Equivalent continuum method for anisogrid composite lattice conical shells with equiangular, equidistant and geodesic spiral ribs

Abstract

This paper is concerned with filament winding trajectories of helical ribs of anisogrid composite lattice conical shells. Filament winding can be designed to coincide with equiangular, equidistant and geodesic spiral trajectories. The unified geometrical formulas of the three types of conical spiral and circumferential curves are established. As a consequence, three types of lattice conical shells are built and the corresponding geometric parameters of lattice conical shells are obtained. Additionally, the smearing method, adopting straight-line and curved-line assumptions for helical ribs, respectively, is applied to calculate the elastic properties and the global stiffness properties along with the classical membrane theory. The finite element analysis verifies the analytical results and also shows a closer correspondence with numerical results for the curved-line assumption than the straight-line assumption. Further, the global stiffness properties of three types of lattice conical shells are compared using the single variable method. The results indicate that the flexural stiffness and the torsional stiffness of the lattice conical shell with equiangular helical ribs are the maximum and the axial stiffness of the shell with geodesic helical ribs is the maximum among them, while the values of all stiffness properties of the shell with equidistant helical ribs are the minimum among them.