中文摘要：

拓扑优化可以在概念设计阶段为工业产品结构的概念设计提供新颖的设计思路。传统的连续体结构拓扑优化方法通常只能获得一个优化的拓扑构型，但在实际工程应用中，这个构型在后续设计阶段可能会由于分析模型逐步细化、设计要求的进一步明确而无法满足改变后的设计目标和约束。针对此问题，提出了多样性设计求解方法（multiple designs approach，MDA），使得能够在优化过程中获得若干个多样性设计，以此减少在可能在设计初期由于信息不完整所带来的风险。给出MDA基本的优化列式，将目标函数定义为多个设计构型的目标性能加权之和，并通过加入对多样性度量的约束条件，在优化过程中驱动各个设计产生几何构型上差异。给出了一种具体的多样性度量方法，并对其物理意义和特征进行描述和讨论。以基于变密度法的最小柔顺性问题作为优化算例，给出了具体的优化列式及敏度推导。在算例中，研究了目标函数和约束中不同参数对结果的影响，并对目标函数之外的其他潜在结构性能进行了讨论和比较。结果表明，通过MDA能够有效地给出一批多样性设计构型，为后续的精细化设计提供多种设计方案和思路。

英文摘要：

Topology optimization can provide creative conceptual designs for structure of industry product in the pre-liminary design stage. However, the traditional topology optimization approaches focus on searching for one optimal solution which may be invalid due to the refinements of models or the additional design requirements. This paper presents the multiple designs approach （MDA） to get two or more diverse topology designs simultaneously in conceptual design, which can reduce the risk of lacking full knowledge of the designs by providing multiple designs. This paper gives general optimization model formulations for MDA in which weighting function is used as the objective function to evaluate the performances of multiple solutions and diversity measure is used as constraint to make difference between configurations. A kind of diversity measure is presented in the paper and its physical significance and features are also discussed at the same time. This paper solves two compliance minimization problems based on variable density method as examples and gives detailed optimization model formulations and sensitivity analysis. The parameters of objective function and con-straints in MDA and latent performances of different solutions are also discussed in the examples. The results show that＆nbsp;MDA could propose multiple diverse designs for detailed design stage.