A free of parasitic shear strain formulation for plane element

Two five-node rectangular elements are developed for analyzing two dimensional infinitesimal elastic strain problems. Several optimization criteria are elaborated, based on strain gradient notation. By utilizing these criteria and satisfying the equilibrium conditions, the SSDD and SSDI elements are formulated. Two additional five-node rectangular elements are also developed by using the traditional displacement approach. The robustness and accuracy of these four elements are assessed via numerical examples. The findings of the paper demonstrate the advantage of the SSDD and SSDI elements over the others. Moreover, these elements are free of the parasitic shear error.