Wavelet solution for hygrothermomechanical bending of initially defected plate undergoing large deformation on nonlinear elastic foundation

An efficient wavelet approach has been developed for geometrically nonlinear bending analysis of largely deformed plate with arbitrary initial curvature on nonlinear Winkler-Pasternak foundation loaded with sinusoidally hygrothermal stresses. Translational and rotational constraints have been analyzed and equivalently transformed into the Cauchy-type boundary conditions of Airy stress function, which are efficiently approached by interpolating Coiflet-type wavelet. A newly hygrothermomechanical bending model of plate subjected to the adiabatically impermeable edges or with boundaries of sinusoidal temperature and humidity has been firstly formulated. The highly coupled and nonlinear governing equations have been decomposed into linear differential terms by homotopy transformation and successfully solved by the Coiflet-type wavelet Galerkin method. The wavelet strategy has been validated superior in dealing with extremely nonlinear bending and high-precision reconstitution of initial deflection in hygrothermal environment, while the obtained solutions are in excellent agreement with published results. Effect of initial deflection, hygrothermal load and elastic foundation has been investigated, which implies the hygrothermal effect on plate in linear bending is prominent but gradually negligible in large deformation, while the nonlinear effects of elastic foundation become significant by the increase of deflection but not obvious at smally deformed state.

Automated summary

In this study, an efficient wavelet approach is developed for the geometrically nonlinear bending analysis of largely deformed plate with arbitrary initial curvature on a nonlinear Winkler-Pasternak foundation loaded with sinusoidally hygrothermal stresses. The translational and rotational constraints are analyzed and transformed into the Cauchy-type boundary conditions of Airy stress function using interpolating Coiflet-type wavelet. A hygrothermomechanical bending model is formulated and the governing equations are solved using the Coiflet-type wavelet Galerkin method. The wavelet strategy shows superior performance in dealing with extremely nonlinear bending and high-precision reconstitution of initial deflection in hygrothermal environment.