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.
Looking for Resources?
Recent News & Events
“The p-type element has been used to great advantage in the finite element system ESRD StressCheck®, . This software provides the engineer with the means to conduct solution verification in an extremely straightforward manner by simply increasing the degree of the element, monitoring convergence and using Richardson extrapolation reliably to estimate the error. This can be conducted automatically by the software thereby enabling the engineer to concentrate on the engineering rather than the simulation. StressCheck® has also been used to develop ESRD’s Handbook and Toolbox applications. The first of these provides engineers with a repository of parameterised standard problems of the type found in texts like Roark’s “Formulas for Stress and Strain”, . The second, Toolbox, is a tool that can be used to parameterise a company’s range of components for rapid and reliable analysis by non-expert analysis. Toolbox then is an exemplary of the way in which the democratisation of simulation can be applied.”
Angus Ramsay, PhDEngineering Director, Ramsay Maunder Associates