利用数学规划的刚塑性成形有限元仿真方法研究

Research on the finite element simulation with mathematical programming for the rigid-plastic forming problem

本文建立了金属刚塑性成形问题的数学规划有限元求解模型 ,将体积不变、边界接触条件和体积不变条件处理为数学规划的约束条件。通过构造迭代算法 ,将变形体分为刚性区域和塑性区域 ,并利用罚函数法消去刚性区约束条件 ,把非线性规划问题归结为求解一系列的二次规划问题。以铅柱镦粗作为仿真计算实例来验证算法的有效性。

The rigid-plastic analysis of metal forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iteration algorithm, which can distinguish the rigid zones and the plastic zone, is used to solve this formulation. This method has been used to carry out the rigid-plastic FEM analysis. An example is given to demonstrate the effectiveness of this method.