金属塑性成形过程的无网格LRPIM方法分析

NUMERICAL SIMULATION OF METAL FORMING PROCESSES BY LOCAL RADIAL POINTS INTERPOLATION METHODS

结合微可压缩刚塑性材料的流动法则,利用局部加权残量法推导金属塑性成形过程的离散系统方程。采用径向基函数耦合多项式基函数构造无网格点插值法的形函数,用三次样条函数作为权函数。建立基于无网格局部径向基点插值法(local radial points interpolation method,LRPIM)的二维金属塑性成形离散控制方程,给出关键算法。径向基函数具有δ函数性质,因此可以很方便地施加本质边界条件。所有数值积分都在规则形状的局部域及其边界上进行,不需要积分背景网格,是一种真正的无网格法。对典型塑性成形过程进行LRPIM方法分析,并将数值结果与刚塑性有限元法计算结果和实验数据进行比较,结果吻合良好,表明所提方法的可行性和有效性。

Combined with the formulation of slightly compressible rigid plastic materials, local weighted residuas method is employed to deduce discrete system equation of metal plastic forming processes. The shape function is constructed with a radial basis function coupled with a polynomial basis function,and with the cubic spline function as weighted function in the weighted residuals method. Control equation is built for two-dimensional metal plastic forming processes based on the local radial points interpolation method （LRPIM） , and key algorithm are presented. Because the radial basis function has the property of Kroneeker delta function, the essential boundary conditions can be enforced easily. All numerical integrals are evaluated on regular shaped domains and boundary, the background cells not needed, thus it is a true mesh-free method. Typical plastic forming process is analyzed by LRPIM, and the simulation results are consistent with those obtained by rigid plastic finite element method and experimental data. The effectiveness and feasibility of the method is demonstrated.