Hybrid hexahedral element for solids, plates, shells and beams by selective scaling

Abstract

A robust two-field hexahedral element capable of handling plate/shell, beam and nearly incompressible material analyses without locking are presented. Starting with the assumed stress element of Pian and Tong, parasitic strain components leading to locking in plate, shell and beam analyses are first identified. Locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix. Unfortunately, the element then fails the patch test. However, patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation. The resulting element is lock-free and very efficient. All matrices involved in constructing the stiffness matrix can be derived explicitly. The accuracy of the element is tested by popular bench-mark problems.