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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“Accurate and reliable stresses and Stress Intensity Factors are required for determination of static and residual strength and for crack growth analyses in analysis tools such as AFGROW. For some geometries, industry solutions are either insufficient or nonexistent. The geometry, applied forces, and crack shapes and dimensions must be modeled reasonably well to obtain useful engineering data. The p-version finite element software StressCheck® (ESRD, Inc., St. Louis, Missouri, USA) is used to demonstrate how accurate finite element solutions can lead to good quality engineering analysis.”