An improved 3-D brick Cosserat point element for irregular shaped elements

Abstract

The original 3-D brick Cosserat point element (CPE) satisfies a nonlinear form of the patch test for general element shapes but the coefficients in the strain energy function for inhomogeneous deformations were motivated by considering solutions for a rectangular parallelepiped. In this paper, a generalized functional form for the strain energy of inhomogeneous deformations is proposed for irregular shaped elements. The coefficients in this strain energy function are determined by matching exact pure bending solutions for three right cylindrical parallelepipeds with their cylindrical axes oriented along three orthogonal base vectors. A generalization is proposed which ensures that this strain energy function remains positive definite for general irregular shaped elements. A number of example problems are considered which show that the performance of this improved CPE is good for irregular shaped elements. Moreover, the improved CPE continues to predict physical results for nonlinear and buckling problems that typically cause lack of convergence with other element formulations due to unphysical hourglassing.