Serving the Numerical Simulation community since 1989 
Building an agentic system on top of legacy finite element modeling practices is like building a skyscraper on quicksand. Any team serious about reaching these capability levels must treat the soundness of numerical simulation as the highest priority, not an afterthought.
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. Learn more in our latest blog post.
Some years ago, I attended a meeting of senior engineers at a Fortune 100 company. The topic of discussion was: What should be done about the significant discrepancies between outcomes predicted by finite element models and those observed in physical tests? The chief engineer, who called the meeting, vented his frustration, declaring he was tired of hearing that the finite element mesh was the problem. He no longer believed the predictions from finite element modeling and had lost confidence in the engineers who produced those results. How could this have been prevented?
In one of my conference presentations, I discussed variational crimes, noting that using point forces and point constraints in finite element analysis serves as examples of such crimes. In the question-and-answer session, I was asked: “If using point constraints is a variational crime, then how is it possible that the structure designed to refloat the Costa Concordia was full of those crimes and yet it worked just fine.” This question presented an opportunity for me to explain that finite element modeling (FEM) and finite element analysis (FEA) are complementary methods when analysts correctly understand their respective domains of application and use them accordingly. However, problems arise when FEM is used outside its scope, which is an all too frequent error.
We at ESRD preach and practice solution verification. We believe that reporting data computed by an approximate method is incomplete without providing an estimate of the size of the relative error. This simple and self-evident statement tends to trigger fierce resistance from those who were schooled in the use of legacy finite element modeling tools. But why?
In a letter published in Science in 1963, Bernard K. Forscher used the metaphor of building edifices to represent the construction of scientific models, also called laws. These models explain observed phenomena and make predictions beyond the observations made.
Building models consistent with the science of numerical simulation should never be confused with finite element modeling, an activity rooted in pre-1970s thinking. We should keep Forscher’s metaphor in mind when evaluating claims about the benefits AI integration is expected to bring to numerical simulation.
Contrary to various claims, IGA is not a new paradigm in the numerical approximation of partial differential equations; it is simply an alternative implementation of the p-version of the finite element method. IGA is one possible implementation of the p-version of the finite element method. Its distinguishing features are: (a) it retains the CAD geometry, (b) the basis functions are the same as those used for CAD representation, typically B-splines or NURBS, and (c) it provides for the enforcement of the inter-element continuity of the derivatives of the basis functions.
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.
Meshless methods, also known as mesh-free methods, are computational techniques used for the approximation of the solutions of partial differential equations in the engineering and applied sciences. The advertised advantage of the method is that users do not have to worry about meshing. However, eliminating the meshing problem has introduced other, more complex issues. Oftentimes, advocates of meshless methods fail to mention their numerous disadvantages.
The World-Wide Failure Exercise (WWFE) was an international research project with the goal of assessing the predictive performance of competing failure models for composite materials. Part I (WWFE-I) focused on failure in fiber-reinforced polymer composites under two-dimensional (2D) stresses and ran from 1996 until 2004. Part II was concerned with failure criteria under both 2D and 3D stresses, and ran between 2007 and 2013. Part III, also launched in 2007, was concerned with damage development in multi-directional composite laminates.
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