分布式柔性机构拓扑优化设计的理论和算法

THEORETICAL AND ALGORITHMIC ON TOPOLOGY OPTIMIZATION DESIGN OF DISTRIBUTED COMPLIANT MECHANISMS

将连续体结构的拓扑优化技术应用到分布式柔性机构的设计中,基于变密度法和优化准则法推导并建立柔性机构拓扑优化的一种显式的设计变量收敛格式。结合分布式柔性机构优化设计的人工弹簧模型和虚拟载荷法,提出一种新型的分布式柔性机构拓扑优化设计的多准则优化模型,同时综合考虑柔性机构设计的机械效率要求和结构的刚度要求,并利用伴随敏度分析法进行敏度分析。数值算例证明研究方法的有效性,并分析和讨论优化模型和收敛格式中有关优化设计参数对柔性机构优化设计结果的影响。用激光快速成形技术验证柔性机构概念设计的合理性。

Topological optimization technology of continuum structures is extended to compliant mechanism designs. A kind of explicit updating scheme of design variables is worked out based on variable density method and optimality criteria. A new multi-criteria formulation is proposed for optimal topology design of compliant mechanisms using artificial spring model and dummy load method, in which the mechanical efficiency of mechanism problems and stiffness of structure problems are both involved. Sensitivity analysis of objective function is performed by applying adjoint sensitivity analysis method. Numerical examples have been presented for demonstration of the effectiveness of the proposed approaches. The influences of some optimal parameters upon the resulting mechanisms are discussed and the reasonable value scopes have been suggested. Prototype manufacturing methodology is also employed to manufacture the typical compliant mechanism to prove the validation of the conceptual design.