基于理想成形理论的板料设计

将基于理想成形理论的板料设计方法推广到一般的各向同性硬化的弹塑性材料。从理想成形的必要条件出发，推导了包括弹塑性理想成形的本构关系在内的有关板料设计公式。推导了线性三角形薄膜单元的变形运动学关系，采用线性三角薄膜元的有限元素法计算了一个弹塑性材料的轴对称拉深实例，并和刚塑性材料的计算结果以及边界元的计算结果进行了对比。结果表明，使用本文的方法可以取得较为精确的板料展开尺寸。该方法具有快速、准确以及实用面广的优点。

Blank Shape Design for Sheet Metal Forming Based on Ideal Forming Theory

Blank design and process planning are two key steps in the development of sheet metal forming technology. In this paper we present a finite element method (FEM) which is based on ideal forming theory and related to those two steps. In ideal homogeneous forming theory, material elements are assumed to deform along the minimum plastic work path. In our study, different elastic plastic constitutive relations with hardening have been integrated into the ideal homogeneous forming theory for modeling different materials. The ideal blank shape and intermediate shapes are solved by optimizing the global plastic work, assuming that all material elements deform in minimum plastic work paths, using a relevant FEM code. The blank shape of an axisymmetric cup of an almost isotropic 08AlM steel sheet has been calculated by the FEM code for demonstrating the validity of the method proposed. The results are in very good agreement with experimental data. They show that our method is more effective than BEM.