Towards improving the 2D-MITC4 element for analysis of plane stress and strain problems

•We improve the performance of the 2D-MITC4 solid finite element in distorted meshes.•The assumed strain field of the original 2D-MITC4 element is simplified.•The geometry dependent Gauss integration scheme is introduced. In this paper, we improve the performance of the 2D-MITC4 element for analysis of plane stress and plane strain problems. While the element shows excellent convergence behavior in regular meshes, it exhibits accuracy loss in distorted meshes, as many other elements do. We focus on improving performance in distorted meshes for general use in engineering practice. We simplify the assumed strain field of the original 2D-MITC4 element and introduce the geometry dependent Gauss integration scheme, in which integration points vary according to element geometry distortion. Consequently, a new 2D-MITC4 element is developed. The new 2D-MITC4 element passes the basic tests: patch, zero energy mode, and isotropy tests. Through various numerical examples, improved convergence behaviors of the new element are demonstrated, especially in distorted meshes.