Theoretical Solutions Of Functionally Graded Thick-walled Tube On The Mechanical-Thermal-Magnetic-Electric Loads

Functionally Graded Materials(FGM)is a new kind of functional materials which possesses the excellent properties such as they can eliminate the stress singularity and their properties change continuously.Due to its particular properties of physics and mechanics,functionally graded intelligent thick-walled tube has attracted wide attention and investigations.FGM has potential applications in many fields,and all these applications should base on the mechanical properties of this material.In this article,the mechanical behaviors of functionally graded thick-walled tube with different structures under different loads are investigated in detail,and the main work is as follows:Elasticity solutions for the functionally graded thick-walled tube subjected to internal pressure are given in terms of volume fractions of constituents.We assume that the functionally graded tube consists of two linear elastic constituents and the volume fraction for one phase is a power function varied in the radial direction.By using the Voigt method,the Reuss method and the Mori-Tanaka method,the theoretical solutions of the corresponding radial displacement and the stresses are presented.The present methods are valid for the materials with different Poisson's ratios rather than constant Poisson's ratios usually used in the existing references to obtain the effective Young's modulus.The effects of the volume fraction and Poisson's ratio as well as the ratio of two Young's moduli on the radial displacement and the stresses are studied.In this work an approximate analytical solution based on the Mori-Tanaka method for functionally graded thick-walled tube subjected to internal pressure is given and the results of these three methods are compared with each other.Also,an elasticity solution of functional graded thick-walled coating tube is given in this work.For the problem of a functionally graded thick-walled tube subjected to internal pressure,we have already presented the elasticity solution based on the Voigt method.Then we discuss the elastic-plastic problem of the functionally graded thick-walled tube subjected to internal pressure,and give the solution in terms of volume fractions of constituents.We assume that the tube consists of two linear work-hardening elastic-plastic constituents and the volume fraction of one phase is a power function varied in the radical direction.The Lame constants and yield stress of the constituents of the FGM tube are given rather than Young's modulus and yield stress with different unknown parameters of the whole material in the existing papers.As the internal pressure increases,the deformations of one phase and two phases from elastic to plastic are analyzed.The present method is valid for the materials with different Poisson's ratios rather than constant Poisson's ratios usually used in the existing references to obtain the effective Young's modulus.More importantly,the influences of linear work-hardening on plastic behaviors are considered in this work.Finally,onset of yield phase and onset of yielding position are discussed.This work discusses the thermoelastic problem of the functionally graded thick-walled tube subjected to both axisymmetric mechanical and thermal loads,and gives the solution in terms of volume fractions of constituents.The theoretical solutions of the displacement and the stresses are presented under the assumption of a uniform strain field within the representative volume element.Based on the relation of the volume average stresses of constituents and the macroscopic stresses of the composite material in micromechanics,the present method can avoid the assumption of the distribution regularities of unknown overall material parameters appeared in existing papers.Further,the present method is valid for the materials with different Poisson's ratios of constituents.The effects of the volume fraction,the ratio of two thermal expansion coefficients and the ratio of two thermal conductivities on the displacement and stresses are systematically studied.This work considers magneto-elastic behavior of a functionally graded thick-walled tube which is placed in a uniform magnetic field and is subjected to mechanical load.Exact solutions for the radical displacement,the stresses and the perturbation of the magnetic field vector are determined based on the Voigt method assuming a uniform strain field within the representative volume element.For the functionally graded intelligent thick-walled tube,we obtain the elastic solution of FGPM which consisted of two piezoelectric materials when subjected to internal pressure.The present methods are valid for the materials with different Poisson's ratios rather than constant Poisson's ratios which are usually used in the existing references to obtain the effective Young's modulus.Finally,the effects of the volume fraction on the radial displacement,the stresses and the perturbation of the magnetic field vector are studied.This work studies the problem of a transversely isotropic functionally graded thick-walled tube subjected to internal pressure.We assume that the tube consists of two isotropic linear elastic materials and a matrix material reinforced by circular cross-section material all aligning the circumferential direction,and that the volume fraction for the reinforced material is identical with the one from the previous work.By using the Mori-Tanaka method,this work obtains the differential equation of the radial displacement and obtains the numerical results of the radical displacement and the stresses.An approximate analytical solution can be obtained that agrees well with the numerical results of the Mori-Tanaka method.Finally,we compared the present model with the result of the-particle distribution model based on the Mori-Tanaka method addressing the problem of an isotropic FGM tube.Furthermore,the effects of the volume fraction as well as the ratio of two Young's moduli on the radial displacement and the stresses are studied.