Two-Dimensional General Solutions And Fundamental Solutions For Orthotropic Thermoelastic Materials, Piezothermoelastic Materials And Electro-magneto-thermo-elastic Materials With Applications

Fundamental solutions or Green's functions play an important role in both applied and theoretical studies on the physics of solids. They are foundations of a lot of further works. For example, fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in numerical method such as boundary element method as well as the study of cracks, inclusions and contacts.Orthotropic thermoelastic materials, orthotropic piezothermoelastic materials and orthotropic Electro-magneto-thermo-elastic materials are widely utilized in the area of composite, smart structures and electric device etc. Most literatures available on the fundamental solutions of above materials are on case of identical temperature, i.e. the thermal effects are not considered. Because the temperature variations are existed in much engineering, the study considering thermal effects is very necessary.Under above engineering background, the two-dimensional fundamental solutions for orthotropic thermoelastic materials, othotropic piezoelectric materials and orthotropic magnetoelectroealstic materials are studied in this paper for point force, point charge, point current and steady point heat source acted in an infinite or a semi-infinite plane. For this object, 2D general solution for the plane problem of three materials are derived in terms of harmonic functions using strict differential operator theory. Based on the obtained general solution, the 2D fundamental solution are obtained by virtue of the trial-and-error method. All components of coupled field are expressed in terms of elementary functions.As an application, boundary integral equations for orthotropic thermoelastic materials are constructed by virtue of the fundamental solutions and the numerical discretization for boundary is carried. According of known boundary condition a engineering example is evaluated using BEM and Matlab. FEM result is used as a benchmark to check the result of BEM.