From all of us at ESRD, we wish you a very happy holiday season! It’s been an incredible year with much to be thankful for, and our StressCheck user community is top of that list! We hope that you and your families enjoy some time away with relaxation, stories from the year past, and excitement for the year coming. Thank you for being such a wonderful part of ours. Cheers!

If you have a few minutes, we’d like to share a few highlights from an action-packed 2024.

Blog Series by Dr. Barna Szabó, ESRD Co-founder

If you’re looking for some quick reads during your holiday break, our Co-founder Dr. Barna Szabó has you covered. Over the past 14 months, he has contributed 22 short articles to the ESRD Blog, with topics ranging from XAI to Isogeometric Analysis. Perfect topics for your dinner party conversation, if you ask us.

StressCheck v12.0 Released

A quick reminder that earlier this year we released StressCheck version 12.0! If you’re ready to upgrade to the latest version, please reach out to your Account Manager or ESRD Support.

ASIP Conference 2024

Thank you to everyone who stopped by our StressCheck booth to say hi at this year’s ASIP Conference! Every year, we look forward to seeing our longtime friends from all over the industry, catching up on each others’ lives, and giving some StressCheck support along the way. We also made many new friends this year, which is wonderful.

Brent Lancaster conducted a Training session on Case Studies in Fracture Mechanics Analysis Using StressCheck v12.0. If you were unable to attend, please reach out to ESRD Support and we will gladly provide you the material.

We are very much looking forward to seeing many of you at ASIP 2025!

Wishing good tidings to you and your family, and looking forward to connecting with you in 2025!

ESRD is very excited to announce the release of StressCheck Professional Version 12.0! Read below for details on the what’s new and a link to download.

This major release of our flagship FEA solution delivers substantial refinements to the user interface and greatly improves your modeling, simulation, and post-processing workflows. You will experience immediate benefits to your analyses — from start to finish.

Watch the StressCheck Professional v12.0 Video Tour!

Key Features and Enhancements in StressCheck v12.0

StressCheck Professional 12.0 delivers an extensive list of new features and upgraded capabilities, including:

• Newly refreshed toolbar icons
• New right-click contextual menus
• New assembly meshing with automatic contact detection
• New mesh seeding feature for improved auto meshing results
• Multiple new features for improved simulation post-processing
• Introduced parameter and formula name input validation
• Introduced independent control over solid body colors
• Enhanced index controls for geometry and mesh objects
• Parameter and object set dependency feedback enhancements
• Object and record selection feedback enhancements

Want to know more?

Browse the Release Notes for detailed descriptions of what you’ll see in StressCheck v12.0:

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Get Familiar with the New Toolbar Icons!

StressCheck v12.0 delivers refreshed Toolbars that improve clarity and offer a consistent design aesthetic. We have not altered their arrangement, but to ensure you’re oriented in the new look of the interface we’ve created a Toolbar Guide. Take a look!

Ready to Download?

Download the StressCheck v12.0 MSI from our StressCheck software download page (Software Downloader membership is required):

Note: To run StressCheck v12.0, a license upgrade (and active Software Maintenance & Technical Support contract) is required. If you have not already requested your upgraded license, please do so using the Request for ESRD Support form.

From all of us at ESRD, we wish you a very happy holiday season! We truly feel that each and every one of our users are part of the ESRD family and we are incredibly grateful to get to work with all of you. We hope that you enjoy your year-end celebrations, quality time with friends and family, and wrap up 2023 with a big automesh-patterned bow 😉

There is much we are thankful for as we approach the end of the year. Our ESRD team has grown, we have had the opportunity to engage with our FEA community in new and important ways, and we’ve continued to strengthen our relationships with many of our beloved StressCheck users through conference visits and in-person trainings. We’d like to take a moment to acknowledge some of the reasons we’re looking back fondly on 2023…

ESRD’s New Account Manager

Patrick Goulding joined ESRD back in June as our new Account Manager. Many of you have had the chance to meet or speak with him this year, but if you have not yet been introduced feel free to reach out and say hi anytime, he would be thrilled to hear from you!

