Stress Fields in the Standard Four-Noded Conforming Finite Element
In considering the capabilities of a finite element, practicing engineers tend to think in terms of the element’s ability to model stresses rather than displacements. For example, if the engineer needs to model a component subject to an applied bending moment then he/she would look for an element capable of modelling a constant moment stress field. For standard conforming finite elements (CFE) the engineer will know the element’s capabilities in terms of displacements since this is given directly by the shape functions, e.g., the four-noded plane stress element has bilinear shape functions which, for isoparametric elements, describe both the shape of the element and also the displacement fields.
The element’s displacement fields can be transformed into strain and then stress fields and doing so is instructive in terms of understanding the element’s capabilities. This article considers the four-noded plane stress element presenting and discussing the five independent modes of stress that it is capable of modelling.