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

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.