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.

By Dr. Barna Szabó
Engineering Software Research and Development, Inc.
St. Louis, Missouri USA

Generally speaking, philosophers are much better at asking questions than answering them. The question of distinguishing between science and pseudoscience, known as the demarcation problem, is one of their hotly debated issues. Some even argued that the demarcation problem is unsolvable [1]. That may well be true when the question is posed in its broadest generality. However, this question can and must be answered clearly and unequivocally in the engineering sciences.

That is because, in the engineering sciences, we rely on validated models of broad applicability, such as the theories of heat transfer and continuum mechanics, the Maxwell equations, and the Navier-Stokes equations.  Therefore, we can be confident that we are building on a solid scientific foundation. A solid foundation does not guarantee a sound structure, however. We must ensure that the algorithms used to estimate the quantities of interest are also based on solid scientific principles. This entails checking that there are no errors in the formulation, implementation, or application of models.

In engineering sciences, we classify mathematical models as ‘proper’ or ‘improper’ rather than ‘scientific’ or ‘pseudoscientific’. A model is said to be proper if it is consistent with the relevant mathematical theorems that guarantee the existence and, when applicable, the uniqueness of the exact solution. Otherwise, the model is improper. At present, the large majority of models used in engineering practice are improper. Following are examples of frequently occurring types of error, with brief explanations.

Conceptual Errors

Conceptual errors, also known as “variational crimes”, occur when the input data and/or the numerical implementation is inconsistent with the formulation of the mathematical model. For example, considering the displacement formulation in two and three dimensions, point constraints are permitted only as rigid body constraints, when the body is in equilibrium. Point forces are permitted only in the domain of secondary interest [2], non-conforming elements and reduced integration are not permitted.

When conceptual errors are present, the numerical solution is not an approximation to the solution of the mathematical problem we have in mind, in which case it is not possible to estimate the errors of approximation. In other words, it is not possible to perform solution verification.

Model Form Errors

Model form errors are associated with the assumptions incorporated in mathematical models. Those assumptions impose limitations on the applicability of the model. Various approaches exist for estimating the effects of those limitations on the quantities of interest. The following examples illustrate two such approaches.

Example 1

Linear elasticity problems limit the stresses and strains to the elastic range, the displacement formulation imposes limitations on Poisson’s ratio, and pointwise stresses or strains are considered averages over a representative volume element. This is because the assumptions of continuum theory do not apply to real materials on the micro-scale.

Linear elasticity problems should be understood to be special cases of nonlinear problems that account for the effects of large displacements and large strains and one of many possible material laws. Having solved a linear problem, we can check whether and to what extent were the simplifying assumptions violated, and then we can decide if it is necessary to solve the appropriate nonlinear problem. This is the hierarchic view of models: Each model is understood to be a special case of a more comprehensive model [2].

Remark

Theoretically, one could make the model form error arbitrarily small by moving up the model hierarchy.  In practice, however, increasing complexity in model form entails an increasing number of parameters that have to be determined experimentally. This introduces uncertainties, which increase the dispersion of the predicted values of the quantities of interest.

Example 2

In many practical applications, the mathematical problem is simplified by dimensional reduction. Within the framework of linear elasticity, for instance, we have hierarchies of plate and shell models where the variation of displacements along the normal to the reference surface is restricted to polynomials or, in the case of laminated plates and shells, piecewise polynomials of low order [3]. In these models, boundary layer effects occur. The boundary layers are typically strong at free edges. These effects are caused by edge singularities that perturb the dimensionally reduced solution. The perturbation depends on the hierarchic order of the model. Typically, the goal of computation is strength analysis, that is, estimation of the values of predictors of failure initiation. It must be shown that the predictors are independent of the hierarchic order. This challenging problem is typically overlooked in finite element modeling. In the absence of an analytical tool capable of guaranteeing the accuracy of predictors of failure initiation, it is not possible to determine whether a design rule is satisfied or not.

Numerical Errors

Since the quantities of interest are computed numerically, it is necessary to verify that the numerical values are sufficiently close to their exact counterparts. The meaning of “sufficiently close” is context-dependent: For example, when formulating design rules, an interpretation of experimental information is involved. It has to be ensured that the numerical error in the quantities of interest is negligibly small in comparison with the size of the experimental errors. Otherwise, preventable uncertainties are introduced in the calibration process.

