基于SIMP的柔顺机构的多目标拓扑优化设计

发布时间：2018-05-20 16:11

本文选题：柔顺机构 + 拓扑优化　；参考：《西安电子科技大学》2012年硕士论文

【摘要】：拓扑优化设计是柔顺机构的研究热点之一。本文以柔顺机构的多目标拓扑优化设计为研究目标，开展了相关工作。首先，以SIMP作为拓扑优化的材料插值方法，利用其中的惩罚项对拓扑优化中容易出现的中间密度单元加以限制；针对优化过程中出现的棋盘格等数值不稳定现象，，利用敏度过滤技术来解决。其次，构造了以体积比为约束、以柔顺机构输出位移最大化为优化目标的拓扑优化模型，并利用有限元方法分别采用优化准则法和MMA算法两种优化求解算法对反向器进行了优化，结果表明两种方法得到的最大输出位移基本一致，证明了两种算法的有效性。再次，建立了自由振动情况下，柔顺机构的特征值优化模型。在对特征值优化的过程中，本文采用了波尔森原理对局部模态进行抑制，从得到的拓扑图可以看出，这种方法是行之有效的。最后，结合多目标优化原理，利用妥协规划法建立了以柔顺机构输出位移最大、一阶固有频率最大为目标的多目标拓扑优化模型。通过典型算例，计算得到不同权值下各单目标的优化值，并利用决定函数找到最优妥协解，验证了模型的可行性和有效性。
[Abstract]:Topology optimization is one of the hotspots in the research of compliant mechanism. In this paper, the multi-objective topology optimization design of compliant mechanism is studied and related work is carried out. Firstly, using SIMP as the material interpolation method of topology optimization, the intermediate density element which is easy to appear in topology optimization is restricted by the penalty term, and the numerical instability such as chessboard and lattice in the optimization process is analyzed. The sensitivity filtering technique is used to solve the problem. Secondly, a topology optimization model with the volume ratio as the constraint and the output displacement maximization of the compliant mechanism as the optimization objective is constructed. Two optimization algorithms, the optimization criterion method and the MMA algorithm, are used to optimize the inverter. The results show that the maximum output displacement obtained by the two methods is basically the same, and the effectiveness of the two algorithms is proved. Thirdly, the eigenvalue optimization model of compliant mechanism under free vibration is established. In the process of eigenvalue optimization, the Poulsen principle is used to suppress the local modes. It can be seen from the topology that this method is effective. Finally, based on the principle of multi-objective optimization, a multi-objective topology optimization model with maximum output displacement and maximum first order natural frequency of compliant mechanism is established by means of compromise programming. Through a typical example, the optimal value of each objective under different weights is obtained, and the optimal compromise solution is found by using the decision function, which verifies the feasibility and validity of the model.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH112

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