Efficient Analysis of 3-D Plates via Algebraic Reduction

3-D finite element analysis (3-D FEA) is not generally recommended for analyzing thin structures such as plates and shells. Instead, a variety of highly efficient and specialized 2-D numerical methods have been developed for analyzing such structures. However, 2-D methods pose serious automation challenges in today’s 3-D design environment. In this paper, we propose an efficient yet easily automatable 3-D algebraic reduction method for analyzing thin plates. The proposed method exploits standard off-the-shelf finite element packages, and it achieves high computational efficiency through an algebraic reduction process. In the reduction process, a 3-D plate bending stiffness matrix is constructed from a 3-D mesh, and then projected onto a lower-dimensional space by appealing to standard 2-D plate-theories. Algebraic reduction offers the best of both worlds in that it is computationally efficient, and yet easy to automate. The proposed methodology is substantiated through numerical experiments.