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Development of Flow Element Method (FLEM) for large deformation and flow problems of a continuum

针对连续体大变形和流动问题的流元法 (FLEM) 的开发

基本信息

批准号：
11650506
负责人：
KIYAMA Hideo
金额：
$ 2.3万
依托单位：
Tottori University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650506/
关键词：
Large deformation analysis Equation of motion Explicit time-iterative solution Continuum Objective stress-rate DEM FLEM

项目摘要

This report describes a practical formulation of Flow Element Method (FLEM)(Kiyama, H.et al., 1991) for large deformation analysis of continua. The basic idea of this numerical method has originated from the principle of Distinct Element Method (DEM)(Cundall, P.A., 1971). The equation of motion is the governing expression for displacements of nodes. The explicit time-marching scheme of DEM is adopted to solve the equation. This scheme enables to avoid large matrix computations. This procedure and numerical examples have been reported by the authors (Kiyama, H.et al., 1995).The so-called Jaumann rate of stress is adopted to formulate FLEM, in which the expression for rotation is derived as an explicit function of the vorticity. This stress rate has been widely used as one of objective stress rates. However, many investigators have observed unrealistic stress responses in simple shear simulation. Considerable effort has been expended on this subject.The relation between the vorticity and the deformation gradient in simple shear is studied. A two-dimensional elastic block subjected to end-displacement in a plain strain condition is also simulated by the FLEM.These are numerical studies on effects of the stress rate on deformations and states of stress.On the basis of this consideration, we introduce two coordinate systems to calculate correction terms in the stress rate. One is the global coordinate for the equation of motion. The other is a set of local coordinates, each origin of which is respectively attached to Gaussian points in an element and is located in the global system. The latter is meant to treat rotation of element. Finally, the practical formulation of FLEM is successfully established to simulate large shear deformation and flow problems.

该报告描述了流元法（FLEM）的实用公式（Kiyama，H.et al.，1991年）的连续体大变形分析。该数值方法的基本思想源自离散单元法（DEM）的原理（昆达尔，P.A.，1971年）。运动方程是节点位移的控制表达式。方程的求解采用离散元法的显式时间推进格式。该方案能够避免大的矩阵计算。作者已经报道了该过程和数值示例（Kiyama，H.et al.，1995).采用所谓的Jaumann应力率来表示FLEM，其中旋转表达式被导出为涡量的显式函数。该应力率已被广泛用作客观应力率之一。然而，许多研究人员在简单剪切模拟中观察到不切实际的应力响应。本文研究了简单剪切中涡量与变形梯度的关系。本文还用有限单元法模拟了平面应变条件下的二维弹性块体在端部位移作用下的变形，研究了应力率对变形和应力状态的影响，在此基础上，引入了两个坐标系来计算应力率中的修正项。一个是运动方程的全局坐标。另一种是一组局部坐标，其每个原点分别与一个单元中的高斯点相连，并位于全局系统中。后者旨在处理元素的旋转。最后，成功地建立了模拟大剪切变形和流动问题的FLEM实用列式。