Further results for enhanced strain methods with isoparametric elements

Abstract

In this contribution the enhanced strain finite element method is investigated further, with particular attention given to the analysis of the method for isoparametric elements. It is shown that the results established earlier (B.D. Reddy and J.C. Simo, Stability and convergence of a class of enhanced strain methods, SIAM J. Numer. Anal. 32 (1995) in press) for affine-equivalent meshes carry over to the case of isoparametric elements. That is, the method is stable and convergent provided that a set of three criteria is satisfied and, for plane elements at least, convergence is at the same rate as in the standard method. A procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress. With regard to computations, a new basis for enhanced strains is introduced, and numerical results are presented for this basis as well as for existing bases. The results for enhanced strain methods are distinguished by the fact that the constant appearing in asymptotic error estimates is much smaller for these methods than for standard approaches.