Topology optimization of finite similar periodic continuum structures based on a density exponent interpolation model
Topology optimization of finite similar periodic continuum structures based on a density exponent interpolation model
复制标题
DOI：
10.3970/cmes.2013.090.211
复制
发表时间：
2013
影响因子：
2.4
通讯作者：
J. Rong;Z. Zhao;Y. Xie;Jijun Yi
中科院分区：
文献类型：
--
作者：
J. Rong;Z. Zhao;Y. Xie;Jijun Yi
类似的周期结构在工程中得到了广泛的应用。为了得到最优的相似周期结构，提出了一种具有多个位移约束的相似周期结构的拓扑优化方法。在该方法中，首先将设计领域划分为子领域。其次，在目标函数中引入考虑密度变量离散条件的惩罚项，将结构单元的倒数密度指数作为设计变量。建立了以结构质量为目标函数，结构位移为约束函数的相似周期连续体结构的拓扑优化模型。介绍了优化对偶方法，建立了一套拉格朗日乘子的迭代公式。然后引入虚拟子域设计变量，建立相似周期连续体结构各子域之间的对应变量关系，以满足结构相似的周期要求。最后给出了三个算例，验证了该方法在优化相似周期结构中的可行性和有效性。
Similar periodic structures have been widely used in engineering. In order to obtaining the optimal similar periodic structures, a topology optimization method of similar periodic structures with multiple displacement constraints is proposed in this paper. Firstly, in the proposed method, the design domain is divided into sub-domains. Secondly, a penalty term considering discrete conditions of density variables is introduced into the objective function, and the reciprocal density exponents of structural elements are taken as design variables. A topological optimization model of a similar periodic continuum structure with the objective function being the structural mass and the constraint functions being structural displacements is constructed in the proposed method. The optimization dual method is introduced and a set of iteration formula for Lagrange multipliers is built. Then, virtual sub-domain design variables are introduced to establish the relation of corresponding variables between all the sub-domains of the similar periodic continuum structure in order to enforce structurally similar periodic requirement. Three examples are provided to demonstrate that the proposed method is feasible and effective for obtaining optimal similar periodic structures.