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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“At DST Group, we have effectively used StressCheck® over the last 10 years to determine accurate stress intensity factors. The results have been used to improve our residual strength and structural life estimates for aircraft in service with the Royal Australian Airforce, including C-130, P-3C and F/A-18 A/B. We have found it to be extremely easy to use and a very versatile code with which to create parametric models.
We have recently used StressCheck® to obtain improved stress intensity factor solutions (Improved stress intensity factors for selected configurations in cracked plates and Improved stress intensity factors for a single corner crack at a loaded fastener hole) for five key generic configurations. These transferable parametric results have been published externally. One specific example is the non-linear contact analysis of a cracked, filled fastener hole, with both fastener and remote plate loading.”
Dr. Manfred Heller, HeadStructural & Damage Mechanics, DST Group