Realizing the Potential of Numerical Simulation

If we examine a representative sample of mathematical models used in the various branches of engineering, we find that the large majority of models suffer from one or more errors like those we described above. In other words, the large majority of models used in engineering practice are improper. There are many reasons for this, caused mainly by the obsolete notion of finite element modeling, deeply entrenched in the engineering community.

As noted in my earlier blog, entitled Obstacles to Progress, the art of finite element modeling evolved well before the theoretical foundations of finite element analysis were established. Engineering books, academic courses, and professional workshops emphasize the practical, intuitive aspects of finite element modeling and typically omit cautioning against variational crimes. Even some of the fundamental concepts and terminology needed for understanding the scientific foundations of numerical simulation are missing. For example, a senior engineer of a Fortune 100 company, with impeccable academic credentials earned more than three decades before, told me that, in his opinion, the exact solution is the outcome of a physical experiment. This statement revealed a lack of awareness of the meaning and relevance of the terms: verification, validation, and uncertainty quantification.

To realize the potential of numerical simulation, management will have to exercise simulation governance [4]. This will necessitate learning to distinguish between proper and improper modeling practices and establishing the technical requirements needed to ensure that both the model form and approximation errors in the quantities of interest are within acceptable bounds.

References

Related Blogs:

• Where Do You Get the Courage to Sign the Blueprint?
• A Memo from the 5th Century BC
• Obstacles to Progress
• Why Finite Element Modeling is Not Numerical Simulation?
• XAI Will Force Clear Thinking About the Nature of Mathematical Models
• The Story of the P-version in a Nutshell
• Why Worry About Singularities?
• Questions About Singularities
• A Low-Hanging Fruit: Smart Engineering Simulation Applications

By Dr. Barna Szabó
Engineering Software Research and Development, Inc.
St. Louis, Missouri USA

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 relying on the predictions of mathematical models is justified. When properly used, numerical simulation can be a major corporate asset. However, it can become a major corporate liability if the reliability of predictions is not guaranteed.

Resource Allocation

Project management is responsible for allocating resources to numerical simulation and physical experimentation.  Consider the two extreme cases: (a) If the decision is not to use numerical simulation, just rely on experimentation, then management is adopting the methodology of the Wright brothers.  (b) If the decision is not to do experiments, and just rely on finite element modeling, then management will risk repeating the costly mistakes of the F-35 program.  The correct balance depends on the justified degree of confidence in the predictive performance of numerical simulation [1].

Simulation Governance

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

A plan for simulation governance has to be tailored to fit the mission of each organization or department within an organization.  We consider three types of mission in the following.  A summary of the main points is presented in the table below.

• If the mission is the application of established design rules, then the goal is to verify that a quantity of interest  does not exceed its allowable value .  Simulation governance is concerned with standardization of recurring numerical simulation tasks 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. The preservation and maintenance of corporate know-how and institutional knowledge are among the important objectives of simulation governance. The productivity of newly hired engineers significantly increases if routine simulation procedures are standardized so that applications consistently produce certifiable results. Economic benefits are realized through improved productivity and improved reliability.

• If the mission is the formulation of design rules, for example, to establish allowable values for a new material system, then the plan should focus on the 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 observations. Economic benefits: Substantial savings through reduction of the number of tests on the sub-component, component, sub-assembly, and assembly levels.
• If the mission is to support condition-based maintenance (CBM), then the goal is to determine the probability that the number of cycles to failure  is smaller than a given number of cycles .  The main activities are: Collection, maintenance, and documentation of fatigue data and unit-specific information on service data, standardization of recurring analysis tasks. Economic benefits: Substantial savings through improved disposition decisions.

Observe that solution, data, and code verification are common to all three types of mission.  Validation and uncertainty quantification are performed in model development projects.

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, ideas, and technology.  Model development projects are open-ended.  Validation and definition of the domain of calibration is conditional on the available data.  Since the available data increases over time, and new ideas are likely to be proposed, there will be opportunities to revise and update mathematical models.  No one has the final word in model development [3].

