Equilibrium of nodal forces in the h- and p-versions of the FEM
Abstract: This note was written in response to questions concerning satisfaction of equilibrium conditions by finite element solutions computed by means of StressCheck. These questions were raised because StressCheck does not report nodal forces, however users, experienced with conventional finite element analysis codes, are expecting to see evidence of equilibrium, based on summation of nodal forces. It is shown in the following that (a) the nodal forces associated with each element are in equilibrium in both the h- and p versions and (b) satisfaction of the equilibrium of nodal forces is a property of the displacement formulation and is unrelated to the quality or reliability of the finite element solution.
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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”