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Discretization Strategy

Home Tag Discretization Strategy
Why Worry About Singularities?

Why Worry About Singularities?

Dec 14, 2023

A mathematician delivered a keynote presentation at an engineering conference some years ago. At the coffee break, following the presentation, a highly respected senior developer of a legacy finite element code, remarked: “I do not understand why the speaker was so worried about singularities. We never see them.”

The remark highlights the lack of a common language between the pre-scientific notion of finite element modeling and finite element analysis, which is a branch of applied mathematics. Read why mathematicians and engineers alike should “worry” about singularities.

The Story of the P-version in a Nutshell

The Story of the P-version in a Nutshell

Nov 30, 2023

The idea of achieving convergence by increasing the polynomial degree (p) of the approximating functions on a fixed mesh, known as the p-version of the finite element method, was at odds with the prevailing view in the finite element research community in the 1960s and 70s. But why?

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  • “We have been having very good success using the P-Version finite element code, StressCheck, to develop the 2-D solutions for two independent cracks in a plate. I have asked one of our AFGROW team members to model the plate and lug cases using StressCheck and compare them to the existing AFGROW closed-form solutions. [He] modeled the cases several different ways to be sure that he was getting the best possible solutions. He has verified that the bearing load option in StressCheck provides excellent results.”

    Jim Harter
    Team Leader-Analytical Fatigue/Fracture Reliability Team Air Force Research Laboratory (AFRL)

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The capabilities available with BAMF, AFGROW and StressCheck are highly advanced and offer significant potential to achieve the high-level goal of TITANS –to reduce the need to conduct expensive and time consuming physical tests and to rely more on simulation.

Dr. Kevin Walker, Defence Science and Technology Group – Melbourne, Australia

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