Formulating an effective generalized four-sided element

A new four-sided element is proposed for plane stress and strain problems. This generalized shape element is formulated based on the strain states. Error assessment, improvement and increase of the efficiency can conveniently be implemented in the suggested approach. The proposed element satisfies equilibrium necessities and produces good results in individual element test. In addition, the optimized stiffness matrix is also obtained by utilizing some important conditions. Insensitivity to the coordinates and aspect ratio, and lack of the parasitic shear errors are some of the specifications of this new generalized four-sided element. The performance of several numerical tests along with comparison between the capabilities of the proposed element and other researchers' well-known elements indicate significant efficiency and accuracy of the new one. The element described in the paper is an incompatible finite element which cannot pass the patch test.

► A new four-sided element is proposed.
► This element satisfies equilibrium necessities and produces good results.
► Insensitivity to the coordinates and aspect ratio, and lack of the parasitic shear errors are its specifications.