Reproducing Kernel Particle Method And Its Application To Rolling Process

As a new numerical simulation method, meshless methods perform the discretization of the workpiece entirely in terms of arbitrarily placed nodes without use of an explicit mesh. Reproducing kernel particle method is one of the meshless methods. The approximation of the unknown function in a domain is accomplished by means of kernel estimates. The kernel estimate of a function is an integral transformation through a kernel function which has a compact support. The reproducing kernel is a class of operators that reproduce the function itself through integration over the domain. This dissertation focus on the validity of the application of the reproducing kernel particle method in metal forming especially in rolling process, in order to provide a new research means for rolling process simulation.The shape function of meshless methods is not an interpolation function, so the enforcement of essential boundary condition is difficult in meshless method. In this dissertation the penalty method is used to enforce the essential boundary, i.e. a penalty term is added in the energy function. For 2D rolling under the plain strain condition of compressible rigid-plastic materials, the interface friction is treated by Koboyashi model. The integration process is accomplished by using the finite element background cell, and different types of Gauss point quadrature schemes is introduced in the interior and the boundary, and the reduced integration is used to prevent the volumetric locking. The tensor product weight function which has brick influence domain is used. The nonlinear system equation is solved by the direct iterative method. The effectiveness of the proposed approach is discussed by comparing theoretical predictions with experimental data found in the literature and the rigid-plastic finite element.On the basis of the previous work in two-dimensional meshless applications, the meshless model is introduced to the three-dimensional steady state flat rolling. The velocity discontinuity at rolling entry can be successfully treated through the implementation of adding a layer of nodes. The simulation results of 3D model with rigid ends is more exact than that ones of 3D model without rigid ends due to it is more resemble to the fact.