Questions for Management

1. Does the engineering team possess the technical expertise and software tools to perform numerical simulation projects effectively?
2. Are mathematical models being defined independently from the way numerical approximations are obtained? – A common mistake is to conflate model definition with its numerical solution, as in “finite element modeling”.
3. Are the errors in numerical approximation properly estimated, controlled, and reported?
4. Physical testing is necessarily tied to the specific test conditions.  Generalization to a larger set of conditions requires a mathematical model.  Testing without a plan to generalize the results does not make sense. – Are physical testing projects properly planned, executed and analyzed in your organization? 
5. Do decision-makers have sufficient confidence in the predictive performance of mathematical models to reduce the number and complexity of physical tests through reliance on numerical simulation?
6. Are the experimental data properly documented and archived?
7. How well are the various professional skills needed for successful execution of numerical simulation projects coordinated?
8. Are mathematical models properly calibrated and their domains of calibration properly defined and documented?
9. How are new data incorporated into model updates when the data fall (a) within the domain of calibration and (b) outside of the domain of calibration?
10. Are the procedures of verification, validation, and uncertainty quantification (VVUQ) properly and consistently applied?
11. Have opportunities to improve design workflows through standardization been fully explored?
12. What is the estimated economic value of your current numerical simulation activities? – Without simulation governance, that value can be a large negative number.

[1] B. Szabó and R. Actis, Planning for Simulation Governance and Management: Ensuring Simulation is an Asset, not a Liability. Benchmark, July 2021, pages 8-12.

[2] B. Szabó and R. Actis, “Simulation governance: Technical requirements for mechanical design,” Computer Methods in Applied Mechanics and Engineering, vol. 249, pages 158-168, 2012.

[3] B. Szabó and I. Babuška, “Methodology of model development in the applied sciences,” Journal of Computational and Applied Mechanics, vol. 16, no. 2, pp. 75-86, 2021 (open source).

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.

By Dr. Barna Szabó
Engineering Software Research and Development, Inc.
St. Louis, Missouri USA

It is generally recognized that explainable artificial intelligence (XAI) will play an important role in numerical simulation where it will impose the requirements of reliability, traceability, and auditability. These requirements will necessitate clear thinking about the nature of mathematical models, the trustworthiness of their predictions, and ways to improve their reliability.

What is a Mathematical Model?

A mathematical model is an operator that transforms one set of data D, the input, into another set, the quantities of interest F. In shorthand notation we have:

\boldsymbol D\xrightarrow[(I,\boldsymbol p)]{}\boldsymbol F,\quad (\boldsymbol D, \boldsymbol p) \in ℂ \quad (1)

where the right arrow represents the mathematical model. The letters I and p under the right arrow indicate that the transformation involves an idealization (I) as well as parameters (physical properties) p that are determined by calibration. Restrictions on D and p define the domain of calibration ℂ, which is also called the domain of application of the mathematical model.

The formulation of mathematical models is a creative, open-ended activity, guided by insight, experience, and personal preferences. The validation and ranking of mathematical models, on the other hand, are based on objective criteria.

The systematic improvement of the predictive performance of mathematical models and their validation is, essentially, a scientific research program. According to Lakatos [1], a scientific research program has three constituent elements: (a) a set of hardcore assumptions, (b) a set of auxiliary hypotheses, and (c) a problem-solving machinery.

In the applied sciences, the hardcore assumptions are the assumptions incorporated in validated models of broad applicability, such as the theory of elasticity, the Navier-Stokes equations, and the Maxwell equations. The objects of investigation are the auxiliary hypotheses.

For example, in linear elastic fracture mechanics (LEFM), the goal is to predict the probability distribution of the length of a crack in a structural component, given the initial crack configuration and a load spectrum.  In this case, the hardcore assumptions are the assumptions incorporated in the theory of elasticity. One auxiliary hypothesis establishes a relationship between a functional defined on the elastic stress field, such as the stress intensity factor, and increments in crack length caused by the application of cyclic loads. The second auxiliary hypothesis accounts for the effects of overload and underload events.  The third auxiliary hypothesis models the statistical dispersion of crack length.

The parameters characterize the relationships defined by the auxiliary hypotheses and define the material properties of the hardcore problem.  The domain of calibration ℂ is the set of restrictions on the parameters imposed by the assumptions in the hardcore hypothesis and limitations in the available calibration data.