Patrick comes to us with several years of technical experience in the CAE industry, primarily with a background in multibody dynamics and mechatronics, and received his Master of Science in Mechanical Engineering from University of Illinois, Chicago. Patrick works remotely from his home office in Long Beach, CA, where he spends much of his time playing beach volleyball and repairing vintage turntables. If you’re looking for a turntable recommendation for your new stereo setup, he’s your guy.

Before Patrick was an engineer he devoted his career to the arts, co-founding a theatre company in Chicago and managing the day-to-day activities of a startup non-profit. From this experience, he learned the tremendous value of genuine and lasting business relationships. Patrick sees his role at ESRD as an opportunity to partner with talented engineers like yourself, help you to achieve your goals, and further his respect and admiration for those in the aerospace community.

• LinkedIn

Connect with Patrick on LinkedIn.

Blog Series Authored by ESRD Co-founder, Dr. Barna Szabó

Starting in October, Dr. Barna Szabó has authored weekly blog articles published to our ESRD Blog. These concise discussions address hot topics in engineering such as XAI, the misconceptions between Finite Element Modelling and Finite Element Analysis, and the importance of Simulation Governance for today’s engineering managers. We think that not only are these critical topics for our ESRD community to engage in, but that they are compelling insights into the fundamental values our software is built upon.

If you have not yet taken a look, we invite you to browse the currently published articles, choose your topic of interest, and share the discussion with others on your team. Dr. Szabó’s invites feedback and discussion, so feel free to reach out to us and to him with your thoughts and insights!

ASIP Conference 2023

We had a fantastic time attending the ASIP Conference this year and getting the chance to spend time with so many from our ESRD community! We look forward to it every year, because we get to catch up with so many of you and attend wonderful presentations demonstrating StressCheck in the ASIP industry.

Take a look at our recap of the 2023 ASIP Conference in Denver and we look forward to seeing many of you in Austin next year!

Looking Forward to 2024!

We’ve been working VERY hard on what we consider the most significant release of StressCheck in years, StressCheck v12.0! Our developers are in the very final stages of testing, making sure we deliver the highest quality analysis tool for you to use in 2024.

While we wait patiently for its debut, we want to make sure each of you know what to expect with the new functionalities, GUI updates, and overall improvements. Please schedule your demo of StressCheck v12.0 using the form below:

Wishing good tidings to you and your family!

At this year’s ASIP 2023 Conference in Denver, CO, ESRD provided a 2-hour training course titled “Enhancements in StressCheck v12.0 for DaDT Analysis of 3D Fastened Connections”, presented a technical paper titled “Experimental Validation of DTA Modeling of Bonded Wing Skin Repairs“, and passed out 3D printed F-35 and C-130 models at our booth inside the Gaylord Rockies Resort & Conference Center. The models were a big hit — look out for some new aircraft next year!

Conference Snapshot

ESRD’s Brent Lancaster, Patrick Goulding, and Brian Lockwood spent the week chatting with ASIP attendees and meeting many enthusiastic StressCheck users. The ASIP Conference has become an exciting platform for demonstrating many strong use cases of StressCheck spanning the ASIP community, with around a dozen technical presentations utilizing our technology for their DaDT analyses. We are honored to be such a prominent part of this event and to have so many talented and loyal users in this industry.

We would like to extend our sincerest gratitude to all those who attended Brent’s training, Brian’s technical paper presentation, and/or stopped by our booth to say hello to us. In addition, this was Patrick’s first ASIP Conference and he was thrilled to have the opportunity to meet you all. We really enjoy getting the chance to see you each year and we’re already looking forward to attending ASIP 2024 in Austin, TX.

ASIP 2023 Training Materials Available

On Monday, November 27th, Brent had the pleasure of providing a training course to a large group of attentive ASIP engineers on Enhancements in StressCheck v12.0 for DaDT Analysis of 3D Fastened Connections. We were thrilled with the level of interest and engagement, and the opportunity to present the latest in StressCheck. Thanks to those who attended the training course in person (as well as virtually)!

