Abstract

A generalized form for the strain energy of inhomogeneous deformations is developed for a 3-D brick Cosserat Point Element (CPE) which includes full coupling of bending and torsional modes of deformation. The constitutive coeficients, which depend on the reference geometry of the element, are determined by solving eighteen bending problems and six torsion problems on special elements that are parallelepipeds with two right angles. The resulting constitutive coeficients ensure that the strain energy for inhomogeneous deformations remains a positive definite function of the inhomogeneous strain measures for all reference element shapes. A number of example problems are considered which show that the generalized CPE produces results as accurate as enhanced strain and incompatible elements for thin structures and is free of hourglass instabilities typically predicted by these enhanced elements in regions experiencing combined high compression with bending.

Keywords

Cosserat point, element irregularity, finite element, nonlinear elasticity

Authors