Problem-Solving

The problem-solving machinery is a numerical method, typically the finite element method. It generates an approximate solution from which the quantities of interest F_num are computed. It is necessary to show that the relative error in F_num does not exceed an allowable value τ_all:

| \boldsymbol F - \boldsymbol F_{num} |/|\boldsymbol F| \le \tau_{all} \quad (2)

To achieve this goal, it is necessary to obtain a sequence of numerical solutions with increasing degrees of freedom [2].

Demarcation

Not all model development projects (MDPs) are created equal. It is useful to differentiate between progressive, stagnant, and improper MDPs:  An MDP is progressive if the domain of calibration is increasing; stagnant if the domain of calibration is not increasing, and improper if the auxiliary hypotheses do not conform with the hardcore assumptions, or the problem-solving method does not have the capability to estimate and control the numerical approximation errors in the quantities of interest.  Linear elastic fracture mechanics is an example of stagnant model development projects [3]. 

Presently, the large majority of engineering model development projects is improper.  The primary reason for this is that finite element modeling rather than numerical simulation is used, hence the capability to estimate and control the numerical approximation errors is absent. 

Finite element modeling is formally similar to equation (1):

\boldsymbol D\xrightarrow[(i,\boldsymbol p)]{} \overline {\boldsymbol F}_{num} \quad (3)

where lowercase i is used to indicate intuition in the place of idealization (I) and F̅_num replaces F.  The overbar is used to distinguish the solutions obtained by finite element modeling and proper application of the finite element method.

In finite element modeling, elements are intuitively selected from the library of a finite element software tool and assembled to represent the object of analysis. Constraints and loads are imposed to produce a numerical problem. The right arrow in equation (3) represents a ”numerical model”, which may not be an approximation to a well-defined mathematical model, in which case F is not defined and F̅_num does not converge to limit value as the number of degrees of freedom is increased. Consequently, error estimation is not possible. Also, the domain of calibration has a different meaning in finite element modeling than in numerical simulation.

Opportunities for Improving the Predictive Performance of Models

There is a very substantial unrealized potential in numerical simulation technology. To realize that potential, it will be necessary to replace the practice of finite element modeling with numerical simulation and utilize XAI tools to aid analysts in performing simulation projects:

• Rapid advancements are anticipated in the standardization of engineering workflows, initially through the use of expert-designed engineering simulation applications equipped with autonomous error control procedures.
• XAI will make it possible to control the errors of approximation very effectively.  Ideally, the information in the input will be used to design the initial mesh and assignment of polynomial degrees in such a way that in one or two adaptive steps the desired accuracies are reached.
• XAI will be less helpful in controlling model form errors. This is because the formulation of models involves creative input for which no algorithm exists. Nevertheless, XAI will be useful in tracking the evolutionary changes in model development and the relevant experimental data.
• XAI will help navigate numerical simulation projects.
  • Prevent the use of intuitively plausible but conceptually wrong input data.
  • Shorten training time for the operators of simulation software tools.

The Main Points

• The reliability and effectiveness of numerical simulation can be greatly enhanced through integration with XAI processes. 
• The main elements of XAI-integrated numerical simulation processes are shown in Figure 1:

• The integration of numerical simulation with explainable artificial intelligence tools will force the adoption of science-based algorithms for solution verification and hierarchic modeling approaches. 

References

Related Blogs:

• Where Do You Get the Courage to Sign the Blueprint?
• A Memo from the 5th Century BC
• Obstacles to Progress
• Why Finite Element Modeling is Not Numerical Simulation?

By Dr. Barna Szabó
Engineering Software Research and Development, Inc.
St. Louis, Missouri USA

Let us be reminded of the timeless wisdom found in The Analects of Confucius (Book XIII, Chapter 3):

“If names be not correct, language is not in accordance with the truth of things. If language be not in accordance with the truth of things, affairs cannot be carried on to success [1]”. 

