An improved mixed finite element based on a modified least‐squares formulation for hyperelasticity

Abstract

The present work deals with the solution of geometrically nonlinear elastic problems solved by the least-squares finite element method (LSFEM). The main goal is to obtain an improved performance and an accurate approximation in particular for lower-order elements. Basis for the mixed element is a first-order stress-displacement formulation resulting from a classical least-squares method. Similar to the ideas in SCHWARZ ET AL.[1] a modified weak form is derived by the introduction of an additional term controlling the stress symmetry condition. The approximation of the unknowns follows the same procedures as for a conventional least-squares method, see e.g. CAI & STARKE [2]. The proposed modified formulation is compared to recently developed classical LSFEMs, in order to show the improvement of performance and accuracy.