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.