A new three-field mixed variational principle for the analysis of linear elastic problems

Abstract

A new three-field mixed functional is proposed for the analysis of linear elastic problems. The functional is constructed by linearly combining the total potential energy, the Hellinger-Reissner functional, the modified Hellinger-Reissner functional and the Hu-Washizu functional. The bilinear form of the functional defined on the admissible space V is shown to be symmetric, continuous, positive definite and V-elliptic, which means that the corresponding mixed model can be converted into a minimization problem which has the unique minimum.