轮胎胎冠形状优化的自适应序列响应面法

复杂工程结构的形状优化问题伴随着隐式的目标函数和约束条件,难以得到显式的灵敏度公式。轮胎有限元分析涉及多重非线性性质,这使轮胎的形状优化问题更加复杂。该文基于响应面法给出了一种序列局部响应面的自适应方案,来求解轮胎胎冠形状优化问题。借鉴线性问题的射线步法,给出了增量射线步的公式来调整违背约束的情况,并采取了一些措施来抑制迭代的振荡。应用到以接地压力分布均匀度为目标、胎冠形状参数为设计变量的优化问题中,经过十几次迭代即得到收敛的结果,验证了该方法处理复杂的优化问题的可行性和高效率性。

Self-adaptive sequential response surface method in shape optimization of tire tread

Shape optimization of complex engineering structures involves an implicit objective function and implicit constraint conditions;therefore,analytical sensitivity expressions are difficult to derive.Finite element analyses of tires are characterized by multiple nonlinearities which make the tire shape optimization more complex.A self-adaptive scheme based on the response surface method was developed to optimize tire tread shapes.This ray step approach uses incremental ray step formulas to treat violations of the constraint conditions,with special treatments to suppress oscillations.The objection function for the optimization problem is based on the uniformity of the contact force with the tread shape parameters as the design variables.Converged results requesting less than twenty iterations verify the feasibility and efficiency of the approach for complex optimization problems.