Bending Analysis of Thickness‐ and Shear‐Deformable Materially Imperfect Composite Shells With von Kármán‐Type Geometric Nonlinearities

ABSTRACT Geometrically nonlinear static analysis of materially imperfect composite doubly curved shells is investigated via the generalised differential quadrature method. The effects of both shear and thickness deformation are considered through a thickness‐ and shear‐deformable third‐order theory formulated in curvilinear coordinates, while the influence of large deformations is accounted for using the von Kármán‐type strain–displacement relationships. On the basis of Hamilton's principle, eight nonlinear deformation equations and associated boundary conditions, assumed to be simply supported with movable edges, are derived and discretised. A direct iterative method of the Newton–Raphson type is used to solve the resulting nonlinear algebraic system of equations. In this study, two different types of doubly curved shells are analysed, namely, spherical and elliptical. To describe the continuous variation in material properties, the Voigt bound method is employed, which is further modified to account for material imperfections, such as porosities (voids). Convergence and comparison studies are conducted to validate the accuracy of the proposed numerical model. Numerical results for displacements and stresses are obtained for the two shell geometries, material gradation profiles, porosity distributions, and radii of curvature.