Reissner’s Mixed Variational Theorem and triangular finite element discretizations: an energetic interpretation

Reissner’s Mixed Variational Theorem (RMVT) presents both displacements and transverse stresses as primary variables. This property allows the a-priori fulfillment of both interlaminar compatibility and equilibrium with potentially excellent numerical performance. However, the triangular finite element based on RMVT has never been assessed from an energetic perspective. This aspect is investigated in the present contribution for the first time: the functional reconstitution technique is extended to RMVT-based triangular elements (retaining transverse normal stress) and it is demonstrated that the elements exhibit significantly lower errors than the corresponding displacement-based formulation. Moreover, the percentage errors on the approximation of the semi-complementary energy is shown to be invariant with the plate thickness-to-width ratio.