The 2D general solution for the plane problem of thermoelastic materials is derived in terms of three harmonic functions using strict differential operator theory for the case of distinct eigenvalues. Based on the obtained general solution, the 2D fundamental solution for a steady line heat source in an infinite and a semi-infinite thermoelastic plane is obtained by three newly introduced harmonic functions. All components of coupled fields are expressed in terms of elementary functions and they are convenient to be used.

2D general solution and fundamental solution for orthotropic thermoelastic materials

Static general solutions, fundamental solutions, piezoelectric effect, 1D hexagonal quasicrystal,inﬁnite/half-inﬁnite spaces.This paper is concerned with the fundamental solutions, in the framework of thermo-electro-elasticity, for an inﬁnite/half-inﬁnite space of 1D hexagonal quasicrystals (QCs). To this end, three-dimensional static general solutions, in terms of 5quasi-harmonic functions, are derived with the help of rigorous operator theory and generalized Almansi’s theorem. Foran inﬁnite/half-inﬁnite space subjected to an external thermal load, corresponding problem is formulated by boundaryvalue problems. Appropriate potential functions are set by a trail-and-error technique. Green functions for the problemsin question are obtained explicitly in the closed forms. The present fundamental solutions can be employed to construct3D analysis for crack, indentation and dislocation problems. Furthermore, these solutions also serve as benchmarks forvarious numerical simulations.

Fundamental thermo-electro-elastic solutions for 1D hexagonal QC

Three-dimensional Green’s functions for transversely isotropic thermoelastic bimaterials

This paper presents a set of axisymmetric analytical solutions of the thermo-elasticity field induced by the external thermal load, in a heterogeneous circular plate. The plate can be either simply supported or clamped, and the properties of the transversely isotropic material are assumed to be functions of the thickness coordinate. Three typical types of thermal boundary conditions are considered and the corresponding temperature fields are determined. A direct displacement method is used to solve the governing equations for the elastic field in plate. The displacement functions pertinent to the current problem are solved by a step-by-step procedure of integration. The corresponding integral constants are determined by using the cylindrical boundary conditions in the Saint-Venant’s sense. In the present solutions, all of the material coefficients can vary independently and continuously along the thickness direction. Numerical calculations are performed to validate the present solutions and to show their ...

Axisymmetric thermo-elasticity field in a functionally graded circular plate of transversely isotropic material

The aim of the present paper is to study the Green's function in orthotropic thermoelastic diffusion media. With this objective, firstly the two-dimensional general solution in orthotropic thermoelastic diffusion media is derived. On the basis of general solution, the Green's function for a steady point heat source in the interior of semi-infinite orthotropic thermoelastic diffusion material is constructed by four newly introduced harmonic functions. The components of displacement, stress, temperature distribution and mass concentration are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced, to depict the effect of diffusion on components of stress and temperature distribution.

Green's functions in orthotropic thermoelastic diffusion media

Fundamental solution for transversely isotropic thermoelastic materials

We use the compact mono-harmonic general solutions of transversely isotropic thermoelastic materials to construct the three-dimensional Green's function of a steady point heat source in a semi-infinite transversely isotropic thermoelastic material by three newly introduced mono-harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for hexagonal zinc are given graphically by contours.

Green's functions for semi‐infinite transversely isotropic thermoelastic materials

Fundamental solutions play an important role in electroelastic analyses and numerical methods of piezoelectric material. However, most works available on this topic are on the case of identical temperature. We use the compact mono-harmonic general solutions of transversely isotropic piezothermoelastic material to construct the three-dimensional fundamental solution of a steady point heat source in an infinite piezothermoelastic material by four newly introduced mono-harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for cadmium selenide are given graphically by contours.

Three-dimensional fundamental solution for transversely isotropic piezothermoelastic material

Employing Reddy’s third-order shear deformation theory (RTSDT) and nonlocal elasticity theory, a nonlinear bending model of the nonlocal three-layer magneto-electro-elastic (MEE) laminated nanobeam resting on elastic foundation is established by considering von Karman’s geometrically nonlinear equations. Nonlinear higher order partial differential governing equations of MEE laminated nanobeams can be obtained employing Hamilton variational principle. The three-layered MEE laminated nanobeam is considered to have simply supported boundary condition in the present paper. Meanwhile, the electric and magnetic potential distributions in the laminated nanobeam are determined through Maxwell’s magnetic-electro equations and boundary conditions. The governing equations of laminated nanobeams are re-expressed in the dimensionless form by introducing the non-dimensional terms. Employing Galerkin method, the nonlinear higher order partial differential governing equations are simplified into lower order equations. Several cases are explored to indicate the effects of foundation parameters, nonlocal parameter, stacking sequence, external electric voltage and external magnetic potential on bending behaviors of MEE laminated nanobeams. 

Size-dependent nonlinear bending analysis of nonlocal magneto-electro-elastic laminated nanobeams resting on elastic foundation

Based on the first-order shear deformation theory (FSDT) and combined with von Karman’s nonlinear strain–displacement relationship, the nonlinear dynamic model of the rectangular magnetoelectroelastic (MEE) laminated plate is established. Then the nonlinear motion control equations of the structure are derived by using Hamilton principle. Through introducing dimensionless parameters, these equations are processed by converted into the dimensionless form. Given simply supported boundary conditions, the nonlinear higher-order equations in the governing equations are transformed into algebraic expression by the Galerkin method. In the numerical examples, the influences of size factors, temperature variation, stacking sequence and external loads on the deflection of the MEE laminated plate are studied. In addition, the distribution rule of electric and magnetic potential along the thickness direction of the MEE laminated plate with two different stacking sequences is given. 

Chang-Ping Chen

Papers

Fundamental solution for transversely isotropic thermoelastic materials

Green's functions for semi‐infinite transversely isotropic thermoelastic materials

Three-dimensional fundamental solution for transversely isotropic piezothermoelastic material

Size-dependent nonlinear bending analysis of nonlocal magneto-electro-elastic laminated nanobeams resting on elastic foundation

Nonlinear analysis of rectangular magnetoelectroelastic moderately thick laminated plates under multi-field coupling loads