Fluid-solid Coupled One-Dimensional Dynamic Responses Problems Of Saturated Porous Media With Generalized Multi-Symplectic Method

Porous media is a representative media in nature and engineering practice,which is applied in many fields,such as civil engineering,geology engineering,hydrology,biomechanics and so on.Many research topics of porous media have already obtained widely attention from academic world.Recently,these research methods are mostly finite element method,integral transform numerical inversion,analytical method,semi-analytical method and so on.There are some limitations about these methods,for which,the solution process are often complex and poor stability when solving differentical equations.Meanwhile,the exsit algorithms don’t study how to maintain the inherent geometric properties of the original system in the numerical calculation process.In this thesis,the generalized multi-symplectic method is applied in the one-dimensional fluid-solid coupled system of saturated porous media in order to investigate its more and deeper dynamic response characteristics.Furthermore,the new numerical method for fluid-solid coupled problems is explored too.Properties of fluid-solid coupled local thermal equilibrium and local thermal non-equilibrium thermal conductions for incompressible fluid saturated poroelastic rod are investigated by generalized multi-symplectic method,respectively.Two types of thermal conduction equations are derived and first-order generalized multi-symplectic forms are constructed.The processes of local thermal equilibrium and local thermal non-equilibrium thermal conductions are simulated numerically,which is compared with analytical solution and Galerkin finite element numerical solution.The errors of generalized multi-symplectic conservation law and generalized multi-symplectic local momentum are recorded in the numerical simulation process.The effects of parameter values on thermal conduction process are also checked later.It can be obtained that the process from local thermal non-equilibrium status to local thermal equilibrium status becomes shorter with the increasing of the heat exchange coefficient between two constituents.But the local thermal equilibrium temperature is independ on the heat exchange coefficient.In the process of local thermal equilibrium thermal conduction,the thermal conduction of every spatial location at the rod and the thermal conduction from the fixed end to out space both become more quickly with the reinforce of fluid-solid coupled thermal diffusion.For dynamic responses of porous media,the properties of fluid-solid coupled imcompressible saturated poroelastic rod are investigated firstly.Based on the porous media theory,fluid-solid coupling axial vibration equation is obtained.Introducing orthogonal variables,a first order generalized multi-symplectic structure-preserving form of axial vibration equation is established and Preissmann Box discrete scheme are constructed.Considering the constraint condition with one end free and the other fixed,axial dynamic responses of saturated poroelastic rod are determined numerically.For the case of considering the temperature effect,the thermal-mechanical coupled response characteristics of saturated poroelastic rod are further investigated.It is found that both axial displacement and effective stress of the solid skeleton are greater than those without considering the thermal effect.Moreover,with the poisson’s ratio of the solid skeleton increasing,the solid displacement and effective stress both increase.The stronger the temperature effect,the greater the influences on the solid axial displacement and effective stress.Generalized multi-symplectic algorithm is applied to investigate the properties of dynamic responses in fluid-solid coupled imcompressible saturated poroelastic beam.Transverse dynamic response equation set is presented firstly,and a first order generalized multi-symplectic form for transverse vibration equation of solid skeleton is established.Generalized multi-symplectic discretization scheme for dynamic response equation and some discretization schemes of local errors are presented,including errors of generalized multi-symplectic conservation law and generalized multi-symplectic local momentum.Taking the incompressible saturated poroelastic simply supported beam with two ends permeable for example,two cases are simulated numerically,including free vibration and forced vibration with transverse distributed load.The responses of transverse displacement and effective stress of the solid skeleton and equivalent moment of the pore fluid pressure are obtained,respectively.The effects of fluid-solid coupled interaction parameter on the transverse dynamic response process and all generalized multi-symplectic errors are revealed numerically.It is shown the attenuation vibration process of solid deflection and solid effective stress response process,as well as the oscillation process of equivalent moment of the pore fluid pressure are all shortened with the increasing of fluid-solid coupled interaction parameter.All the responding processes approach to their corresponding static values at last.Based on the porous media theory and Timoshenko beam theory,properties of fluid-solid coupled responses for incompressible saturated poroelastic Timoshenko beam are investigated by generalized multi-symplectic method.Dynamic response model is presented and a first order generalized multi-symplectic form is constructed.In view of the dynamic responses and quasi-static responses of saturated poroelastic Timoshenko cantilever beam with two ends permeable and free end subjected to the concentrated load,the response processes of the solid deflection,solid effective normal stress and effective shear stress are simulated numerically.Moreover,the evolution process for equivalent moment profile of the pore fluid pressure over time is presented and analyzed.The effects of fluid-solid coupled interaction parameter and slenderness ratio of the beam on the dynamic response process are revealed,and the effects on all generalized multi-symplectic errors are also checked simultaneously.From results obtained,the processes for solid deflection and solid effective stresses approaching to their corresponding static response values are both shortened with the increasing of fluid-solid coupled interaction parameter,while the processes for solid deflection is lengthened with the increasing of slenderness ratio of the beam.And the steady state value of solid deflection is much closer to the static deflection value of classic single phase elastic Euler-Bernoulli beam with the increasing of slenderness ratio.As time goes on,the solid skeleton of the beam will support all outside load,so equivalent moment of the pore fluid pressure becomes zero at last.In addition,all generalized multi-symplectic numerical errors decrease with the decreasing of parameters representing the system dissipation effect.The results obtained in this thesis are helpful for analyzing the mechanical behavior of porous media structures,and provide some theoretical basises for designing and testing various porous media structures in engineering practice.The numerical errors of generalized multi-symplectic local conservation laws for one-dimensional fluid-solid coupled systems are all fully analyzed.It is concluded the generalized multi-symplectic method has favourable local structure-preserving properties and long-time numerical stability.