A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements for plane elasticity problems

In a previous paper1 a modiÞed HuÐWashizu variational formulation has been used to derive an accurate four node plane strain/stress Þnite element denoted QE2. For the mixed element QE2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case. In this paper an alternative approach is discussed. The new formulation leads to the same accuracy for linear elastic problems as the QE2 element; however it turns out to be more e¦cient in numerical simulations, especially for large deformation problems. Using orthogonal stress and strain functions we derive B1 functions which avoid numerical inversion of matrices. The B1 -strain matrix is sparse and has the same structure as the strain matrix B obtained from a compatible displacement Þeld. The implementation of the derived mixed element is basically the same as the one for a compatible displacement element. The only di¤erence is that we have to compute a B1 -strain matrix instead of the standard B-matrix. Accordingly, existing subroutines for a compatible displacement element can be easily changed to obtain the mixed-enhanced Þnite element which yields a higher accuracy than the Q4 and QM6 elements. Copyright