Seminar - Miles Rubin - A Generalised Cosserat Point Element (CPE) for Isotropic Nonlinear Elastic Materials Including Irregular 3-D Brick and Thin Structures

Professor Miles B. Rubin
Gerard Swope Chair in Mechanics
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology
32000 Haifa, Israel


Thursday 21 August 2008, 1.10 - 1.55 pm
Civil Engineering Lecture Theatre 3

Abstract:

A generalised 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 coefficients, 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 coefficients 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 generalised 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.