Analysis and optimization of shells

• Main Author: Lee, S. J.
• Published: Swansea University 1999
• Subjects: 502.85
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637865

Three computer programs are written, implemented and tested in this study: (a) shell finite element analysis program, LFEAP, for linear static, free vibration and geometrically nonlinear analyses, (b) a shape and size optimization program, LIBRA-DS, based on mathematical programming methods, and (c) a topology optimization program, LIBRA-OTS, based on optimality criteria method with layered artificial material model. A rigorous study of various shell element formulations is presented. In particular, an assumed natural strain shell element is developed and two well-known and reliable shell elements are employed to provide benchmarks for linear static and free vibration analyses. In addition, a shell element based on the element-based Lagrangian formulation is developed for post-optimization analysis where the nonlinear buckling loads of optimized shells are investigated. For the shape and size optimizations, consideration is given to the role of automatic mesh generation in conjunction with various surface definitions such as Coons patch and Bezier surface representations. Design sensitivity analysis is carried out using finite difference and semi-analytical methods. Appropriate perturbation step sizes are determined from a series of benchmark tests. The basic concepts of mathematical programming methods available in the adopted optimizer are explained. Various benchmark tests are then carried out to prove the capability of the developed shell design optimization system. For the topology optimization, a layered artificial material model is proposed and a standard resizing algorithm based on an optimality criteria method is employed. Numerous benchmark examples are presented to show the performance of the proposed methodology for shell topology optimization in various situations. The influence of various optimization parameters used in the adopted resizing algorithm on topology optimization process is also investigated. An algorithm for integrated design optimization is proposed and implemented to fine the stiffest shape, size or topology of various shells under linear static conditions.