Large deflection analysis of plates and cylindrical shells by an efficient four-node flat element with mesh distortions

This study reports an improved finite element computational model using a flat four-node element for nonlinear bending analysis of plates and cylindrical shells with element distortions. The von Kármán’s large deflection theory and the total Lagrangian approach are employed in the formulation to describe small strain geometric nonlinearity with large deformations using the first-order shear deformation theory. The most important feature of the developed element is the evaluation of linear membrane bending and nonlinear geometric stiffness matrices based on integration along the boundary of smoothing elements. This technique can give more accurate numerical integrations even with badly shaped elements or coarse meshes when compared to other flat elements using domain integration techniques. The accuracy and predictive capability of the present model is demonstrated by several numerical investigations and comparative studies with analytical/experimental and other numerical solutions available in the literature.