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

In a previous paper(1) a modified Hu-Washizu variational formulation has be en used to derive an accurate four node plane strain/stress finite element denoted QE2 For the mixed element QE2 two enhanced strain terms are used an d the assumed stresses satisfy the equilibrium equations a priori for the l inear 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 efficient in numerical sim ulations, especially for large deformation problems. Using orthogonal stres s and strain functions we derive (B) over bar functions which avoid numeric al inversion of matrices. The (B) over bar-strain matrix is sparse and has the same structure as the strain matrix B obtained from a compatible displa cement field. The implementation of the derived mixed element is basically the same as the one for a compatible displacement element. The only differe nce is that we have to compute a (B) over bar-strain matrix instead of the standard B-matrix. Accordingly, existing subroutines for a compatible displ acement element can be easily changed to obtain the mixed-enhanced finite e lement which yields a higher accuracy than the Q4 and QM6 elements. Copyrig ht (C) 1999 John Wiley & Sons, Ltd.