工程力学 ›› 2019, Vol. 36 ›› Issue (4): 37-43,51.doi: 10.6052/j.issn.1000-4750.2018.01.0074

• 基本方法 • 上一篇    下一篇

热弹性动力学耦合问题的插值型移动最小二乘无网格法研究

王峰1,2, 郑保敬1, 林皋3, 周宜红1,2, 范勇1,2   

  1. 1. 三峡大学水利与环境学院, 宜昌 443002;
    2. 湖北省水电工程施工与管理重点实验室(三峡大学), 宜昌 443002;
    3. 大连理工大学建设工程学部, 大连 116024
  • 收稿日期:2018-01-26 修回日期:2019-01-13 出版日期:2019-04-25 发布日期:2019-04-15
  • 通讯作者: 王峰(1987-),男,山东人,讲师,博士,主要从事水工结构温控及抗震数值计算研究(E-mail:wangfeng@mail.dlut.edu.cn). E-mail:wangfeng@mail.dlut.edu.cn
  • 作者简介:郑保敬(1983-),男,湖北人,讲师,博士,主要从事无网格法和边界元法研究(E-mail:zheng_bj@126.com);林皋(1929-),男,江西人,教授,博导,中科院院士,主要从事核电与水工结构抗震研究(E-mail:gaolin@dlut.edu.cn);周宜红(1966-),男,湖北人,教授,博士,博导,主要从事水工施工组织和管理研究(E-mail:zyhwhu2003@163.com);范勇(1988-),男,湖北人,副教授,博士,主要从事工程爆破与岩石动力学研究(E-mail:yfan@whu.edu.cn).
  • 基金资助:
    湖北省教育厅科学技术研究项目中青年人才项目(Q20181207)

MESHLESS METHOD BASED ON INTERPOLATING MOVING LEAST SQUARE SHAPE FUNCTIONS FOR DYNAMIC COUPLED THERMOELASTICITY ANALYSIS

WANG Feng1,2, ZHENG Bao-jing1, LIN Gao3, ZHOU Yi-hong1,2, FAN Yong1,2   

  1. 1. College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang 443002, China;
    2. Hubei Key Laboratory of Construction and Management in Hydropower Engineering, China Three Gorges University, Yichang 443002, China;
    3. Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
  • Received:2018-01-26 Revised:2019-01-13 Online:2019-04-25 Published:2019-04-15

摘要: 该文基于插值型移动最小二乘法,将无网格局部Petrov-Galerkin(MLPG)法用于二维耦合热弹性动力学问题的求解。修正的Fourier热传导方程和弹性动力控制方程通过加权余量法来离散,Heaviside分段函数作为局部弱形式的权函数,从而得到描述热耦合问题的二阶常微分方程组。然后利用微分代数方法,温度和位移作为辅助变量,将上述二阶常微分方程组转换成常微分代数系统,采用Newmark逐步积分法进行求解。该方法无需Laplace变换可直接得到温度场和位移场数值结果,同时插值型移动最小二乘法构造的形函数由于满足Kroneckerdelta特性,因此能直接施加本质边界条件。最后通过两个数值算例来验证该方法的有效性。

关键词: 耦合热应力, 移动最小二乘法, 无网格局部Petrov-Galerkin法, Heaviside函数, 微分代数方法

Abstract: The two-dimensional structural dynamic coupled thermoelastic problem is solved by meshless local Petrov-Galerkin (MLPG) method based on the interpolating moving least-squares (IMLS) method. The local weak forms are developed using the weighted residual method from the modified Fourier heat conduction equations and elastodynamic equations, in which the Heaviside step function is used as the test function in each sub-domain. Then the second-order ordinary differential equations describing the coupled thermoelasticity problem are obtained. Using the differential algebraic method, these second-order ordinary differential equations can be transformed into ordinary differential algebraic systems, in which temperature and displacement are chosen as auxiliary variables. The Newmark step-integration method is used to solve the ordinary differential system. The temperature and displacement numerical results can be obtained directly without the Laplace transform. Since the shape functions constructed from the IMLS method possess the Kronecker delta property, the essential boundary conditions can be implemented directly. Finally, two numerical examples are studied to illustrate the effectiveness of this method.

Key words: coupled thermoelasticity, moving least square method, meshless local Petrov-Galerkin method, Heaviside step function, differential algebraic method

中图分类号: 

  • O343.6
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2018年11月15日