Solid elements with rotational dofs by explicit hybrid stabilization

Abstract

Two brick elements equipped with Allman's rotation are presented. Strain energy of both elements is sub-integrated by the second order quadrature which gives rise to the hourglass mechanisms. Inasmuch as Allman's rotation is employed, the elements are also plagued by the equal-rotation mechanisms, Variational functional containing independently assumed stress, displacement and rotation is employed to formulate the stabilization devices for the elements. Computational cost of the elements is reduced by incorporating the explicit hybrid stabilization technique. Popular numerical benchmarks are studied and the present elements found to be competitive to other state-of-the-art elements.