Multi-objective Topology Optimization Of Compliant Mechanism Based On Physical Programming

At present, Most of research in the topological optimization design of compliant mechanisms is focused on the statics of the single objective optimization problem. However, the study of the dynamics and multi-objective topology optimization of compliant mechanisms are lacking. To solve above problems, by taking the physical programming as the method of multi-objective optimization, static and dynamic multi-objective topology optimization of compliant mechanisms are studied in aspects of the multi-objective topology optimization, key technology of topology optimization of compliant mechanisms and engineering application in this dissertation. First of all, interpolation scheme, numerical instabilities and optimization algorithm of the structural topology optimization design are studied. The design process of topology optimization of compliant mechanism design based on SIMP is given. Then, the statics, dynamics single objective topology optimization design of compliant mechanisms is studied and is verified by a numerical example respectively. On this basis, the statics and dynamics multi-objective topology optimization of compliant mechanisms based on physical programming is proposed by the introduction of the physical programming method. Finally, through the application on the topology optimization design of 3-RRR fully compliant parallel mechanisms, the method is validated in this paper. The specific content can be summarized as the following:(1)The basic theory of continuum structure topology optimization design is studied. Stiffness continuum topology optimization design mathematical model is deduced based on SIMP density-stiffness interpolation scheme and the method of moving asymptotes(MMA). Numerical instabilities of the structural topology optimization design are discussed and studied the causes and solutions. The sensitivity filtering method and the density filtering method are put forward and compared in dealing with the effect of the checkerboard phenomenon and mesh dependence phenomenon.(2)According to the characteristics of the compliant mechanisms, the topology optimization mathematical models are established by the minimum compliance and maximum flexibility which meet both stiffness and flexibility requirements, respectively. The hybrid filtering method is proposed to eliminate the one-node connected hinges which is the numerical instability phenomenon peculiar to the topology optimization of compliant mechanisms. Dynamic topology optimization model of compliant mechanism was improved by means of investigation of localized modes, the oscillation problem of frequency, the non-structural mass problem and multi-model eigenvalue solution. The improved dynamic topological mathematical model is established by the maximum mean eigenvalue.(3)Combining the statics, dynamics single objective of topology optimization, the physical programming method is used to establish the multi-objective topology optimization mathematical model, in which both the minimum compliance, the output displacement of compliant mechanism and maximum mean eigenvalue are regarded as static and dynamic optimization objectives. At last, by using in the optimization of compliant gripper, the model is verified the feasibility and effectiveness.(4)Based on differential motion analysis of rigid 3-RRR planar parallel mechanism, a planar 3-DOF fully compliant parallel mechanism is designed. The multi-objective topology optimization design method of compliant mechanism based on physical programming is applied to the configuration design of the fully compliant parallel mechanism in this paper. The obtained new topology optimization result is reconstructed. The statics simulation of planar 3-DOF fully compliant parallel mechanism is analyzed and compared with the theoretical value of rigid planar parallel mechanism. The results show that two structures have the same differential motion characteristic. This method not only meets its static motion characteristics and increases its natural frequency, but also enhance the stability and reliability of the planar parallel mechanism.