平均应力耦合的接触应力优化方法

Contact Stress Optimization Method under Mean Stress Coupling

摘要: 接触界面应力分布的优化在摩擦接触系统设计中具有重要意义，其核心问题在于协调应力均匀化与摩擦演化之间的相互作用。针对传统模型中摩擦行为与应力分布相互独立的不足，本文提出一种全局耦合摩擦模型，将摩擦系数表示为平均接触应力的函数，从而建立摩擦状态与整体应力水平之间的耦合关系。在此基础上，构建了一类同时包含应力均匀化机制、摩擦风险调节机制和名义载荷约束惩罚项的接触应力优化模型，并揭示了各组成部分之间的权衡关系。由于摩擦项依赖平均应力，模型通过平均应力引入全局耦合效应，使目标函数呈现非可分的非凸结构。针对该问题，本文设计了动态正则近端梯度算法进行求解，并结合模型结构讨论了其收敛性质。数值结果表明，所提出模型能够有效刻画摩擦–应力耦合关系，所设计算法能够改善接触应力分布，降低局部峰值，并在优化精度、峰值控制和分布均匀性方面表现出较好的综合性能。

Abstract: The optimization of contact stress distribution plays an important role in the design of frictional contact systems, where the key issue lies in coordinating the interaction between stress uniformity and friction evolution. To address the limitation of traditional models in which friction behavior is independent of stress distribution, a globally coupled friction model is proposed, where the friction coefficient is expressed as a function of the mean contact stress, thereby establishing a coupling relationship between the friction state and the overall stress level. On this basis, a contact stress optimization model is constructed, which incorporates a stress uniformity term, a friction risk regulation term, and a nominal load constraint penalty term, revealing the trade-off among these components. Due to the dependence of the friction term on the mean stress, a global coupling effect is introduced, leading to a nonseparable and nonconvex objective function. To solve the resulting problem, a dynamic regularized proximal gradient algorithm is developed, and its convergence properties are discussed based on the model structure. Numerical results demonstrate that the proposed model can effectively characterize the friction-stress coupling relationship, and the designed algorithm is capable of improving the contact stress distribution, reducing local peaks, and achieving good overall performance in terms of optimization accuracy, peak control, and distribution uniformity.