ideas on how the failure criteria should be formulated. How will you decide which one to use?

Scenario #6

The cost of unscheduled maintenance is much higher than the cost of scheduled maintenance. You would like to justify postponing maintenance actions relating to safety critical components to scheduled times. How would you go about establishing guidelines?

Scenario #7 – The JSF Story

In 2011 and 2012, two high-ranking US military officials commented on the (costly) lessons learned from the Joint Strike Fighter (JSF) project. From JSF program chief Vice Admiral David Venlet (AOL Defense, 2011):

JSF’s build and test was a miscalculation…. Fatigue testing and analysis are turning up so many potential cracks and hot spots in the Joint Strike Fighter’s airframe that the production rate of the F-35 should slowed further over the next few years… The cost burden sucks the wind out of your lungs.

And, from Gen. Norton Schwartz, Air Force Chief of Staff (Defense News, 2012):

There was a view that we had advanced to a stage of aircraft design where we could design an airplane that would be near perfect the first time it flew. I think we actually believed that. And I think we’ve demonstrated in a compelling way that that’s foolishness.

What do you think should have been done differently? What steps did your organization take to avoid similar problems in the future?

Scenario #8

You asked your principal vendor of finite element analysis software; what tools are provided to support solution verification? The response was that the software had been tested against all NAFEMS benchmark problems and the correct solutions were obtained. Should you be satisfied with this answer? Have you communicated your technical requirements to your software vendors? Is solution verification among your technical requirements? – Should it be?

Planning For Simulation Governance

The concept of simulation governance is easily grasped, however formulation of a plan for simulation governance for a particular organization is not simple at all.

Recognizing that technology advances and the available information increases over time, planning must incorporate data management and systematic updates of simulation practices so as to take advantage of new data and technology.

The preservation and maintenance of corporate know-how and institutional knowledge are important objectives of simulation governance. The productivity of newly hired engineers rapidly increases if routine simulation procedures are standardized so that applications consistently produce certifiable results.

A plan for simulation governance has to be tailored to fit the mission of each organization or department within an organization:

• If the mission is application of existing design rules, then the goal should be:
  • Standardize recurring numerical simulation procedures through the creation of smart applications. Smart applications, also called “simulation apps” are expert-designed, in such a way that the use of those applications does not require expertise in numerical simulation.
  • Economic benefits: Improved productivity and improved reliability.
• If the mission is formulation of design rules, then the plan should focus on:
  • Collection, maintenance and documentation of experimental data.
  • Management of solution and data verification procedures.
  • Revision and updating mathematical models in the light of new information collected from physical experiments and field observation.
  • Economic benefits: Substantial savings through optimization of design and certification procedures.
• If the mission is to support condition-based maintenance (CBM), then the main activities are:
  • Collection, maintenance and documentation of field data.
  • Update calibration records based on unit-specific information.
  • Standardize recurring analysis tasks.
  • Economic benefits: Substantial savings through improved disposition decisions.

Implementation

The first and perhaps the most challenging problem is to overcome widespread misunderstanding of what numerical simulation is. Most managers and many individuals who present themselves as experts in numerical simulation confuse numerical simulation with “finite element modeling” or “numerical modeling “. Those are outdated concepts, responsible for much of the disappointing results.

Existing simulation and data management practices have to be reviewed and evaluated in terms of efficiency and reliability. When a need for change is identified, a business case and consensus among the stakeholders have to be developed.

Metrics that measure the economic value of numerical simulation have to be established.

References

[1] Szabó B. and Actis R. Simulation governance: New technical requirements for software tools in computational solid mechanics. International Workshop on Verification and Validation in Computational Science University of Notre Dame 17-19 October 2011.
[2] Szabó B. and Actis R. Simulation governance: Technical requirements for mechanical design. Comput. Methods Appl. Mech. Engrg. 249-252 158-168, 2012.
[3] Meintjes J. Simulation Governance: Managing Simulation as a Strategic Capability. NAFEMS Benchmark Magazine, January 2015.
[4] Imbert J-F. Simulation Governance – Building confidence, a key dimension of simulation strategy. NAFEMS World Congress NWC15 San Diego, June 2015.
[5] Oberkampf WL and Pilch M, Simulation Verification and Validation for Managers. NAFEMS, 2017. ISBN 978-1-910643-33-4.

Request a Simulation Governance Briefing

Would you like to request a Simulation Governance briefing with our team of experts? Complete the form below and we’ll be happy to reach out with more information:

SAINT LOUIS, MISSOURI – October 2, 2019

ESRD Chairman and Co-Founder Dr. Barna Szabó

The idea of simulation governance is easy to understand:  The application of numerical simulation technology must be properly governed in every organization. The responsibility for simulation governance rests with board-level executives.  They exercise this responsibility through setting the goals, objectives and metrics to ensure that the economic value of numerical simulation is positive.  If numerical simulation is not managed properly then it can and often does lead to poor decisions that result in economic loss.  There are many well-documented examples of substantial economic loss that can be attributed to lack of simulation governance and management.

Recognizing the need to clarify the issues associated with the governance and management of numerical simulation, the Simulation Governance and Management Working Group of NAFEMS[1] has undertaken to develop a document on “What is Simulation Governance and Management”. An extract was published in the July 2019 issue of the NAFEMS quarterly Benchmark.

Beware the bottlenecks preventing the adoption of simulation governance.

While the concept is easily grasped, the existence of two bottlenecks must be recognized:  The first is that board-level executives generally lack the expertise to properly formulate realistic policies, expectations and metrics for numerical simulation and to assess the economic risks associated with numerical simulation activities within their organization.  Therefore it is necessary to engage outside consultants who have proper credentials and experience.   The problem is that it is extremely difficult to find consultants who are competent in this area.  This is because there are very few experts in numerical simulation and the consultant must also understand the intricacies of corporate change management.