Confucius (551-479 BC) tells us, engineers working in the 21^st century AD, that having a firm grasp on terminology is an essential prerequisite to success. For example, if we are interested in setting up a numerical simulation project then we cannot set realistic goals and expectations unless we understand what numerical simulation is. We cannot understand what numerical simulation is unless we understand what simulation is. We cannot understand what simulation is unless we understand the difference between physical reality and an idea of physical reality, and so on.

Misleading or Meaningless Terms

There are many popular but misleading or meaningless terms floating around in engineering presentations, technical papers, blog articles, training and workplace environments such as; “physical reality”, “laws of nature”, “physics-based model”, “physics-informed model”, “computational model”, “governing equations“, “finite element modeling”, and “artificial intelligence”, not in accordance with the truth of things.  Brief explanations follow.

Physical Reality

Quoting Wolfgang Pauli (Physics Nobel Prize 1950); “The layman always means, when he says ‘reality’ that he is speaking of something self-evidently known; whereas to me it seems the most important and exceedingly difficult task of our time is to work on the construction of a new idea of reality [2]”.

A mathematical model is a precisely formulated idea about some aspect of physical reality and must never be confused with reality itself.  Many different models can be formulated about the same aspect of reality.  If the predictive performance of two or more models were found to be the same then the models would be equally valid. This view is known as model-dependent realism.  Quoting Stephen Hawking: “I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation [3].” – In other words, aspects of physical reality are seen and understood through mathematical models.

You may ask, since Pauli and Hawking were theoretical physicists, and you are interested in engineering, how would all this pertain to you?  – The answer is that engineering models deal with aspects of reality as well.  As engineers, we benefit from operating within established conceptual frameworks like continuum mechanics, fluid dynamics, and electromagnetism. Working in the foundational sciences, physicists are laboring to formulate and validate a comprehensive conceptual framework.  They are progressing very slowly. A physicist even argued that theoretical physics has been stagnating for about forty years [4].

Laws of Nature

Nature is what it is and if there are such things as laws of nature, they are not known and probably are not knowable.  Laws of great generality and elegance have been formulated to describe aspects of physical reality.  For example, Newton’s laws were considered to be laws of nature for about two centuries, but we now know that they are approximations to a more comprehensive model, the theory of relativity, which has its limitations also.

Physics-based Model

In view of the foregoing, this is a meaningless term.

Physics-informed Model

This vague term is also meaningless.

Computational Model

This term conflates the operations that transform the input data D into the quantities of interest F, called mathematical model, with the procedures by which a numerical approximation F_num is obtained.  Understanding the difference between F and F_num is essential.

Governing Equations

This term is misleading. Natural processes are not governed by our equations. Nature knows nothing about our equations. Our equations describe certain aspects of natural processes, subject to limitations imposed by the underlying assumptions and the available calibration data.

Finite Element Modeling

This term refers to the obsolete practice of constructing numerical problems by assembling elements from the library of a finite element code.  In these libraries, the model form and the approximating functions are mixed.

Artificial Intelligence (AI)

This is an umbrella term referring to computer systems designed to perform tasks, such as visual perception, speech recognition, and translation between languages. The term is misleading because these tasks involve the execution of clever algorithms that form only a small subset of the functions we associate with human intelligence. Importantly, there is no algorithm for theory choice [5], that involves elements of creativity, innovation, and, possibly, paradigm-shifting approaches. It would be more accurate to interpret the ‘I’ in AI as signifying ‘idiot savant’ rather than ‘intelligence’.

[1] Translated by James Legge.

[2] Wolfgang Pauli.  Letter to Markus Fierz, 1948.

[3] Stephen Hawking and Roger Penrose.  The nature of space and time. Princeton University Press, 2010.

[4] Sabine Hossenfelder. Lost in math: How beauty leads physics astray. Hachette UK, 2018.

[5] Thomas Kuhn. Postscript to the second edition of “The Structure of Scientific Revolutions”, University of Chicago Press, 1970.

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.

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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 mid-May 2023, ESRD’s Co-Founder and Chairman Dr. Barna Szabó delivered 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 was 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.

We are pleased to announce that the 45-minute recording of Dr. Szabó’s keynote presentation is now available for playback:

Would You Like a Simulation Governance Briefing?

Would you like to connect with Dr. Szabó on this topic? Feel free to complete the following form and we will be happy to schedule a Simulation Governance briefing with you:

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.