Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Abstract

This paper presents two hybrid stress four-node tetrahedron solid elements which are equipped with the rotational d.o.f.s proposed by Allman. Inasmuch Allman's rotation is employed, the elements are plagued by zero-energy rotation modes which induce no strain. A modified Hellinger-Reissner functional that treats the rotation and the skew symmetric stress as independent fields is employed to formulate a stabilization scheme. Particular effort has been made to reduce the number of stress modes to minimum without sacrificing the frame invariance and proper rank of the element. The computational cost of the element is reduced by adopting orthogonal constant and non-constant symmetric stress modes. Numerical benchmark tests indicate that accuracy of the element with the minimum number of stress modes is close to another multi-field element which, however, is not frame invariant and exhibits unsuppressed zero-energy deformation modes. Copyright © 2000 John Wiley & Sons, Ltd.