A mixed formulation of a four-node mindlin shell/plate with interpolated covariant transverse shear strains

Abstract

A four-node Mindlin/Reissner shell element based on interpolation of the covariant transverse shear strains and assumed bending and membrane stresses is developed using the Hellinger-Reissner principle. For general shell geometry, the coupling entries of the bending and membrane stress components in the complementary energy matrix do not vanish. However, numerical investigations indicate that when the above coupling matrix entries are artificially set to zero, the finite element predictions of the element remain virtually unchanged. The resulting element is more efficient than the former one and only two 5×5 symmetric matrices are required to be inverted. Both elements are able to strictly pass various bending, transverse shear and stretching patch tests when they take up flat plate geometry. Two point quadrature is sufficient to integrate the element matrices without triggering any spurious kinematic modes. A number of numerical examples are given and the achieved accuracy and convergence are satisfactory. © 1991.