| GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA |
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| 作者姓名： | Yang Xiao Cheng Changjun |
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| 作者单位： | Yang Xiao Cheng Changjun Department o，f Mechanics，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200436，China |
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| 基金项目： | Project supported by the National Nattural Science Foundation of China(No.10272070) |
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| 摘 要： | Based on the theory of porous media,a general Gurtin variational principle for theinitial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid andfluid phase.The finite element formulation based on this variational principle is also derived.Asthe functional of the variational principle is a spatial integral of the convolution formulation,thegeneral finite element discretization in space results in symmetrical differential-integral equationsin the time domain.In some situations,the differential-integral equations can be reduced to sym-metrical differential equations and,as a numerical example,it is employed to analyze the reflectionof one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results canprovide further understanding of the wave propagation in porous media.
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GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA |
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| Yang Xiao Cheng Changjun.GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA[J].Acta Mechanica Solida Sinica,2003,16(1):24-32. |
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| Authors: | Yang Xiao Cheng Changjun |
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| Institution: | (1) Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200436, China, CN |
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| Abstract: | Based on the theory of porous media,a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase.The finite element formulation based on this variational principle is also derived.As the functional of the variational principle is a spatial integral of the convolution formulation,the general finite element discretization in space results in symmetrical differential-integral equations in the time domain.In some situations,the differential-integral equations can be reduced to sym- metrical differential equations and,as a numerical example,it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results can provide further understanding of the wave propagation in porous media. |
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| Keywords: | saturated porous media Gurtin variational principle finite element method longitudinal wave |
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