对连续体结构拓扑优化合理模型的再探讨

A Further Discussion on Rational Topology Optimization Models for Continuum Structures

连续体结构拓扑优化存在不同的建模方式,针对不同优化模型,有必要比较不同模型间的异同以避免错误地理解及使用优化模型,同时也有必要探讨不同优化模型的适用性及合理性问题.结构重量及刚度指标是结构优化中最常用的两个指标,论文通过建立体积约束下结构柔顺度极小化模型,及位移约束下重量极小化模型,详细分析比较了在不同荷载形式、单荷载工况及多荷载工况下两种优化模型的异同,并以高层建筑大型支撑结构的拓扑优化设计应用为例,讨论了两种模型的适用性,最后在结论中给出了两种模型的优缺点及适用性.所得结论对连续体结构拓扑优化在工程中的应用及此领域内的学术研究均具有参考价值.

Different optimization models have been established for the topology optimization of continuum structures.It is necessary to compare the similarities and differences between various optimization models in order to avoid the misunderstanding or misuse of these models.At the same time,it is also necessary to discuss the applicability and rationality of different optimization models for practical engineering application.Structural weight（or volume）and stiffness are the most commonly used indicators for structural optimization.In this study,two topology optimization models were established：one with minimizing compliance subject to specified volume constraint（named as MCVC model）;and the other with minimizing weight subject to displacement constraints（named as MWDC model）.The SIMP method was adopted to establish and solve the MCVC model;and the ICM method was adopted to establish and solve the MWDC model.Detailed analysis and comparison on the similarities and differences between the two models were carried out under different forms of loading,such as single and multiple load cases.The topology optimization design of the mega braced frame system of a high-rise building was illustrated as a typical example of engineering application to discuss the applicability and rationality of the two models.Finally,conclusions were drawn by summarizing the advantages,disadvantages,applicability and rationality of the two models,which provided useful knowledge for engineering application and academic research on topology optimization of continuum structures.