An improved Cosserat point element for axisymmetric problems in nonlinear elasticity: Comparison with other element formulations

Abstract

SUMMARYAn improved quadrilateral Cosserat point element (CPE) has been developed for modeling torsionless axisymmetric problems in nonlinear elasticity. The CPE approach differs from standard finite element methods in that the element is considered to be a structure that is modeled using a strain energy function for homogeneous and inhomogeneous responses. The strain energy function for inhomogeneous deformations is generalized to include dependence on the reference geometry of irregular-shaped elements. The quadrilateral CPE has four nodes with eight degrees of freedom, it needs no integration over the element region or user specified hourglass parameters. A number of examples have been considered which compare the response of the improved CPE with those of all of the four noded hyperelastic elements implemented in the computer codes ABAQUS, ADINA, ANSYS and FEAP. These examples demonstrate that the improved CPE is applicable for thin plates and shells, is as accurate as elements based on enhanced strain and incompatible mode methods and is as robust as the full integration element. Consequently, the CPE is truly a user-friendly element that can be used with confidence for challenging problems in axisymmetric nonlinear elasticity.