# 3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions
## 1 Introduction  
The environmental conditions characterizing the service life of structural components can be adverse in many applications. The aerospace field gives several examples of changing environments, which results in temperature gradients and moisture concentration variability. It is crucial to consider such two factors and to include them in a proper structural analysis: the thermal and hygrometric fields induce an internal stress distribution, which changes as soon as the environmental conditions change. As with any stress field, it might induce failures on the structure [1], either on its own or because it sums up to that caused by classical mechanical loads. Composite, multilayered, and FGM-embedding structures require a special focus. Composite materials can also be degraded by moisture absorption and the following diffusion through the matrix [2]; multilayered structures highlight a strong heterogeneity in the hygro/thermal/mechanical properties; FGMs induce a further complication due to non-constant terms in governing equations. However, their boosted implementation in critical structural applications recently increased the attention of the researchers on these effects. Laminated structures and composite materials suffer from a clear variation of the properties at the interfaces, which is the critical source of the delamination process [3]. Eliminating this discontinuity and substituting it with a smooth trend is the key achievement of Functionally Graded Materials (FGMs). They are advanced composite materials made by two or more different phases mixed with a continuous graded distribution. As a result, they are heterogeneous materials, delivering optimized responses for each application: theadvancements in processing technologies made it possible to control a unidirectional and even multidirectional variation. Combinations of a metallic and a ceramic phase are classic examples of FGMs finding application in severe thermal environments: they overcome the differences in thermal properties of the two constituents and, at the same time, deliver a reduced thermal stress distribution. Stiffness coefficients, hardness, thermal conductivity, moisture diffusivity, and corrosion resistance are just some examples of the performance characteristics that can be combined and enhanced [4]. Several recent and relevant works focused on structures embedding FG layers underline their importance in practical applications. From an analytical perspective, [PERSON] et al. recently proposed several analytical results in the frame of the vibration analysis of FG shells. First, the governing equations followed the First-order Shear Deformation Theory (FSDT); then, they used the Generalized Differential Quadrature Method (GDQM), a semi-analytical solution method, to solve the system of partial differential equations. They studied conical shells embedding hybrid matrix/fiber nanocomposites in [5]; the approach was then extended to paraboloidal and hyperboloidal shells embedding polymer matrix, carbon fiber, and graphene nanoplatelets in [6]. Using the same approach, they studied sandwich conical-cylindrical-conical shells [7]. The layers are reinforced with functionally graded carbon nanotubes and graphene nanoplatelets; they described the elastic coefficients following an Equivalent Single Layer approach. They also studied five different patterns of CNT fibers distribution inside of the matrix while defining the vibrational behavior of coupled conical-conical shells [8]. They used the five-parameter shell theory and solved the differential equations through GDQM. Three-phase nanocomposites were also studied in hemispherical-cylindrical shells exploiting a similar approach [9] and defining the governing equations through the first-order shear deformation theory. From a numerical perspective, [PERSON] et al.