流体饱和多孔热弹性对称平面的动力学分析

doi:10.12066/j.issn.1007-2861.2264

Abstract

Abstract:

To address problems related to geometric nonlinearity and the local thermal equilibrium, the thermodynamic characteristics of an incompressible fluid-saturated porous thermo-elastic half-plane subjected to surface temperature loadings are studied. First, a mathematical model of the problem of geometric nonlinearity is established based on the porous media theory. Then, a synthetic numerical computation method is presented to simulate the numerical results of the problem. Here, the differential quadrature method and second-order backward difference scheme are applied to discretize the mathematical model in the spatial and time domains, respectively. In addition, the Newton-Raphson iterative method is used to solve nonlinear algebraic equations and to present the numerical results of the problem. The method presented in this study is proven to be effective and reliable, where its advantages include a small calculated amount and high accuracy. Finally, the thermodynamic characteristics of the fluid-saturated porous thermo-elastic half-plane subjected to surface temperature loadings are studied, and the effects of material parameters and geometric nonlinearity on the dynamic characteristics are considered in detail.

Key words: porous media theory, fluid-saturated porous thermo-elastic half-plane, geometric nonlinearity, differential quadrature method, thermodynamic

CLC Number:

TU311

ZHU Yuanyuan, YANG Xiao, WU Haitao. Thermodynamic analysis of a fluid-saturated porous thermo-elastic symmetric plane[J]. Journal of Shanghai University（Natural Science Edition）, 2022, 28(1): 145-156.

Figures/Tables 9

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References 15

[1]	Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid[J]. Journal of Applied Physics, 1955, 26(2): 182-185. doi: 10.1063/1.1721956
[2]	de Boer R. Theoretical poroelasticity-a new approach[J]. Chaos Solitons & Fractals, 2005, 25(4): 861-878. doi: 10.1016/j.chaos.2004.11.076
[3]	de Boer R, Ehlers W, Liu Z. One-dimensional transient wave propagation in fluid-saturated incompressible porous media[J]. Archive of Applied Mechanics, 1993, 63(1): 59-72. doi: 10.1007/BF00787910
[4]	Heider Y, Markert B, Ehlers W. Dynamic wave propagation in infinite saturated porous media half spaces[J]. Computational Mechanics, 2012, 49(3): 319-336. doi: 10.1007/s00466-011-0647-9
[5]	Hu Y J, Zhu Y Y, Cheng C J. DQM for dynamic response of fluid-saturated visco-elastic porous media[J]. International Journal of Solids & Structures, 2009, 46(7): 1667-1675.
[6]	刘林超, 杨骁. 饱和土中桩-桩竖向动力相互作用及群桩竖向振动[J]. 工程力学, 2011, 28(1): 124-130.
[7]	de Boer R, Kowalski S J. Thermodynamics of fluid-saturated porous media with a phase change[J]. Acta Mechanica, 1995, 109(1): 167-189. doi: 10.1007/BF01176821
[8]	He L W, Jin Z H. A local thermal non-equilibrium poroelastic theory for fluid saturated[J]. Journal of Thermal Stresses, 2009, 33(8): 799-813. doi: 10.1080/01495739.2010.482358
[9]	Yang X. Gurtin-type variational principles for dynamics of a non-local thermal equilibrium saturated porous medium[J]. Acta Mechanica Solida Sinica, 2005, 18(1): 37-45.
[10]	朱媛媛, 胡育佳, 程昌钧, 等. 基于 DQM 的空间轴对称流体饱和多孔热弹性柱体动力学特性研究[J]. 振动与冲击, 2017, 36(23): 83-91.
[11]	Bellman R E, Casti J. Differential quadrature and long term integration[J]. Journal of Mathematical Analysis & Applications, 1970, 34(2): 235-238.
[12]	Bellmam R E, Kashef B G, Casti J. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations[J]. Journal of Computational Physics, 1972, 10(1): 40-52. doi: 10.1016/0021-9991(72)90089-7
[13]	程昌钧, 朱正佑. 微分求积方法及其在力学应用中的若干新进展[J]. 上海大学学报 (自然科学版), 2009, 15(6): 551-559.
[14]	Zhu Y Y, Li Y, Cheng C J. Analysis of nonlinear characteristics for thermoelastic half-plane with voids[J]. Journal of Thermal Stresses, 2014, 37(7): 794-816. doi: 10.1080/01495739.2014.912094
[15]	聂国隽, 仲政. 用微分求积法求解梁的弹塑性问题[J]. 工程力学, 2005, 22(1): 59-62.

Thermodynamic analysis of a fluid-saturated porous thermo-elastic symmetric plane

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