A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods

LIU Xue-mei; DENG Zi-chen; HU Wei-peng

doi:10.3879/j.issn.1000-0887.2015.03.002

Volume 36 Issue 3

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LIU Xue-mei, DENG Zi-chen, HU Wei-peng. A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods[J]. Applied Mathematics and Mechanics, 2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002

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A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods

doi: 10.3879/j.issn.1000-0887.2015.03.002

¹Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;²Department of Engineering Mechanics, Chang’an University, Xi’an 710064, P.R.China

Funds: The National Natural Science Foundation of China(11372252；11172239；11372253)

Received Date: 2014-12-02
Rev Recd Date: 2014-12-26
Publish Date: 2015-03-15

Abstract

Abstract

Dynamic responses of incompressible saturated poroelastic rods were investigated. Based on the theory of porous media, the 1D axial vibration equation for a fluid saturated elastic porous rod was established, in which the saturated porous material was modeled as a 2-phase system composed of an incompressible solid phase and an incompressible fluid phase. Then a 1st-order multi-symplectic form for the axial vibration equation and several local conservation laws for the saturated poroelastic rod were derived with the multi-symplectic method. Moreover, the midpoint Box multi-symplectic scheme for the axial vibration equation, and the discrete schemes for the local energy conservation law and local momentum conservation law were constructed with the midpoint method. Finally, the axial vibration process of the incompressible saturated poroelastic rod was simulated numerically and numerical errors of the local energy conservation law and local momentum conservation law were also discussed by means of the numerical results of each time step and each time-space step, respectively. The results show that the proposed multi-symplectic scheme has advantages of high accuracy, long-time numerical stability and good conservation properties, and this method provides a new way to solve the dynamic responses of saturated porous media.
- saturated poroelastic rod,
- multi-symplectic method,
- dynamic response,
- discrete

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References(15)

References

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