Analytical Calculation Method Of Multi-field Coupling For Layered Structures With Application Based On Green’s Function

Layered structures such as functional coatings and piezoelectric films are becoming more and more common in new engineering equipments,such as new intelligent structures and high performance aircraft engines.These structures will be inevitably subjected to multi-field coupling loads such as force-heat-electricity-liqiuid loads.Due to the complexity of coupling load,the very thin thickness of each layer,and the difference of material parameters between layers,the internal stress field of each layer and the interlayer interface stress field are in a very complex high-gradient or even discontinuous stress state.The existing commercial computing platforms are difficult to accurately calculate such stress field.In order to solve the above technical difficulties,the doctoral thesis studies the efficient and fine calculation method of the coupling field for multilayer structures composed of anisotropic materials.From the perspective of three dimensions,the Green’s function solution of the coupling field of multilayer structures are obtained.Based on the obtained Green’s functions,the coupling fields of layered structures under various loads are obtained by combining the analytical solution and numerical calculation methods.The influences of various physical parameters on the coupling fields of layered structures such as thermoelectric fluid and interface response characteristics are studied comprehensively,which provides a theoretical basis for engineering design.The main work includes the following aspects:(1)Based on the general solution of transversely isotropic materials,the simple harmonic functions with undetermined constants are constructed by using the mirror image method and the trial-and-error method.The undetermined constants are obtained by considering the boundary conditions,interface conditions and the force-thermal-liquid equilibrium conditions.The Green’s function solutions of the mechano-thermal,force-thermal-electric and force-liquid elastic fields of layered structures are obtained.(2)Based on the Green’s function of layered structure under different loads,the 3D full-field exact solutions under arbitrary distributed load are derived using the numerical integration method.Based on the obtained theoretical solution,the response characteristics of the 3D coupled field are analyzed in detail,and it is verified that the calculation method has good computational accuracy,computional efficiency and computational stability.(3)Detailed numerical tests are designed to systematically study the effects of thermal parameters,piezoelectric parameters,elastic modulus and coating thickness on the stress field of coating structure.The complex interfacial effects of coating and substrate are revealed,and the regions where tensile delamination occurs and the tensile failure behavior of interface are analyzed,which provides a basis for the fine design of layered structures such as thermal resistance coatings and piezoelectric coatings.(4)Based on the above research results,the Green function method is further extended to solve the three-dimensional coupling field problem of the transversely isotropic porous elastic layered structure under the liquid source,which reveals the mechanical behavior of the layered structure in porous media.In summary,this dissertation mainly carries out the research on the calculation method and performance analysis of layered structures,and puts forward the exact calculation method of Green’s function for the force-thermal-electric-hydraulic coupling field of layered structures.A series of Green’s function solutions for layered structures are proposed.Based on Green’s functions,the fine calculation and parameter influence analysis of three-dimensional coupling field of layered structures are carried out.The results of this work will enrich and develop the coupled field mechanics calculation methods of layered structures.Through the Green’s functions,the influence of geometric structure and physical parameters on the response characteristics of the coupling field and interfacial stress field can be studied comprehensively and systematically.The obtained results can provide theoretical guidance for all kinds of layer structure in the engineering detailed design and a variety of valuable engineering conclusion.