On The Mechanical Analysis Of Receding Contact Between Two Functionally Graded Plates

The receding contact phenomenon,in which the contact region shrinks when two bodies are pressed against each other,often occurs in the hidden part of the contact interface and generates greater contact stress compared with the advancing contact and stationary contact,which seriously threatens the safety and reliability of engineering structures.It has conformed that functionally graded materials play an important role in regulating and optimizing in receding contact mechanics.However,the existing research work on receding contact mechanics mostly focuses on the mechanical performance analysis of receding contact between homogeneous plates as well as homogeneous platefunctionally graded plate structure,but rarely involves the problem of receding contact between two functionally graded plates.In view of this,this thesis concentrates on the receding contact problem between two functionally graded plates by using semi-analytical method and finite element method.The dependency relationship between the parameters,such as nonhomogeneous of plates,coefficient of friction,nature of the foundation,load,etc,with the receding contact stress and receding contact length was systematically studied.The main research content of this thesis is divided into the following aspects.Firstly,the frictionless receding contact problem between two functionally graded plates on a rigid foundation is studied by semi-analytical method and finite element simulation.Assuming that the shear modulus of the functionally graded plate follows an exponential distribution along the thickness direction and the Poisson’s ratio is constant,the implicit expression of the displacements and stresses in the functionally graded plate is derived using the basic theory of elastic mechanics and the Fourier integral transformation method.Then,the boundary conditions and supplementary conditions are transformed into the first type of Cauchy type singular integral equations,which will transform to nonlinear algebraic equations about receding contact stress and length obtained by using the Gauss-Chebyshev numerical quadrature formula.After that,an iterative algorithm is developed to solve the nonlinear algebrac equations,the correctness of which is confirmed in the analysis of parameters such as nonhomogeneous coefficient,half length of load,thickness ratio and interface shear modulus ratio,compared with the finite element solution obtained by the uniform layer method.Secondly,further study on the receding contact problem involving friction between the two functionally graded plates on the rigid foundation is carried out.In this case,the boundary conditions and supplementary conditions are transformed into the second type of Cauchy type singular integral equations due to the existence of friction,which is more complex.Correspondingly,the Gauss-Jacobi numerical quadrature formula is used to get the nonlinear algebrac equations,and we independently developed an iterative algorithm to solve the equations based on the dichotomy and secant method.The reliability of the algorithm was verified by comparing with the finite element numerical simulation solution in analyzing the influence of the friction coefficient and nonhomogeneous coefficient on the receding contact stress and contact length.Finally,considering that the foundations in engineering practice are not always ideally rigid,the problem of frictional receding contact between two functionally graded plates on Winkler foundation is further solved.The research methods and numerical calculation methods used are similar to the frictional receding contact problem between two functionally graded plates on a rigid foundation.In the process of analyzing the influence of the foundation coefficient of the Winkler foundation and nonhomogeneous coefficient on receding contact stress and contact length in the frictionless receding contact problem and frictional receding contact problem on the Winkler foundation.Particularly,the reliability of the algorithm considering the Winkler foundation is confirmed by comparing to the semi-analytical results in the frictional receding contact problem on a rigid foundation.Based on the calculation results and parameter analysis,it can conclude when the stiffness of the plate monotonously increases from bottom to top,the thickness of the lower layer is greater than the upper layer or the foundation with lower rigidity is selected for support in the design of the structure involving two functionally graded plates,lower peak contact stress will arise which will lead the structure to be safer.In this thesis,the problem of frictionless and frictional receding contact between two functionally graded plates on a rigid foundation and Winkler foundation under surface load is solved for the first time,and a numerical algorithm for solving the first and second Cauchy type singular integral equations is independently developed.It has greatly enriched the research achievements in the field of the receding contact mechanics of functionally graded materials,and has certain theoretical guidance value for the optimal design of multilayer functionally graded plate structures.