基于时域自适应精细算法的插值型无单元Galerkin法及其在弹性动力学中的应用

doi:10.19596/j.cnki.1001-246x.8573

计算物理 ›› 2023, Vol. 40 ›› Issue (3): 353-358.DOI: 10.19596/j.cnki.1001-246x.8573

基于时域自适应精细算法的插值型无单元Galerkin法及其在弹性动力学中的应用

陈莘莘(), 祝显毅, 李庆华

华东交通大学土木建筑学院, 江西南昌 330013

收稿日期:2022-06-06 出版日期:2023-05-25 发布日期:2023-07-22
作者简介:
陈莘莘(1977-)，男，博士，教授，博士生导师，研究方向为计算力学及其工程应用，E-mail：chenshenshen@tsinghua.org.cn
基金资助:
国家自然科学基金(12172131); 国家自然科学基金(12162014)

An Interpolating Element Free Galerkin Method Based on Self-adaptive Precise Algorithm in Time Domain and Its Application in Elastodynamics

Shenshen CHEN(), Xianyi ZHU, Qinghua LI

School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, Jiangxi 330013, China

Received:2022-06-06 Online:2023-05-25 Published:2023-07-22

摘要/Abstract

摘要：

将插值型无单元Galerkin法与时域自适应精细算法相结合, 提出一种求解弹性动力学问题的方法。通过时域分段展开, 将时空耦合的初边值问题转换为一系列的空间边值问题, 进而采用加权残值法推导递推形式的插值型无单元Galerkin法求解方程。该方法不仅能方便地直接施加本质边界条件, 并且可以避免时间步长较大造成的精度损失。数值算例给出的结果验证了该方法的有效性。

关键词: 弹性动力学, 时域自适应精细算法, 移动最小二乘插值法, 无网格法

Abstract:

Combining the interpolating element free Galerkin (IEFG) method and the self-adaptive precise algorithm in time domain, a novel algorithm is proposed for structural dynamic analysis in this paper. By expanding variables in each discretized time interval, the coupled spatial and temporal problem is transformed into a series of spatial problems, which are recursively solved by the IEFG method. The corresponding discretized governing equations for structural dynamic analysis are derived using the weighted residual technique. The proposed method can directly impose the essential boundary conditions directly and avoid possible loss of precision resulting from large time steps. The computational results shown in the numerical examples are satisfactory, which can demonstrate the effectiveness of the proposed method.

Key words: elastodynamics, self-adaptive precise algorithm in time domain, interpolating moving least squares method, meshless method

陈莘莘, 祝显毅, 李庆华. 基于时域自适应精细算法的插值型无单元Galerkin法及其在弹性动力学中的应用[J]. 计算物理, 2023, 40(3): 353-358.

Shenshen CHEN, Xianyi ZHU, Qinghua LI. An Interpolating Element Free Galerkin Method Based on Self-adaptive Precise Algorithm in Time Domain and Its Application in Elastodynamics[J]. Chinese Journal of Computational Physics, 2023, 40(3): 353-358.

图/表 5

图1 受内压的厚壁圆筒

Fig.1 A thick-walled cylinder subjected to internal pressure

图2 厚壁圆筒内表面的径向位移

Fig.2 Radial displacement history at the inner surface of the thick-walled cylinder

图3 受轴向载荷的矩形平面

Fig.3 A rectangular plate subjected to axial load

图4 A点的水平位移

Fig.4 Horizontal displacement of point A

图5 B点的水平位移

Fig.5 Horizontal displacement of point B

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基于时域自适应精细算法的插值型无单元Galerkin法及其在弹性动力学中的应用

An Interpolating Element Free Galerkin Method Based on Self-adaptive Precise Algorithm in Time Domain and Its Application in Elastodynamics

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