基于滑动Kriging插值的MLPG法求解结构非耦合热应力问题

王峰; 周宜红; 郑保敬; 林皋

doi:10.21656/1000-0887.370189

基于滑动Kriging插值的MLPG法求解结构非耦合热应力问题

doi: 10.21656/1000-0887.370189

¹三峡大学水利与环境学院, 湖北宜昌 443002;²大连理工大学水利工程学院, 辽宁大连 116024

基金项目: 国家自然科学基金（51479103）；国家自然科学基金青年科学基金（51109134）；中国博士后科学基金（2013T60283）

详细信息

作者简介:
王峰（1987—），男，讲师，博士(通讯作者. E-mail: wangfeng@mail.dlut.edu.cn).

中图分类号: O343.6
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- 被引次数: 0
出版历程
- 收稿日期: 2016-06-14
- 修回日期: 2016-08-30
- 刊出日期: 2016-11-15

A Meshless Local Petrov-Galerkin Method Based on theMoving Kriging Interpolation for Structural Uncoupled Thermal Stress Analysis

¹College of Hydraulic & Environmental Engineering, China Three Gorges University,Yichang, Hubei 443002, P.R.China;²School of Hydraulic Engineering, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（51479103）；The National Science Fund for Young Scholars of China（51109134）；China Postdoctoral Science Foundation（2013T60283）

摘要

摘要: 将基于滑动Kriging插值的无网格局部Petrov-Galerkin(MLPG)法用来求解二维结构非耦合热应力问题，首先进行瞬态热传导的求解，然后再通过顺序耦合法将不同时刻节点温度作为附加体力项施加到应力分析中.瞬态温度场和非耦合热应力分析通过加权余量法来离散，同时用Heaviside分段函数作为局部弱形式的权函数.由于滑动Kriging插值构造的形函数满足Kronecker δ函数的性质，因此方便了本质边界条件的施加.刚度矩阵形成过程中只涉及到边界积分而没有涉及到区域积分，因此可以减少计算工作量，最后通过两个数值算例来验证本文方法的有效性.
- 热应力 /
- 滑动Kriging插值 /
- 无网格局部Petrov-Galerkin法 /
- Heaviside函数 /
- 顺序耦合法
Abstract: A meshless local PetrovGalerkin (MLPG) method based on the moving Kriging interpolation was employed for the solution of 2D structural uncoupled thermal stress problems. The transient heat conduction problem was solved firstly and then the thermal solutions were imposed as body loads with the sequential coupledfield method in the stress analysis. The local weak forms were developed with the weighted residual method locally from the partial differential equations of transient heat conduction and structural dynamics, where the Heaviside step function was used as the weighted function in each subdomain. The essential boundary conditions can be implemented directly since the shape functions constructed from the moving Kriging interpolation possess the Kronecker δ property. This method does not involve the subdomain integral during generation of the global stiffness matrix except for the boundary integral, so the computational costs are reduced largely. The results of 2 numerical examples show the effectiveness of this method.
- thermal stress /
- moving Kriging interpolation /
- meshless local Petrov-Galerkin method /
- Heaviside step function /
- sequential coupled-field method

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参考文献(24)

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