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

PDF(1063 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (23) : 83-91.

论文

朱媛媛 1 ，胡育佳 2，程昌钧 3，郑晓妹 1

作者信息 +

Dynamic characteristics for a spatial-axisymmetric fluid-saturated porous thermo-elastic cylinder based on DQM

ZHU Yuan-yuan 1 HU Yu-jia 2 CHENG Chang-jun 3 Zheng Xiao-mei 1

Author information +

文章历史 +

摘要

在热局部平衡条件下研究了空间轴对称不可压流体饱和多孔热弹性柱体在表面温度载荷作用下的动力学特性。首先基于de Boer多孔介质混合物理论，给出了问题的数学模型；其次综合采用微分求积方法-二阶向后差分法-Newton-Raphson迭代法求解了数学模型，得到柱体各离散点处未知物理量的数值结果，进而可分析柱体的动力学特性。为了验证本文方法的正确性，计算了不可压流体饱和多孔弹性柱体的动力固结问题，并与de Boer等的解析结果进行了比较，两者吻合良好，也证明DQM有较小的计算量和较高的精度。最后分别研究和比较了柱体只受到表面外载荷作用下的动力学特性和受到两种表面温度载荷与外载荷联合作用下的动力学特性，考察了材料的某些参数对柱体动力学特性的影响。

Abstract

Dynamic characteristics of an incompressible spatial-axisymmetric fluid-saturated porous thermo-elastic cylinder subjected to a surface temperature loading were studied in case of local thermal equilibrium. Firstly, the mathematical model of the problem was established based on de Boer porous media theory. Then, the differential quadrature method, the second-order backward difference scheme and Newton-Raphson iterative method were synthetically used to solve the mathematical model and obtain the numerical results of the unknown quantities at every discretized point, and the dynamic characteristics of the cylinder were further studied. In order to verify the validity of the proposed method, the dynamic consolidation problem of an incompressible fluid-saturated porous elastic cylinder was computed with this method. The obtained numerical results agreed well with the analytical ones published by de Boer et.al, it was shown that the proposed method has two advantages: smaller amount of computation and higher accuracy. Finally, the dynamic characteristics of a spatial-axisymmetric fluid-saturated porous thermo-elastic cylinder subjected to mechanical load or both mechanical load and temperature load were studied and compared, the effects of material’s some parameters on the dynamic characteristics of the cylinder were investigated.

导出引用

朱媛媛 1,胡育佳 2，程昌钧 3，郑晓妹 1. 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

ZHU Yuan-yuan 1 HU Yu-jia 2 CHENG Chang-jun 3 Zheng Xiao-mei 1. Dynamic characteristics for a spatial-axisymmetric fluid-saturated porous thermo-elastic cylinder based on DQM[J]. Journal of Vibration and Shock, 2017, 36(23): 83-91

参考文献

[1] Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid[J]. Journal of Applied Physics, 1955, 26(2): 182-185.
[2] Cui Y J, Sultan N, Delage P. A thermomechanical model for saturated clays[J]. Canadian Geotechnical Journal, 2000, 37(3): 607-620.
[3] Wu W H,Li X K,Charlier R, et al. A thermo-hydro-mechanical constitutive model and its numerical modeling for unsaturated soils[J]. Computers & Geotechnics, 2004, 31(2): 155-167.
[4] 刘干斌, 姚海林, 杨洋, 等. 考虑热-水-力耦合效应多孔弹性地基的动力响应[J]. 岩土力学, 2007, 28(9): 1784-1795.
LIU Gan-bin, YAO Hai-lin, Yang yang, et al. Coupling thermo-hydro-mechanical dynamic response of a porous elastic medium[J]. Rock and Soil Mechanics, 2007, 28(9): 1784-1795.
[5] 白冰. 循环温度荷载作用下饱和多孔介质热-水-力耦合响应[J]. 工程力学, 2007, 24(5): 87-92.
BAI Bing. Thermo-hydro-mechanical responses of saturated porous media ynder cycle thermal loading[J]. Engineering Mechanics, 2007, 24(5): 87-92.
[6] de Boer R. Theoretical poroelasticity-a new approach[J]. Chaos Solitons & Fractals, 2005, 25(4): 861–878.
[7] Bowen R M. Compressible porous media models by use of the theory of mixtures[J]. International Journal of Engineering Science, 1982, 20(6): 693-735.
[8] Schrefler B A. Mechanics and thermodynamics of saturated /unsaturated porous materials and quantitative solution[J]. Applied Mechanics Reviews, 2002, 55(4): 351-388.
[9] Placidi L, Dell'lsola F, Ianiro N, et al. Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena[J]. European Journal of Mechanics A/Solids, 2007, 27(4): 582-606.
[10] 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.
[11] Heider Y, Markert B, Ehlers W. Dynamic wave propagation in infinite saturated porous media half spaces[J]. Computational Mechanics, 2012, 49(3): 319-336.
[12] 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.
[13] de Boer R, Kowalski S J. Thermodynamics of fluid-saturated porous media with a phase change[J]. Acta Mechanica, 1995, 109(1): 167-189.
[14] 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.
[15] 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.
[16] Qin B, Chen Z H, Fang Z D, et al. Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(12): 1561-1576.
[17] Ehlers W, Häberle K. Interfacial mass transfer during gas-liquid phase change in deformable porous media with heat transfer[J]. Transport in Porous Media, 2016, 114(2): 1-32.
[18] Bellman R E, Casti J. Differential quadrature and long term integration[J]. Journal of Mathematical Analysis & Applications, 1970, 34(2): 235-238.
[19] 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.
[20] Bert C W, Malik M. Differential quadrature method in computational mechanics: a review[J]. Applied Mechanics Reviews, 1996, 49(1): 1-28.
[21] Chen C N. The two-dimensional frames model of the dfferential quadrature element method[J]. Computers & Structures, 1997, 62(3):555-571.
[22] 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.