If you are interested in this topic, you can download Brent’s training presentation (in PowerPoint show or PDF format) and watch the video demo via the below link (note: you must be a registered user to view the training materials):

We are looking forward to receiving your feedback on the training course presentation, as well as your ideas for ASIP 2024 training course topics.

ASIP 2023 Technical Paper Presentation Available

On Thursday, November 30th, Brian had the honor of presenting his technical paper “Experimental Validation of DTA Modeling of Bonded Wing Skin Repairs” to a strong audience of engaged ASIP attendees. The paper was a collaboration between ESRD, AP/ES (Dr. Scott Prost-Domasky) and USAF AFMC WRALC/ENC (Laura Pawlikowski), and continued their project discussed in last year’s presentation (“DTA of Bonded Repairs on the Wing Skin of the C130 Using Finite Elements“) by providing experimental testing data to validate their simulation results.

If you are interested in this topic, you can view Brian’s technical paper presentation (in PowerPoint show or PDF format) via the below link (note: you must be a registered user to view the training materials):

Preview StressCheck v12.0!

Would you like to schedule a preview demonstration of the new features in StressCheck v12?

We would be happy to walk you through the exciting updates to the user interface design, model navigation and visualization tools, and enhanced meshing features.

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.

Request Application Demo

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…

On February 7, 2023 a 2-hour webinar titled “What’s New and Improved in StressCheck Professional” was provided by ESRD’s Brent Lancaster to a group of StressCheck enthusiasts. This webinar provided demonstrations of the “latest and greatest” enhancements in StressCheck v11.1, and a look toward future development activities happening in StressCheck v11.2. In case you missed it, the webinar slides and the webinar recording are now available!

Some highlights of the webinar included:

• Overview of recent features and enhancements already implemented in StressCheck Professional
• Demonstration of key features and enhancements available in StressCheck v11.1
• Overview of current development activities and future plans for StressCheck Professional
• Demonstration of key features and enhancements expected with the release of StressCheck v11.2
• Open discussion and Q&A

Many thanks to the StressCheck enthusiasts who attended the live webinar and subsequent Q&A session, as well as the StressCheck enthusiasts taking the time from their busy schedules to view the webinar recording.

As always, feel free to contact us with any questions or concerns about StressCheck Professional and we’ll be happy to assist!

Clicking on the above link will redirect you to the original webinar post and will automatically scroll you to the webinar recordings section. For your viewing convenience the 2-hour webinar recording was edited into two parts, each approximately 57 minutes in length.

Clicking the above link will redirect you to the ESRD Resource Library where you may download a PDF of the PowerPoint slides presented during the webinar. Note: as the webinar slides are in PDF format, they do not included the video demonstrations. These demonstrations can be found individually at the following links (or viewed from the webinar recordings):

• StressCheck Tutorial: Automeshing Thin Regions with Pentas and Hexas via the Thin Section Method
• StressCheck Tutorial: Mixed (Hexa/Penta) Boundary Layer Automesh Refinement
• StressCheck Tutorial: Crack Front Automeshing with Mixed Mesh, Integration Layer and Grade Toward Ends Options
• StressCheck Tutorial: Parametric TLAP Scaling for Nonlinear Events

Interested in a StressCheck Training Course?

If you would like to learn more about mastering StressCheck via an instructor-led training course, virtual or on-site, please complete the form below and we will be happy to reach out to you at your earliest convenience.

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!

Learn More

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…

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%.

Learn More (Video)

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.

As we continue to adapt to a mix of remote and in-office work, we hope that this past year you found our software products, customer support, training options/courses, “StressCheck Tip of the Week” posts, and e-Learning resources to be helpful and accommodating. We certainly couldn’t do it without your valuable feedback and contributions! We are committed to supporting your current and future engineering endeavors and look forward to what the future holds in 2023.

