现代复杂装备结构通常不仅处于热力耦合的复杂环境,而且承受着不可忽视的惯性力作用.针对这一类问题,提出了一种考虑拓扑相关惯性载荷的热力耦合拓扑优化高效求解方法.首先,构建了考虑热载荷、机械载荷以及惯性载荷的热力耦合拓扑优化模型,在体积约束条件下优化结构的柔顺度;其次,给出了惯性载荷的计算方法,针对低密度区域材料分布不收敛的问题提出了一种改进的材料插值惩罚模型,并基于此推导了结构柔顺度关于拓扑设计变量的敏度;最后,采用了基于梯度的移动渐近线法(Method of moving asymptotes,MMA)更新拓扑设计变量.此外,开发了基于MATLAB和ABAQUS的热力耦合拓扑优化平台,可适用于复杂工程中不规则结构设计域的拓扑优化问题.数值算例结果表明,所提出方法可有效避免低密度区域结构分布模糊的现象,具有良好的收敛性.
Thermal-mechanical Coupled Topology Optimization for Structures with Inertial Loads
Modern complex equipment structures are usually not only in a complex environment of thermal-mechanical coupling,but also subject to inertial forces that cannot be ignored.A high-efficiency solution method for thermoelastic topology optimization considering topology related inertial loads is proposed for this type of problem.First,a thermoelastic topology optimization model considering thermal,mechanical,and inertial loads is constructed to optimize the compliance of the structure under volume constraints;Secondly,a calculation method for inertial loads is provided,and an improved material interpolation penalty model is proposed to address the issue of non-convergence of material distribution in low density areas.Based on this,the sensitivity of structural compliance to topological variables is derived.Finally,the gradient based Method of Moving Asymptotes is used to update the topology design variables.In addition,a thermal coupling topology optimization platform based on MATLAB and ABAQUS has been developed,which can be applied to topology optimization problems of irregular structural design domains in complex engineering.The numerical example results show that the proposed method can effectively avoid the phenomenon of fuzzy structural distribution in low density areas and has good convergence.
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