在结构可靠性形状优化的基础上 ,推导了接触问题随机有限元的灵敏度解析分析表达式 ,给出了优化分析的基本步骤 ,并对某发动机燕尾型榫头 /榫槽接触结构 ,选取榫头齿颈宽和齿面倾斜角为设计变量 ,以榫头最大拉伸应力、齿面挤压应力及可靠度指标为约束条件 ,对榫头边界上节点的最大当量应力进行了优化分析。结果表明 ,优化后榫头和榫槽接触面上的接触压力、当量应力及可靠度指标的分布更加均匀 ,验证了优化分析模型的合理性及所提出的可靠性形状优化设计方法的有效性 ,为榫头 /榫槽的结构设计提供有价值的参考 Based on the shape optimization of structural reliability, the expression of sensitivity analysis of stochastic finite element method for contact problem is deduced. The basic steps of optimization analysis are given. And the dovetail / tongue and groove contact structure of a certain engine, The width and tooth surface tilt angle are the design variables. The maximum equivalent stress of the joints on the tenon boundary is optimized by the tenon maximum tensile stress, the tooth surface compressive stress and the reliability index as the constraint conditions. The results show that the distribution of contact pressure, equivalent stress and reliability index on the contact surface of the tenon and mortise are more uniform, which verifies the rationality of the optimization analysis model and the validity of the proposed method. Tenon / tongue and groove design provides a valuable reference