基于ICM法的传热结构周期性拓扑优化设计

PERIODIC TOPOLOGY OPTIMIZATION DESIGN FOR THERMAL CONDUCTIVE STRUCTURE USING ICM METHOD

为了获得复合材料稳态导热性优化微结构构型,基于独立连续映射法,建立了周期性结构拓扑优化模型。在优化模型中,以重量最小化为目标、散热弱度为约束。采用一阶泰勒展开近似表达散热弱度约束函数。基于偏微分方程实施的图像过滤方法消除了棋盘格现象和网格依赖性问题。为了满足周期性约束,设计区域划分为若干相同大小的子区域,散热弱度贡献系数被重新分配。对比分析循环周期数、不同约束载荷工况下的拓扑优化构型。数值算例结果验证提出方法可以有效实现热传导下的复合材料微结构优化设计。

To obtain the optimal topological configuration for thermal conductive microstructures of composite materials, a topological optimization model of the periodic structure is established by the Independent Continuous Mapping method. In this model, minimized weight is taken as the objective and thermal compliance is the constraint condition. The thermal compliance constraint is approximately formulated using a first-order Taylor expansion. The image-filtering method is implemented by a partial differential equation to eliminate checkerboard patterns and mesh-dependence problems. To satisfy the periodic constraint, the designable domain is divided into a certain number of identical subdomains and the contribution coefficients of thermal compliance are redistributed. Optimal topological configurations with different periodic numbers and different loading conditions are compared and analyzed. Numerical results verify the validity of the proposed topology optimization method in designing the microstructures of composite materials for thermal conduction.