金属板材冲压成型过程的有限单元法模拟

FINITE ELEMENT SIMULAIIO OF SHEET METAL FORMING PROCESS

用有限单元法模拟了金属板材的冲压成型过程。在模拟过程中，应用了同时考虑了薄膜力和弯矩的板壳大变形理论，考虑了板材在塑性阶段各向异性的强化性质，考虑了模具和工件的接触和摩擦条件，分析了金属板在冲压过程中的屈曲现象，建立了增量形式的变分原理。弹塑性薄壳单元被引入，它的位移模式在变分的意义上满足单元边界上一阶导数连续的条件，并有足够的秩来适应单元的有限拉伸、转动和弯曲，计算中采用了罚函数方法，即在模具和工件的接触面上，模具的表面被假设为文克尔地基，采用了修正的库伦摩擦定律，迭代法被用来决定模具与工件的接触条件和金属板的塑性行为。本文最后提供了一个算例。

A general formulation for sheet metal forming process is developed by means ofthe finite element method.The membrane and bending finite deformations,workpiece andtool contact,frictional stick-slip conditions,bifurcation and post-bifurcation developmentof wrinkles of a sheet metal are analyzed.A nonlinear shell theory in a form of incremen-tal variational principle is employed in the incremental Lagrangian formulation for sheetmaterials of normal anisotropy.Elastic-plastic thin shell finite elements,which fulfill theinter-element C￣1 continuity condition in a variational sense and have a sufficient rank toallow finite stretching,rotating and bending of shell elements,are employed.The penaltymethod.in a form of Winkler foundation and a modified Coulomb friction on the contacttool surface,which has the relat ive advantage of t reating the contact constraints withoutincreasign the number of degrees of freedom,is employed.Based on the formulation,a finiteelement computer program for an incremental and numerical solution of the problem is writ-ten. An iteration scheme is developed to obtain the convergence of the contact conditionsof contact,separation,stick or slip. Numerical results of forming a rectangular pan withround corners are shown.