Finite Element Study on the Optimization of an Orthotropic Composite Toroidal Shell

Abstract

In this research, an analysis technique is developed to model orthotropic composite toroids and optimize the fiber layup, accounting for the natural variation in thickness due to fiber stacking. The behavior of toroids is difficult to model using membrane shell theories due to a singularity in the strain-displacement relations occurring at the toroid crest that yields discontinuous displacement results. A technique is developed here where the constitutive properties of multilayered toroidal shells are determined using lamination theory, and the toroid strains and line loads are determined using finite element analysis. The toroid strains are rotated into the fiber directions, allowing the fiber stress and transverse stress distributions to be determined for each layer. The fiber layup is modified heuristically until an optimum is found. An optimum is reached when the maximum fiber and transverse direction stresses of each shell layer are equal, minimizing wasted fibers and excess weight. Test cases are analyzed to verify the accuracy of the finite element model and an example composite toroid with Kevlar/epoxy material properties is optimized. The analysis technique developed here can decrease the time and cost associated with the development of orthotropic toroidal pressure vessels, resulting in lighter, cheaper, and more optimal structures. The models developed can be expanded to include a steel liner and a broader range of fiber winding patterns.