Abstract
By interpreting the first two stress invariants as the mean and Gaussian curvatures of the Airy stress function, theories in differential geometry can be used to investigate the plane stress elements develoed by using the hybrid stress finite element method. Gertain intrinsic properties of the hybrid stress elements can be revealed by using this approach. New ways of formulating the 4-node quadrilateral element can also be suggested and successfully verified. The theories developed can be generalized further to the three dimensional case and to the plate bending problems.