Hybrid finite element formulation in plane elasticity by using complex variable function

Abstract

It is pointed out that, if the equilibrium and compatible displacement-stress field is used in the hybrid finite element formulation, the 3-D integrals involved in a 3-D problem can be reduced to 2-D integrals, and 2-D integrals involved in a 2-D problem to line integrals. Using the polynomials of z=x+iy to be the complex potentials in plane elasticity, the equilibrium and compatible displacement-stress field within the element is obtainable. A square element using hybrid finite element formulation and complex variable function is suggested. Several numerical examples are given to prove the efficiency of the proposed formulation.