Hygro-thermo-mechanical modelling and analysis of multilayered plates with embedded functionally graded material layers

This work addresses the modelling and analysis of multilayered plates with embedded functionally graded material (FGM) layer(s) under hygro-thermo-mechanical loadings. The hygroscopic, thermal and mechanical problems are all solved simultaneously using a new layerwise mixed model based on least-squares formulation with multi-field independent variables, namely, displacements, temperature, moisture, transverse stresses, transverse heat flux, transverse moisture flux, in-plane strains and in-plane components of both thermal and moisture gradients. This mixed formulation ensures that interlaminar C0 continuity requirements, where the material properties may actually change, are fully fulfilled a priori. An added feature is included to fully describe the FGM layer z-continuous effective properties through-thickness, using any homogenization method, by applying a high-order z-expansion to its effective properties, similarly to finite element approximations. The numerical results demonstrate the effects of hygrothermal environments in the analysis of distinct multilayered plates with embedded FGM layers, considering different side-to-thickness ratios, under a series of hygro-thermo-mechanical loadings. The rule of mixtures is used to estimate the FGM layer effective properties, including different material gradation profiles. Three-dimensional (3D) approximate solutions corroborate this model’s capability to predict accurately a quasi-3D hygro-thermo-mechanical description of the through-thickness distributions of displacements and stresses, temperature and heat flux, moisture and moisture flux.