Engineering Software Research & Development

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.