In 2022, we re-designed StressCheck’s documentation to include online and offline versions, attended ASIP 2022 as exhibitors and presenters, released StressCheck v11.1 (our best release yet!), and made numerous additions to our resource library to aid in a more efficient and enjoyable StressCheck onboarding process. The following are a few highlights that we’d like to share from this past year.

ASIP Conference 2022 Impressions…

In late November 2022, ESRD exhibited at the ASIP Conference and enjoyed re-connecting with StressCheck users, industry colleagues and our partners Hill Engineering (BAMpF 3D fatigue crack growth software developers) and LexTech (AFGROW developers). We also provided a training course and conference paper on the modeling and analysis of bonded doubler repairs.

Read more about our conference proceedings here.

StressCheck v11.1 Released…

We were pleased to release StressCheck v11.1 in late July 2022, made possible by the dedication and hard work of our development and QA teams. This release was packed with new features and enhancements in the areas of automatic meshing, fracture mechanics and global-local applications:

For a quick recap of the highlights in StressCheck v11.1 view the following short video:

Does your organization have an active StressCheck SM&TS contract but hasn’t yet upgraded to StressCheck v11.1? Contact us to get started with the upgrade!

Live Webinar Coming Soon…

On February 7th, 2023, we are planning for a live webinar to review what’s new and improved with the release of StressCheck v11.1, as well as preview the new features and enhancements under development for StressCheck v11.2 (targeted for release in Summer 2023).

Some highlights of features under development include (but are not limited to):

• Mesh seeding to guide the Automesh by automatically using pre-existing node locations.
• Upgraded toolbar icons for a clear and improved user experience.
• New option to select the toolbar icons between 16×16 (default), 20×20 and 24×24 pixels size.
• Movable Min/Max labels for Results plotting and extractions.
• A Dependencies button on the Parameter pane which lists all dependencies on the selected parameter.
• Column sorting and filtering for Parameters pane table including “Go To” to search for parameters.
• Predictive text on input fields has been implemented for parameter and formula names.
• Enhanced Index controls for filtering and sorting Geometry and Mesh object lists. including “Go To ID…” to access a specific ID.
• Improved visualization of Selected status on dropdown lists containing assignment/set records.
• Overhauled the Display Objects pane to support selective number ranges and additional object types.
• Re-designed color definitions pane.
• A list of object IDs belonging to a set “Contents:” and a list of objects that reference the set “Used By:” are now displayed when selecting a record on the Sets page.
• Improved consistency of DeLast/Undo functionality

Pre-register for the “What’s New and Improved in StressCheck” webinar by completing the form below:

Wishing for Good Tidings and Good Health

Finally, we’d like to wish all of our customers, partners and friends Happy/Safe Holidays and a Happier/Healthier 2023!

Keep up with the latest from ESRD by subscribing to our newsletter:

In case you missed it, ESRD is pleased to announce that we’ve released product updates for StressCheck Professional and StressCheck-Powered Apps (CAE Handbook and StressCheck Tool Box).  Many customer-defined enhancements were added, and the software user experience improved.

Figure 1: StressCheck’s default interface layout. A contour plot was produced in the Model View via the Results dialog.

StressCheck Professional v11 includes many new features, enhancements and improvements such as:

• Upgraded User Interface and User Flow Improvements
• Enhanced Automeshing Functionality
• New Crack Front Automeshing Method
• Automatic Extraction Radius for Fracture Mechanics Parameters
• Enhanced Solver Settings for Multi Body Contact Analysis
• New Extraction Functions for Multi Body Contact Results
• Full Online Documentation
• And more!

Watch the StressCheck v11 Demo

Watch this short video for a demonstration of some of the new features and enhancements in StressCheck Professional v11:

Learn More About StressCheck v11

Click below to view detailed descriptions of the new StressCheck Professional v11 features and enhancements:

Get the Latest Software Updates

To download the latest product updates and to view additional product release notes, click the links below:

• StressCheck Professional v11
• CAE Handbook v11/SCTB 5.0