A comparative formulation of DKMQ, DSQ and MITC4 quadrilateral plate elements with new numerical results based on s-norm tests

This paper presents a review of the formulation of four plate bending quadrilateral elements and new advanced validation test results. The four elements are DKQ, MITC4, DSQ and DKMQ published between 1982 and 1993. The first is valid for thin plates and the three others include transverse shear effects. All elements have 4 nodes and 3 dof per node (one displacement and two rotations) and give good results in classical benchmark and patch tests for thin plates. The paper presents the respective formulation of the four elements in a unified and comparative manner, starting from the formulation of the classical DKQ element published in 1982. The paper includes new convergence behavior analysis using the s-norm tests. The numerical results using DKMQ, DSQ and MITC4 elements show the optimal and uniform convergence for thin and thick plates with a slight advantage for DKMQ due to quadratic terms for the rotation variables.