A unified analysis for stress/strain hybrid methods of high performance

Several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower-order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium. This paper is devoted to a unified analysis of convergence for Pian–Sumihara’s, Chen–Cheung’s and Piltner–Taylor’s enhanced stress/strain schemes. By virtue of the energy compatibility and the rank condition, error estimates for these typical finite elements of high performance are obtained in a unified framework, and especially, weakly locking-free error estimates with respect to the Poisson’s ratio ν in energy norms are obtained uniformly for ν⩽(1−Ch)/2 as h→0, where C is a constant independent of ν and the mesh size h. Very much the same about the three methods is pointed out.