This work extends force coupling in the topology optimization of fluid-structure interaction problems from hydrostatic to total stresses through the inclusion of viscous stress components. The superconvergent patch recovery technique is implemented to remove the discontinuities in velocity derivatives over the finite elements boundaries. The sensitivity analysis is derived analytically for the superconvergent patch recovery approach and further verified through the use of the complex-step derivative approximation method. Numerical examples demonstrate a differentiation in the optimized designs using pressure vs. total stress coupling depending on the flow characteristics of the design problem.

翻译：本研究通过引入黏性应力分量，将流固耦合问题拓扑优化中的力耦合从静水压力扩展至总应力。采用超收敛片状恢复技术消除有限单元边界上速度导数的不连续性。针对超收敛片状恢复方法解析推导了灵敏度分析，并通过复步长导数逼近法验证其准确性。数值算例表明，根据设计问题的流动特性，采用压力耦合与总应力耦合的优化设计存在差异。