Energy element method for large deflection analysis of arbitrarily shaped plates

Abstract

The Ritz-based energy element method (EEM) is presented for large deflection analysis of arbitrarily shaped plates. The geometric model of an arbitrarily shaped plate is constructed by creating cutouts within a minimum rectangular domain covering the plate, in which a discrete energy system is established to simulate the plate based on the global admissible function, extended interval integral, Gauss quadrature, energy elements, and global variable stiffness. The energy element is defined to simulate strain energy of a rectangular subregion within the minimum rectangular domain, which contains a distinct number of Gauss points and allows geometric boundaries to pass through. Energy elements are generated by taking both the plate geometry and the distribution characteristic of Gauss points into consideration, resulting in a significant reduction of the required number of Gauss points than the Discrete Ritz method. By assigning variable stiffness properties on Gauss points, geometric boundaries of arbitrarily shaped plates can be captured in the numerical integration process. After removing the energy characterized by zero stiffness Gauss points out of the plate domain, the Gauss points based discrete model is constructed and the arbitrarily shaped plate can be simulated using discrete energy. The trust-region-dogleg method is utilized to solve the nonlinear algebraic equations of large deflection problem, and the numerical solution is produced. The solution procedures of EEM are standard and consistent applicable for plates of any shape. Comparisons regarding deflection and stresses with existing literature are presented.