Development and investigation of nonlinear shell elements with drilling degree of freedom

Abstract

The generality and simplicity has made the shell element employed in a wide rage of finite element analysis for mechanics problems. The demand of shell models are rapidly growing to perform large-scale computations in important industrial applications to structural problems, sheet forming processes and composite shell structures. Since the general shell element has no stiffness associated with the drilling direction, any slight disturbance to the drilling rotation in the generalized load vector tends to amplify the rotation to an unrealistic large amount, which results in an unreliable solution. In addition, most shell elements fail in the analysis of non-smooth shell structures or shell structures with stiffener connections where three rotation components have to be considered. For remedy of that, many recent efforts have been done to include the sixth degree-of-freedom of the drilling rotation compatible to the physical meaning. In this paper, a four-node degenerated shell element with the implicit numerical scheme is developed to calculate non-linear problems based on the Belytschko-Leviathan's linear one-point quadrature shell element with the drilling degree of freedom. In formulating for the shell element, the physical stabilization scheme is used to control the zero-energy mode of the element for one-point quadrature shell elements. The element is then extended for the nonlinear elasto-plastic analysis of shell structures undergoing large deformation in conjunction with the updated Lagrangian formulation. Many numerical problems including patch tests and benchmark tests are solved to investigate the performance of the element in comparison with conventional ones. Typical problems are the shell structure subjected to drilling moments, warped shells, and structures with sharp edges within the shell. The performance tests have been carried out focusing on the accuracy of the deformed shape and the convergence as well as the computing time. In order to demonstrate the versatility and applicability of the present shell element, the static buckling analysis of a thin-walled S-beam structure has been solved and compared with commercial codes