Hybrid element method for incompressible and nearly incompressible materials

Abstract

A new hybrid element method suitable for problems with different Poisson's ratios, including incompressible and nearly incompressible materials is proposed. This hybrid model does not exhibit any locking phenomenon for nearly incompressible materials and is capable of producing correct displacement and stress solutions in the case of uniform stress and zero displacement state for incompressible materials. In addition, the model has other favourable characteristics such as having no extra zero energy modes, being coordinate invariant, possessing high accuracy and requiring simple manipulations in the formulation. A new variational functional suitable for different Poisson's ratios is proposed here. This functional is given in terms of a number of independent variables which include two stresses, one strain, two displacements and two average compressive stresses. A plane strain quadrilateral element Q4-LL can be established based on the proposed hybrid element method. Through a scries of worked examples it is demonstrated that the element can be used for various Poisson's ratios, possesses high accuracy and will not exhibit locking. By comparing the proposed element with existing elements for incompressible and nearly incompressible materials, it is possible to determine their relationship and to establish the fact that the hybrid method is a unified method incorporating many displacement models. © 1989.