Transient response of a hygrothermoelastic cylinder based on fractional diffusion wave theory

A coupled fractional hygrothermoelasticity theory is formulated within the framework of fractional calculus. Both the classical Fourier’s and Fick’s laws are generalized to anomalous diffusion which is characterized by the time- fractional diffusion-wave equation. Based on the fractional hygrothermoelasticity theory, the transient response of an infinitely long cylinder subjected to hygrothermal loadings at the surface is analyzed. The finite Hankel integral transform method and decoupled technique are used to derive closed-form expressions for temperature, moisture, displacement, and hygrothermal stresses in the solid. The coupling effect of temperature and moisture on elastic fields is discussed. Numerical results of transient response of hygrothermoelastic fields are presented graphically for the cases of subdiffusion, normal diffusion, and superdiffusion, respectively.     

Application of meshless local integral equations for two-dimensional transient coupled hygrothermoelasticity analysis: Moisture and thermoelastic wave propagations under shock loading

This work develops the application of meshless local integral equations based on the meshless local Petrov–Galerkin (MLPG) method for two-dimensional (2D) coupled hygrothermoelasticity analysis. A unit Heaviside step function is used as the test function in the local weak forms. The analyzed domain is divided into some small subdomains with a circular shape. The radial basis functions are used for approximation of the spatial variation of field variables. For discretization of time variations, the Laplace transform technique is used. The moisture concentration diffuses through 2D domain with a finite speed similar to thermoelastic waves. The propagation of moisture diffusion, temperature, and elastic waves is obtained and discussed at various time instants. The MLPG method has a high capability to track the moisture diffusion, elastic and thermal wave fronts at every arbitrary time instant in 2D domain. The distribution profiles of moisture concentration, temperature, and displacements along two orthogonal directions are illustrated at various time instants.     

Hygrothermoelastic response in the bending analysis of elliptic plate due to hygrothermal loading

Abstract

This study investigates the theoretical outline to couple both classical Fourier’s and Fick’s laws to frame a new model of two-temperature hygrothermoelastic diffusion theory for a non-simple rigid material. Based on hygrothermoelasticity method, a system of linearly coupled partial differential equations for the thermal and moisture diffusion for the case of a non-simple medium is established. The transient response using the decoupled technique of a multilayered elliptic plate perpendicular to the axial axis, subjected to hygrothermal loading is considered, to derive closed-form expressions for temperature, moisture, deflection, bending moments, and hygrothermal stresses. The solutions to the governing coupled equations and its boundary conditions are solved by employing a new integral transform technique. The small deflection equation is found and utilized to preserve the intensities of bending moments and stresses, involving the Mathieu functions and its derivatives. Moreover, the elliptical region can be degenerated into a circular part by applying limitations. Numerical results of the transient response of hygrothermoelastic fields are established graphically for the better understanding the underlying elliptic structure, improved understanding of its relationship to circular profile, and better estimates of the effect of the associated hygrothermoelastic responses.