基于RAMP插值模型结合导重法求解拓扑优化问题

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在连续体拓扑优化领域中,寻求更好的建模方法和更快的求解算法一直是研究人员的研究重点。为此,针对拓扑优化设计方法中的变密度法进行深入分析。研究和比较各向同性惩罚微结构法（Solidisotropicmicrostructurewithpenalization,SIMP）和材料属性有理近似模型（Rationalapproximationofmaterialproperties,RAMP）的优缺点后,建立基于RAMP法的优化模型,并结合导重法求解算法,用于结构拓扑优化领域。详细推导单、多工况的最小柔度拓扑优化的迭代公式,给出导重法各变量的物理定义,并分别对单工况和多工况两个典型算例进行拓扑优化计算。算例结果令人满意,同时表明RAMP插值模型结合导重法求解结构拓扑优化问题具有设计变量少、迭代次数少、收敛速度快、优化效率高的特点,验证了其可行性和高效性。 Finding better modeling and solution methods for topology optimization of continuum structures is always paid much attention to by the researchers.Thus the variable density methods in continuum topology optimization are discussed.After in-depth analysis of the advantages and disadvantages of the solid isotropic microstructure with penalization method（SIMP） and rational approximation of material properties method（RAMP）,the optimization model is established based on the RAMP method.Guide-weight method is used as an algorithm combining for solving topology optimization problems.The iteration formulas of the least compliance in single and multi working conditions are derived and the physical definitions of variables in guide-weight method are proposed.Two typical examples of single-objective and multi-objective optimization problems are calculated respectively.The results are satisfactory and show that RAMP method combined with Guide-Weight method has the advantage of the less design variables,less number of iterations,fast convergence speed and high efficiency,which also verify its feasibility and efficiency.