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 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 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
