弹塑性问题的杂交无网格有限体积差分法

HYBRID MESH-FREE FINITE VOLUME DIFFERENCE METHOD FOR ELASTOPLASTIC PROBLEMS

为了提高无网格法的应力精度,将应力与位移作为独立变量进行插值。将整个求解域分为边界域和内部域,对于位于边界域上的节点通过有限体积法建立离散方程,域内节点则利用有限差分法对节点应力梯度进行离散,逐点建立离散方程。在小变形假设的前提下,提出基于增量本构关系的弹塑性杂交无网格有限体积差分法,并用来模拟隧道开挖过程,算例表明,增量形式的杂交无网格有限体积差分法具有较高的计算精度和一定的工程实践价值。

To improve the precision of stresses with the mesh-free method, the stresses as well as displacements are interpolated independently. The whole domain is divided into boundary-domain and inside-domain. For the nodes on the boundary, the mesh-free finite volume method is used to establish the discrete equations. For the other nodes inside the domain, the mesh-free finite difference method is employed to discretize the gradients of stress node by node. Under the hypothesis of the small deformation, the hybrid mesh-free finite volume difference method for elasto-plastic analyses is proposed based on the incremental constitutive equations. The course of tunnel excavation is stimulated. Numerical examples show that the proposed incremental hybrid mesh-free finite volumetric difference method has high precision and efficiency, moreover it is of some practical value.