## 1 Introduction  
Laminated composite materials are increasingly preferred in major industries such as aerospace, naval, and construction due to their high strength-to-weight and stiffness-to-weight ratios (reducing fuel consumption), and, more importantly, their ability to be tailored to achieve optimal design through manipulation of the composition of composite materials, stacking ply orientation, etc. Over the years, the mechanical behavior of laminated composites such as glass/epoxy, graphite/epoxy, boron/epoxy, Kevlar-49/epoxy, etc., has been researched by many scientists. However, the anisotropic behavior and bending-stretching coupling of composite materials and the need to satisfy distinct boundary conditions create additional problems for the analysis of those structures. Over the years, several well-known shell theories with many assumptions have been established in order to investigate the static behavior of plate and shell structures, such as those provided by [PERSON] [1], [PERSON] [2], [PERSON] [3], [PERSON] [4], and [PERSON] [5]. A literature review including refined theories of laminated composite plates and shells is given in [6; 7; 8; 9; 10; 11]. Many approximate numerical techniques and analytical methods have been employed in the literature to analyze the static behavior of composite shells. The Levy method has been the most popular analytical method for the analysis of two edges fixed by simply supported laminated plates and shells, and it is able to analyze cross-ply and antisymmetric angle-ply laminates. Such solutions are based on the well-known method of separation of variables. A view of the comprehensive study on the boundary value problems of laminated plates and shells using analytical methods can be found in the following studies. [PERSON] [12] constructed three-dimensional elasticity solutions for cross-ply rectangular plates for simply supported boundary conditions. [PERSON] and [PERSON] (1970) presented an elasticity solution for the static and dynamic analysis of cross-ply composite plates with Navier-type boundary conditions. [PERSON] and [PERSON] [13] introduced a similar procedure, using an elasticity solution on doubly curved cross-ply shells with simply supported boundary conditions. In a recent overview, various three dimensional (3D) analytical approaches have been introduced for resolving multilayered panels with arbitrary boundary conditions. [PERSON] and [PERSON] [14] improved an analytical three-dimensional elasticity solution based on a multi-term EKM along with a mixed formulation for the static bending of single- and multi-layer composite thick, moderately thick, and thin cylindrical shell panels. The proposed technique can yield accurate results with better computational efficiency using just one or two terms and two or three iteration steps in comparison to 3D FE for arbitrary boundary conditions (SS, CS, CF). [PERSON] et al. [15] presented exact 3-D Levy-type solutions for the static analysis of thick composite plates based on 3-D elasticity and various shear deformation theories with different types of classical boundary conditions, namely simply supported, clamped, and free edge. [PERSON] and [PERSON] [16] analyzed the bending of rectangular laminated plates with arbitrary lamination and various combinations of simply supported, clamped, and free-type boundary conditions by employing the Extended Kantorovich method. Analytical solutions may fail to carry out complex analyses such as those of surface-parallel orthotropy/anisotropy, lamination asymmetry, and curvature effect (leading to bending, stretching, and coupling), which usually involve the use of laminated composite shell equations. Therefore, a different methodology should be proposed to enable effective solutions. Methodologies integrating the Fourier series have great potential to solve the problems encountered in conventional analytical solutions. The following studies include these Fourier series-based methodologies.