Dynamic Finite Element Analysis and Optimization in GENESIS

This paper describes several aspects in the implementation of dynamic finite element analysis and optimization in the commercial program GENESIS. Dynamic capabilities discussed are: normal mode analysis, frequency response, and Guyan reduction with or without Craig-Bampton modes. Approximation concepts used in optimization to reduce the number of full system analyses are also discussed. Most of the dynamic responses in shape and sizing optimization are fully integrated so that in the optimization problem they can be combined with other existing analysis responses resulting from statics, buckling and/or heat transfer. In addition, these responses can be combined with existing geometric and/or user responses. In topology optimization the normal modes analysis is available and frequency responses can be combined with displacements and strain energies calculated from static analysis. Example problems using dynamic responses are presented. INTRODUCTION Engineers use dynamic analysis to insure and to improve the quality of their designs. Dynamic analysis is a well-established discipline and many papers and books on the theory can be found. This work explains the implementation of linear dynamic finite element analysis in the GENESIS program to solve the dynamics problem. The optimization problem in GENESIS is solved using the approximation concepts approach. In this approach, an approximate analysis model is created and optimized at each design cycle. The design solution of the approximate optimization is then used to update the full model, and a full system analysis is performed to create the next approximate analysis * Genesis Project Manager, Senior Member AIAA † Senior Engineer, Senior Member AIAA ‡ Senior R&D Engineer, Member AIAA § VR&D President, Fellow AIAA Copyright  2002, VR&D. Published by the American Institute of Aeronautics and Astronautic, Inc., with permission. model. The sequence of design cycles continues until the approximate optimum design converges to the actual optimum design. When compared to optimizing using full model structural analyses, the approximation concepts approach typically reduces the number of analyses required to find an optimum design by an order of magnitude. Schmit et al. introduced approximation concepts for traditional structural optimization, in the midseventies . In the eighties and early nineties, these concepts were refined to improve the quality of approximations. In the late nineties these refined concepts were used to solve the topology optimization problem. This paper discusses the application of these refined approximations to the dynamic responses. This work also discusses the optimization capabilities added to GENESIS related to dynamic analysis and other existing optimization capabilities that can be used simultaneously with dynamic responses. NORMAL MODES ANALYSIS The following governing equation is used: