A general methodology for recovering equilibrating finite element tractions and stress fields for plate and solid elements

Abstract

A recent geometric presentation of a general and efficient methodology for recovering equilibrating tractions and stress fields from 2-D conforming displacement finite element models is reviewed, and further considered in the context of plate elements in 2-D and 3-D. This methodology requires the resolution of corner nodal forces/moments, and this presents localised problems which are solved in a simple way by exploiting Maxwell force diagrams. For more complex 3-D models including solid elements where higher degrees of element connectivity occur, the geometric procedure is adapted so as to retain the computational efficiency gained from recognising the topological and geometrical properties of a finite element model. Graph-theoretic and algebraic topological concepts are invoked in this context. The equilibrating tractions recovered for each element enable statically admissible stresses to be computed element by element, and local Trefftz fields may be exploited.