The second bottleneck is that, with very rare exceptions, the technical staff do not have a clear understanding of what numerical simulation is.  There are historical reasons for this:  The primary tool of numerical simulation is the finite element method.  The legacy finite element codes, whose origins can be traced to the 1960’s and 70’s, were not designed to support numerical simulation.  In fact, numerical simulation, as the term is understood today, did not yet exist at that time.

An essential aspect of numerical simulation is that mathematical models must be formulated independently from how the numerical solution is obtained.  In contrast, legacy finite element software tools have the model definition and approximation conflated in their element libraries, making it very difficult, at times impossible, to separate model form errors from numerical approximation errors.  As a consequence, solution verification and model validation, which are essential elements of numerical simulation, cannot be reliably performed.

To eliminate this bottleneck it will be necessary to re-train the technical staff so that they will become proficient in the use of quality assurance procedures in numerical simulation.

ESRD/Revolution in Simulation Webinar on Democratization of Simulation.

Management should also seek professional advice on the benefits and risks associated with Democratization of Simulation which must be subject to the rules of simulation governance.  The term means that numerical simulation tools are made available to engineers who do not have expertise in numerical simulation.  The goal is to increase productivity without sacrificing reliability through standardization of recurring numerical simulation tasks.  These tools must be carefully designed, tested and certified by experts for safe and efficient use.

The reasons why democratization tools should not be deployed without meeting the technical requirements of simulation governance are outlined in a 2018 presentation as well as in a joint webinar hosted by ESRD & Revolution in Simulation.

[1] NAFEMS is the International Association for the Engineering Modelling, Analysis and Simulation Community.  The parent organization was the National Agency for Finite Element Methods and Standards, established in the UK in 1983 with the objective to promote the safe and reliable use of finite element and related technology.

References

NASA Standard 7009: This NASA Technical Standard provides an approved set of requirements, recommendations, and criteria with which models and simulations (M&S) may be developed, accepted, and used in support of NASA activities.

Szabó B and Actis R. Simulation governance: Technical requirements for mechanical design. Computer Methods in Applied Mechanics and Engineering.  249-252, 158-168, 2012.

To receive future S.A.F.E.R. Simulation posts…

In mid-May 2023, ESRD’s Co-Founder and Chairman Dr. Barna Szabó will deliver a keynote presentation at the ASME VVUQ 2023 Symposium in Baltimore, Maryland, USA. Dr. Szabó’s presentation, entitled “Simulation Governance: An Idea Whose Time Has Come”, will focus on the goals and means of Simulation Governance with reference to mechanical/aerospace engineering practice.

The abstract of the keynote presentation is as follows:

Mathematical models have become indispensable sources of information on which technical and business decisions are based.  It is therefore vitally important for decision-makers to know whether or not  they should rely on the predictions of a particular mathematical model.

The presentation will focus on the reliability of information generated by mathematical models.  Reliability is ensured through proper application of the procedures of verification, validation and uncertainty quantification.  Examples will be presented.

It will be shown that mathematical models are products of open-ended evolutionary processes.  One of the key objectives of simulation governance is to establish and maintain a hospitable environment for the evolutionary development of mathematical models.  A very substantial unrealized potential exists in numerical simulation technology.  It is the responsibility of management to establish conditions that will make realization of that potential possible.

Dr. Szabó has published several papers on numerical simulation.  He has also published a textbook entitled Finite Element Analysis: Method, Verification and Validation (2nd edition, John Wiley & Sons, Inc. in 2021) that covers the fundamentals of numerical simulation and the technical requirements for numerical simulation software products.

For more information about this symposium, visit the official ASME VVUQ 2023 Symposium page.

Last week, ESRD wrote a guest contribution for Altair’s Innovation Intelligence blog titled “Hyper-Fidelity Structural Analysis for S.A.F.E.R. Numerical Simulation in the Aerospace Industry“.  Thanks to Altair for their collaboration and support of S.A.F.E.R. Simulation.

This guest contribution was intended to compliment and preview Altair’s October 17th ESRD use case webinar (don’t worry if you missed this webinar, the recording is already available).

Here’s an excerpt from the Innovation Intelligence blog article:

Across the engineering community there is much discussion about the democratization of simulation; meaning the reliable use of numerical simulation by non-simulation experts who may be design engineers, new analysts, or occasional users. The hope is that much of the complexity, time, and risk of performing FEA can be wrung out of simulation in a way that finally allows simulation-driven design to be led by design engineers. Indeed democratization has great potential in the A&D industry to compress the product development lifecycle, but is it realistic? The answer few may want to hear is that this will not be easy to accomplish using legacy FEA technologies, methodologies, and software tools.

The key takeaways are as follows:

• The pressure on engineering organizations to support the increasing complexity, higher performance, shorter design cycles, and longer life expectancy of products they produce and maintain is relentless.
• Legacy computational methodologies, software tools, and simulation processes that have been used for years to perform FEA are slow to master, precarious to use, and unreliable in the hands of the non-expert or infrequent user. Sources of errors are numerous and results are often dependent on the user, model, mesh, and software.
• There is unfortunately a reluctance by some managers and team leaders to support the performance of more computationally-based 3D detail stress analysis due to the perceived time and complexity involved, especially when compared to relying on handbook solutions, design curves, closed form approximations, homegrown spreadsheets, higher margins of safety, or ultimately more time for physical prototyping and testing.
• A different approach to numerical simulation has been developed and commercialized by APA partner ESRD which takes much of the art and craft out of finite element modelling.
• The result is that the performance of structural analysis is more simple, accurate, fast, efficient, and reliable for both the frequent expert and only occasional user (S.A.F.E.R.).

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