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基于DQEM的分层流体饱和热弹性多孔介质轴对称问题的动力响应分析
叶东生, 朱媛媛, 王笑梅, 王玉善
上海师范大学 信息与机电工程学院
摘要:
本文研究了一维分层不可压流体饱和热弹性多孔介质轴对称问题的动力响应问题。基于de Boer多孔介质混合物理论,给出了问题的数学模型。其次在空间域内采用微分求积单元法离散控制微分方程、边界条件和连接条件,再在时间域内采用二阶向后差分格式处理时间导数,最后在离散化的初始条件下运用Newton-Raphson法进行迭代求解,从而可得各离散点处未知物理量的数值结果。比较性研究表明,本文方法是有效的,结果是可靠的,并具有精度高,计算量小,数值稳定等优点。最后,利用本文方法研究和比较了一维分层不可压流体饱和热弹性多孔介质在表面受到温度载荷下的热动力学特性,考察了材料参数的影响,得到了一些有益的结论。
关键词:  流体饱和多孔热弹性介质  多孔介质混合物理论(PMT)  微分求积单元法(DQEM)  热动力学响应
DOI:
分类号:TU311
基金项目:上海市自然科学基金
Dynamic response analysis of axisymmetric problems for layered fluid-saturated thermo-elastic porous media based on DQEM
YE Dong-sheng, ZHU Yuan-yuan, Wang Xiao-mei, Wang Yu-shan
The College of Information,Mechanical and Electrical Engineering,Shanghai Normal University
Abstract:
In this paper, the dynamic response of one dimensional axisymmetric problem for layered incompressible fluid saturated thermo-elastic porous medium is studied. Firstly, based on the theory of porous medium mixture, the mathematical model of the problem is given. Secondly, the differential quadrature element method is used to discrete the differential equations, boundary conditions and connected conditions on the space domain, and the second-order backward difference scheme is used to process the time derivative on the time domain, then the Newton-Raphson method is used to solve the discrete problem and the numerical results of unknown physical quantities at discrete points can be derived. Comparative studies show that the proposed method is effective, the result is reliable, and has the advantages of high precision, small amount of calculation, stable value and so on. Finally, the thermal-mechanical characteristics of one-dimensional layered incompressible fluid saturated thermo-elastic porous media under surface temperature load are studied and compared by using the method of this paper. The influence of material parameters is investigated, and some useful conclusions are obtained.
Key words:  fluid-saturated porous thermo-elastic medium  Porous Media Theory (PMT)  differential quadrature element method (DQEM)  thermo-dynamic responses