Improvement of 2D-MITC4 solid and MITC4+ shell finite elements

Abstract

The objectives of this thesis were to develop a new 4-node quadrilateral solid (2D-MITC4) and shell (MITC4+) finite elements to improve the predictive capabilities, especially in distorted meshes. The proposed elements consist of two key concepts including the new assumed membrane strain field and the geometry dependent Gauss integration scheme. More specifically, the complicated assumed strain field of the previous 2D-MITC4 solid and MITC4+ shell elements are simplified and become more intuitive by directly using the strain coefficients. In addition, the geometry dependent Gauss integration is introduced to improve the membrane performance of the proposed elements. The geometry dependent Gauss integration with the new assumed strain field provides smoother solutions and good convergence, and thus the proposed elements can be used with relatively coarse meshes. In addition, it needs no additional degrees of freedom and does not reveal any numerical instability that is shown in the incompatible modes element. The new 2D-MITC4 solid and MITC4+ shell elements pass the three basic numerical tests: including zero energy mode, isotropy, and corresponding patch tests. It has been also thoroughly demonstrated that the proposed elements are very effective and reliable both in linear and nonlinear problems.