Level-set method for design of multi-phase elastic and thermoelastic materials

The problem of designing composite materials with desired mechanical properties is to specify the materials microstructures in terms of the topology and distribution of their constituent material phases within a unit cell of periodic microstructures. In this paper we present an approach based on a multi-phase level-set model for the geometric and material representation and for numerical solution of a least squares optimization problem. The level-set model precisely specifies the material regions and their sharp boundaries in contrast to a raster discretization of the conventional homogenization-based approaches. Combined with the classical shape derivatives, the level-set method yields a computational system of partial differential equations. In using the Eulerian computation scheme with a fixed rectilinear grid and a fixed mesh in the unit cell, the gradient descent solution of the optimization captures the interfacial boundaries naturally and performs topological changes accurately. The proposed method is illustrated with several 2D examples for the synthesis of heterogeneous microstructures of elastic and/or thermoelastic composites composed of two and three material phases.     

基于变频率区间约束的结构材料优化设计

针对频率约束的结构材料优化问题,基于结构拓扑优化思想,提出变频率区间约束的结构材料优化方法。借鉴均匀化及ICM(独立、连续、映射)方法,以微观单元拓扑变量倒数为设计变量,导出宏观单元等效质量矩阵及导数,进而获得频率一阶近似展开式。结合变频率区间约束思想,获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型;采用对偶方法求解。通过算例验证该方法的有效性及可行性,表明考虑质量矩阵变化影响所得优化结果更合理。     

OPTIMAL STRUCTURAL TOPOLOGY DESIGN USING THE HOMOGENIZATION METHOD WITH MULTIPLE CONSTRAINTS

In applications of the homogenization method for optimal structural topology design the solution is obtained by solving the optimahty conditions directly. This reduces the computational burden by taking advantage of closed-form solutions but it restricts the optimization model to having only one constraint. The article develops a generalized class of convex approximation methods for mathematical programming that can be used for the optimal topology homogenization problem with multiple constraints in-eluded in the model, without substantial reduction in computational efficiency. A richer class of design models can be then addressed using the hotnogenization method. Design examples illustrate the performance of the proposed solution strategy.     

基于宏观性能的微观多孔材料拓扑优化

基于均匀化理论,建立与微观材料拓扑形状相关的宏观结构材料等效弹性张量。集成宏观结构所得到的位移场,推导出带有宏观结构力学特性的微观敏度。从而实现在给定材料体积分数前提下,以宏观结构最大刚度为目标,对材料微结构进行拓扑优化的目的。相关算例说明该方法可以得到与宏观力学性能相对应的各种微观结构蜂窝材料或复合材料。揭示了材料的微观结构拓扑形状依赖于宏观结构尺寸、载荷及初始边界条件等因素。     

含自重载荷作用下桁架拓扑优化的功射极法

由含自重载荷功约束下桁架重量最小化问题的一阶极值条件导出功-重量分配准则,即结构重量应按外力功与自重载荷所做功之差的大小来正比分配才能达到最优。桁架拓扑优化的功射极法是依据不等式约束的Kuhn-Tucker极值条件以及射线步对功函数一阶偏导数的影响规律而构造的,它包括3个步骤,即：解析确定最佳射线步步长与乘子、求解功准...