Fundamental Solutions Of Several Kinds Of Multi-field Coupling Problems Of Porous Media

Porous materials have profound application potentials in such engineering fields as automobile industry,medical science,environmental protection and atomic energy,etc.Some progresses for the researches on the theory of porous media have been achieved.However,porous media own the reputation of complex and anisotropic structure with multi-field coupling effects,making the problems more complicated.Because of the inherent structural properties and excellent mechanics performance of porous media,it possesses significant for researches on its mechanical behaviors in both practical and theorical fields.For the plane problems in a steady state,the general solutions of orthotropic(transversely isotropic)thermoporoelastic media for plane problems are derived by Lur’e operator method;the fundamental solutions of infinite and semi-infinite thermoporoelastic planes,thermoporoelastic bi-material subjected to line fluid and heat sources are given by the general solutions;numerical examples are given and contours of field components are drawn.Correlative examples are brought up to analyze the influences of the liquid-solid coupling properties on the mechanical behavior of poroelastic materials by changing Biot’s effective stress coefficients.For the three-dimensional problems in a steady state:1.Starting from the fundamental equations of porous media,Timpe’s general solutions of axisymmetric isotropic porous media are given;The refined analysis on an axisymmetric isotropic porous circular cylinder is made.The refined equations and approximate solutions of the coupled field are obtained by Bessel’s functions when the circular cylinder is subjected to applied loads.2.On the base of general solutions of axisymmetric transversely isotropic thermoporoelastic media,the refined theory of an axisymmetric transversely isotropic thermoporoelastic circular cylinder is given.The fundamental solutions of a solid cone and a hollow cone under the action of a point fluid source and a point heat source,are derived by introducing the general solutions and potential functions,respectively;some numerical results are given under different loading conditions.3.In virtue of three-dimensional general solutions of thermoporoelastic media for non-axisymmetric problems,the fundamental solutions of an infinite thermoporoelastic bi-material structure subjected to a point fluid source and a point heat source are obtained.For quasi-static problems,the quasi-static general solutions of thermoporoelastic media for coupling problems are derived by using differential operators.The coupled fields are given when an infinite thermoporoelastic body is subjected to a step point heat source or a harmonic one by the general solutions,and contours of field components are drawn.According to fundamental equations of dual-porosity media based on the Nunziato-Cowin theory,solutions for dynamic problems are derived by Cramer’s rule.Popularizing the meshless local Petrov-Galerkin method into the researches on magneto-electro-thermo-poroelastic media,the integral calculation is performed without applying background grid.Firstly,the fundamental equations of magneto-electro-thermo-poroelastic media are introduced for its plane problem and axisymmetric problem;then according to the control equations in a weak form,its integral equations under the sub-domains can be obtained by the decomposition of Gaussian divergence theorem,in which the unit step function is regarded as the test function.Introducing the approximate expressions of spatial variables by moving least square method,the approximate expressions are plugged into the integral equations in a weak form;the integral equations in a discrete form are obtained by essential boundary conditions,and the numerical results are derived by means of Houbolt method at last.