Non-linear hygrothermal analysis of imperfect multilayer functionally graded shallow shell with a porous core

This research investigates the non-linear static and dynamic hygrothermal behaviors of imperfect multilayer functionally graded (MFG) shallow shells, which consist of a functionally graded porous core (FGPC). The non-linear model of the shells is established based on the stress function and first-order shear deformation theory (FSDT). The MFG shallow shell consists of five layers, including ceramic, FGM, FG porous, FGM, and ceramic. Also, the FGPC with four types of porosity distributions is considered. According to the FSDT, Hooke's law, and von-Karman equation, the stress-strain relations are developed for the shells. Galerkin method is utilized for discretizing the non-linear governing equations. To obtain the dynamic responses, the fourth-order P-T method is utilized. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named P-T method. The hyperbolic paraboloid shell as a specific case of the shallow shells is studied, and the influences of various material and geometrical parameters on the non-linear dynamic hygrothermal buckling (NDHTB), non-linear static hygrothermal buckling (NSHTB), and non-linear hygrothermal vibration (NHTV) are also studied on the basis of the model established. The verification of the model and the results generated are presented. Moreover, to further validate the NDHTB and NHTV, comparisons are made with the fourth-order Runge-Kutta method (FRKM).