基于改进BESO法连续体结构拓扑优化研究

Research on Structural Topology Optimization Based on Improved BESO Method

拓扑优化与传统尺寸优化和形状优化相比,提供了更广泛的设计灵活性,其应用越来越广泛。伴随着结构拓扑优化的发展,其优化方法也在不断进步,因此,其方法的研究凸显出重要的理论及工程应用价值。由于双向渐进结构优化方法(bi-directional evolutionary structural optimization,BESO)有很强的通用性,理论和程序实现简单,优化效率高,能够得到一系列黑/白分布的拓扑构型,正日益广泛地应用于工程实际当中。但双向渐进结构优化方法和其改进的方法在对于解决应力约束下的拓扑优化问题上一直都存在着不可忽视的问题。针对连续体结构,采用ABAQUS软件和改进双向渐进结构优化方法相结合来实现结构的拓扑优化,从而能够解决应力约束拓扑优化问题,进而证明其优越性以及应用在工程实例的可行性,详细描述BESO方法及其在工程领域中的应用,分析双向渐进结构优化方法成功的根本原因,以及相较于其他拓扑优化方法的优点,然后基于约束条件优化问题,提出约束条件与拓扑变量的关系。以结构应变能最小化为目标,利用拉格朗日方法推导出以应力约束作为约束条件,对C形夹、工字钢梁结构进行拓扑优化,验证了改进双向渐进结构优化法的有效性,提高了材料利用率,从而验证了改进双向渐进结构优化法在实际工程中的可行性。

Compared with traditional size optimization and shape optimization,topology optimization provides a wider range of design flexibility,and its application is becoming more and more widespread.With the development of structural topology optimization,its optimization methods are also improving,so the research of its methods highlights important theoretical and engineering application value.Because the bi-directional evolutionary structural optimization(BESO)method has strong universality,simple theory and program implementation,and high optimization efficiency,a series of black/white distribution topological configurations can be obtained.It is increasingly widely used in engineering practice.However,the bidirectional asymptotic structure optimization method and its improved methods have some problems in solving topological optimization problems under stress constraints.In this paper,ABAQUS software and improved bidirectional progressive structure optimization method are used to realize the topology optimization of continuous structure,so as to solve the stress constrained topology optimization problem,and then prove its superiority and feasibility of application in engineering examples.This paper describes BESO method and its application in engineering field in detail,analyzes the fundamental reasons for the success of bidirectional progressive structure optimization method and its advantages compared with other topology optimization methods,and then proposes the relationship between constraint conditions and topology variables based on constraint optimization problem.With the aim of minimizing the strain energy of the structure,the Lagrange method is used to derive the topological optimization of the C-type clamp and I-beam structure with the stress constraint as the constraint condition,which verifies the effectiveness of the improved bidirectional progressive structure optimization method and improves the material utilization rate,thus verifying the feasibility of the improved bidirectional progressive structure optimization method in practical engineering.