Hygrothermoelastic analysis of the nano-circular plate with memory effect

In hygrothermal environments, the coupling effects of temperature and moisture substantially impact deflection and stresses play a significant role. This study presents a coupled hygrothermoelastic model with non-Fourier and non-Fick effects established by introducing relaxation times or phase lags of heat and moisture flux accompanied by memory-dependent derivatives. The boundary value problem is formulated by considering a thin circular plate as an exemplary example, where the perimetric edge is clamped. The upper and lower edges of the plate is subjected to zero temperature, whereas the curved surface is exposed to hygrothermal shock. The closed-form solution of temperature and moisture distribution is obtained via the integral transform approach. The Fourier series expansion approach is used to calculate the numerical Laplace inversion. The effects of both heat and moisture flux relaxation times on the thermal deflection/stresses of the plate are analyzed and illustrated graphically.