Structural analysis of transversally loaded quasi-isotropic rectilinear orthotropic composite circular plates with Galerkin method

Bending analysis of rectilinear orthotropic composite plates have been scarcely investigated taking into account the increasing use of composite materials in structural applications in the last years. This kind of plates are laminates with axisymmetric geometry and they are made up of unidirectionally reinforced layers with different orientations. Transversally loading this kind of circular plates, the deflected mid-surface is not independent from the circumferential coordinate, unlike the case of isotropic circular plate. Nevertheless, the quasi-isotropic stacking sequence makes still possible to introduce the hypothesis of axisymmetry for the mid-surface deflection under transversal load, disregarding the circumferential variation of the vertical displacement connected to the variable bending stiffness. Then, the constitutive equations for this specific family of plates were obtained finding the stress resultants-strains relations in the global cylindrical coordinate system. These expressions, along with the equilibrium equations, made it possible to derive the governing equation of the problem in the frame of Kirchhoff-Love hypothesis of the classical lamination theory. The Galerkin method was applied to solve the governing third order differential equation in terms of mid-surface deflection, introducing appropriate polynomial approximation functions compliant with the boundary conditions. In particular, fully clamped constraint conditions were considered for the outer diameter of the plate in conjunction with an internal rigid core. The characterization of this model allows to define the stiffness matrix terms of a custom composite bolted joint finite element, that is the object of future developments of this work. Results of the original proposed method are presented and compared to those obtained by means of FEA performed with a refined reference model, demonstrating a good agreement.