With the increasing development of topology optimization theory in thermal-fluid problems, it has been widely applied in design problems of cooling structures. However, little researches have concurrently considered the design-dependent mechanical problems of optimized structures. This paper deals with porosity-based topology optimization of forced convection planar heat sinks considering out-of-plane design-dependent deformation problems. The optimization is performed on the middle cross-section and the mechanical behaviors of the upper cover plate are considered. Governing equations of fluid flow, heat transfer, and structural mechanic fields are constructed. Particularly, to concurrently model design-dependent loads and boundary conditions, a spring term with design-dependent stiffnesses and a design-dependent pressure term are introduced into the out-of-plane mechanical model. Numerical examples in fluid-mechanical decoupled and weakly-coupled cases are given to demonstrate the validity and potential of the present approach. Additionally, the presented scheme is also evaluated in cases considering the global mechanical behavior and cases considering the local mechanical behavior. Comparisons and verifications show that the proposed approach is effective in yielding planar heat sinks with optimized heat transfer capabilities and well-controlled out-of-plane mechanical behaviors.

随着热工问题中拓扑优化理论的不断发展，已将其广泛应用于冷却结构的设计问题中。但是，很少有研究同时考虑优化结构的设计相关的机械问题。本文考虑了平面外设计相关的变形问题，对基于对流的强迫对流平面散热器进行了拓扑优化。优化是在中间截面上进行的，并考虑了上盖板的机械性能。构造了流体流动，传热和结构力学领域的控制方程。特别是要同时建模与设计相关的载荷和边界条件，将具有与设计有关的刚度的弹簧项和与设计有关的压力项引入到平面外机械模型中。给出了在流体-机械解耦和弱耦合情况下的数值例子，以证明本方法的有效性和潜力。另外，在考虑整体机械性能的情况下和在考虑局部机械性能的情况下，还对提出的方案进行了评估。比较和验证表明，所提出的方法可有效地产生具有最佳传热能力和良好控制的平面外机械行为的平面散热器。在考虑整体力学行为的情况下和考虑局部力学行为的情况下，也对所提出的方案进行了评估。比较和验证表明，所提出的方法可有效地产生具有最佳传热能力和良好控制的平面外机械行为的平面散热器。在考虑整体力学行为的情况下和考虑局部力学行为的情况下，也对所提出的方案进行了评估。比较和验证表明，所提出的方法可有效地产生具有最佳传热能力和良好控制的平面外机械行为的平面散热器。