Thermoelectroelastic response of a piezoelectric cylinder with D_∞ symmetry under axisymmetric mechanical and thermal loading

Abstract

Carbon-neutral and biodegradable materials such as wood and poly-L-lactic acid play an important role in reducing environmental loads. Therefore, this study theoretically analyzed the thermoelectroelastic problem for a solid cylinder with D_∞ symmetry subjected to a distributed torsional shear stress as a mechanical input and to a nonuniform temperature distribution as a thermal disturbance, in order to gain an elementary understanding of the thermal effects on the electroelastic field in cylindrical bodies with D_∞ symmetry. The displacement components are expressed in terms of the elastic displacement potential function, the piezoelastic displacement potential function, and the thermoelastic displacement potential functions, and the electric field components are expressed in terms of the electric potential function. Subsequent to presenting the fundamental equations for thermoelectroelasticity, the governing equations for the above potential functions are derived based on the above fundamental equations. These governing equations are solved by a Fourier transform technique, and the theoretical solutions of the thermoelectroelastic field quantities are obtained. Furthermore, by performing numerical calculations, the distributions of the field quantities are illustrated graphically, and the structures of the thermoelectroelastic field are discussed qualitatively and quantitatively. Moreover, by quantitatively evaluating the ratio of the thermally disturbed electric displacement to the undisturbed electric displacement reflecting the mechanical input, the necessity of the thermoelectroelastic analyses, as treated in this paper, is clearly demonstrated.