Optimum First Failure Loads of One- and Two-Core Doubly Curved Sandwich Shells

Abstract

For fixed values of the areal mass density, product of the midsurface curvilinear lengths, and the choice from three unidirectional fiber (glass, graphite, or aramid) reinforced composites for facesheets, one- and two-core doubly curved sandwich shell’s geometries, fiber material, and fiber orientations for the facesheets are found that maximize the first failure load. Also determined are the locations of failure points and stress components significantly contributing to the failure, as well as the effects of uncertainties in values of material parameters on the failure load. The shell’s quasi-static and infinitesimal deformations are analyzed with a third-order shear and normal deformable plate/shell theory, in-plane stresses are found by using the plate theory deformations and transverse stresses using a one-step stress recovery scheme. The Tsai–Wu failure criteria, and honeybees inspired nest-site selection optimization algorithm are employed. Effects of uncertainties in material parameters are quantified by the Latin hypercube method and a statistical software, JMP. The predicted failure load and the failure point location agree well with their experimental values. It is observed that the first failure occurs in a core (facesheet) due to the transverse shear stress (in-plane transverse axial stress) exceeding its critical value. The methodology can be used to design the minimum weight optimal doubly curved multicore sandwich shells.