金属预成形优化设计及凝聚函数方法

OPTIMIZATION DESIGN OF METAL PREFORMING WITH AGGREGATE FUNCTION METHOD

研究了金属预成形设计中的形状优化设计问题及相应的求解算法,并讨论了凝聚函数在这类问题中的应用。金属预成形设计在本质上是一类反问题,给出采用形状优化设计方法求解这类问题的数学模型,讨论了目标函数构造方法对数值计算收敛性的影响。提出采用凝聚函数将∞-范数形式的形状误差函数转化为光滑可微的目标函数,显著提高了求解以金属预成形设计为背景的优化问题的收敛性。采用流动模型描述金属材料高温下的变形过程,利用基于梯度的数学规划方法求解了金属预成形优化设计问题。数值算例验证了所提出方法的有效性。

This paper addresses the shape optimization formulation for metal preform design problem, as well as the corresponding solution techniques. The metal preform design is an inverse problem in nature and it is stated as a shape optimization problem in the present paper. Different objective functions are discussed from the computational point of view. A mathematical statement of the metal preform design problem is proposed based on the Aggregate Function, with the purpose to convert the ∞-Norm of the shape error into a smooth and differentiable objective function and thus to improve the convergence of the solution of the optimization problem. The flow formulation is adopted for simulation of the metal forming process at high temperatures. With a gradient-based mathematical programming approach, the metal preform design optimization problem can be solved. A numerical example demonstrates the validity of the proposed method.