On the variational foundations of the substitute shape function technique

In this paper, an element recently developed by Whitcomb (Comput. Struct. 22, 387–398, 1986) along the lines of the so-called substitute shape function technique (SSFT) has been re-examined. It is shown that a varialional basis can be found for this element in the form of a modified version of the variational theorem due to Hellinger and Reissner. On the basis of this theorem, a two-dimensional element has been developed using separate trial functions for the displacements and the shear strain. The element is identical to Whitcomb's element; however, the proposed approach appears to have certain advantages over SSFT.