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为了研究离散型拓扑优化理论在实际工程中的应用,在遗传算法和渐进结构优化算法的基础上对有支撑钢框架的离散型拓扑优化设计进行了分析。通过引入拓扑变量并修改无效杆件的弹性模量,提出了一个能适用于桁架结构、刚架结构和桁架刚架混合结构的离散型拓扑优化问题统一数学列式。该统一数学列式能解决桁架拓扑优化问题中以截面面积作为设计变量而造成的奇异最优解问题。在此基础上,通过结合遗传算法和渐进结构优化算法,形成了一种求解大型多变量复杂离散型拓扑优化问题的复合拓扑优化算法,并将其应用于有支撑钢框架结构的拓扑优化设计中。通过一个3跨12层有支撑钢框架拓扑优化设计实例的对比分析,证明了上述复合拓扑优化算法能够克服遗传算法无法对生成的拓扑构形进行冗余检查的缺点,可有效地对大型多变量有支撑钢框架结构进行离散型拓扑优化设计。
In order to study the application of discrete topology optimization theory in practical engineering, the discrete topology optimization design of supported steel frame is analyzed based on genetic algorithm and incremental structure optimization algorithm. By introducing topological variables and modifying the elastic moduli of ineffective members, a unified mathematical formulation of discrete topology optimization problems that can be applied to truss structure, rigid frame structure and truss frame hybrid structure is proposed. The unified mathematical formulation can solve the singular optimal solution problem caused by the cross-sectional area as the design variable in the truss topology optimization problem. Based on this, a hybrid topology optimization algorithm for solving large multivariable complex discrete topological optimization problems is proposed by combining genetic algorithm with progressive optimization algorithm, and applied to topology optimization of supported steel frame structures . The comparison and analysis of a three-span 12-story supported steel frame topology optimization design proves that the above-mentioned composite topology optimization algorithm can overcome the disadvantage that the genetic algorithm can not perform redundant check on the generated topology configuration, and can effectively reduce the large multi-variable Supported steel frame structure for discrete topology optimization design.