基于密度法的热传导结构拓扑优化准则算法

热传导结构优化设计研究主要集中在形状及尺寸优化方面，这类方法由于结构初始估计构形带有经验性，通常并不是结构的最优拓扑，使设计具有局限性；为了有效求解热传导结构的最优拓扑，将结构力学中成熟的拓扑优化思想及其方法拓展到热传导结构的拓扑优化设计中，同时以最小热量传递势容耗散为优化目标，基于密度法建立热传导结构拓扑优化设计数学模型，并推导相应的优化准则；计算过程中应用基于卷积的滤波技术处理迭代密度场，消除数值计算不稳定性；不同条件下的数值算例验证了本文思想和算法的正确性、有效性，所得拓扑优化结果为后继的形状和尺寸优化提供了可靠的依据．

Algorithm of Topology Optimization Criteria for Heat Conduction Structure Based on Density Approach

The existing methods for the optimal design of heat conduction structures mainly focus on the optimization of the shape and the size. But the obtained topology may not be the optimal one due to the absence of the initial optimal topology. To seek the optimal topology for heat conduction structures, the well-rounded topology methodology and algorithms in structural mechanics are adopted in the optimal design of heat conduction structures, with the least dissipation of heat transport potential capacity as the optimal objective. Then the topology optimization model of heat conduction is established and the corresponding optimization criteria are proposed based on the density approach. Moreover, during the calculation process, a filtering technique based on the convolution is employed in density field to eliminate numerical instability. Numerical examples in different conditions are finally presented to demonstrate the correctness and validity of the proposed method, with the results laying a reliable foundation for the subsequent shape and size optimizations in thermal engineering.