Green’s Function Of Layered Structure And Three-Dimensional Contact

Various layered structures,including composite materials and coatings,manufactured by new processes such as lay-up combinations,3D printing,chemical or physical vapor deposition,etc.,are widely used in engineering fields such as machinery,materials,medical,electronics,and aerospace.Transverse isotropic multilayer structure is a multiphase structure composed of different material types,material thicknesses and material arrangement sequences,and there are a large number of interfaces.In the service state,the working load will induce a complex distribution of high gradients and discontinuous coupling fields within it.For the calculation of the coupling field,commercial software has insurmountable difficulties.The approximate analysis method often used in engineering is to equate the multilayer structure as a uniform single-phase continuum for calculation analysis and design.But,the fine design of multilayer structure urgently needs an efficient and stable computing platform that can perform fine calculation of the coupling field,especially the fine calculation of the interface coupling field,which is the main factor causing the failure of the multilayer structure,is particularly important and difficult.Based on this engineering background,this dissertation is based on the multi-phase,multi-layer,multi-field fine mechanical model of the multi-layer structure,using the general solution and the new mirror method,and firstly obtains a series of 2D and 3D Green’s function solutions of multi-layer structures under the action of various concentrated loads.Then,based on the obtained Green’s function,the superposition principle is used to obtain the fine solution of the internal coupling field of the multi-layer structure common in various engineering under the action of arbitrary loads.It has also developed a user-friendly multilayer structure dedicated fine calculation platform,which is used to solve the problems of structural design,process improvement,strength evaluation and efficient use that are closely related to the analysis of the interface coupling field of the multi-layer structure in the engineering field.The research results mainly include the following three aspects:For the piezoelectric coupling problem,the Green’s function of the twodimensional orthotropic piezoelectric plate and the three-dimensional transversely isotropic piezoelectric plate under the action of two different force or electrical concentrated loads are deduced.Using the superposition principle,the analytical expression under the action of any distributed force or electrical loads are obtained.On this basis,the general distribution law of piezoelectric coupling field under different force or electric distributed loads are explored.The results show that the electric field distribution of piezoelectric plate under mechanical load is more complicated than that under electric load;The elastic field distribution under load is more complex than that under force load.For the transversely isotropic multi-layer structure,according to the new mirror image theory,a series of harmonic functions of three-layer variablethickness layered structure are constructed under the action of two concentrated force loads in the normal and tangential directions.Starting from the general solution of transversely isotropic material,the Green’s function of layered structure under concentrated load and its exact solution under arbitrary distributed loads are obtained.The solution overcomes the problems of the difficulty of meshing thin layers in multi-coating structures and the low efficiency of 3D full-field fine calculation in large-scale multi-layer structures.In the numerical analysis section,the effects of parameters such as interlayer thickness,material anisotropy and elastic constant etc.on the stress and displacement distribution in multilayer structures are discussed.The results show that the coating thickness and the elastic constant c11,c44 of the coating material have the most significant influence on the interface stress,and the thinner the bonding layer,the greater the stress peak at the interface and the greater the stress gradient in the horizontal direction.Comprehensive consideration of different parameters to optimize the interface stress distribution and improve the mechanical properties of layered structures.For the contact problem,the 3D contact of a rigid spherical indenter acting on a variable-thickness double-coating structure is analyzed in this paper.Based on the new mirror image theory,the contact harmonic functions are constructed,and the analytic general solution for full-field stress and displacement expressed by elementary functions are obtained.The relationship between load,contact radius and coating thickness(absolute thickness,specific thickness),and the influence of external load,contact type,coating material and coating thickness on the 3D full-field displacement and stress of the coating structure are studied.At the same time,the concept of interface equivalent stress was proposed to characterize the interface bonding strength.the stress distribution on the interface is optimized by combining different parameters to reduce the interface equivalent stress.In addition,in view of the mismatch between the coating and the substrate,a feasible intermediate layer design method is proposed,which provides a very useful theoretical and experimental guidance for the selection of coating materials and the determination of coating thickness ratio.