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.

A review of toroidal composite pressure vessel optimisation and damage tolerant design for high pressure gaseous fuel storage

“…A torus is an axisymmetric shell of revolution created by rotating an arbitrary two-dimensional shape through 360° around a central axis to form a ring-shaped structure where the cross-sectional shape does not intersect the axis of revolution [31]. The torus has emerged as a promising gaseous fuel tank design due to its space-saving and weight-reducing potential, its lack of structurally inefficient domed heads and the potentially improved protection of the pressure regulator [8]. It is particularly attractive for spaces with limited height and length, for example the spare tire cavities in passenger vehicles, referring to Figure 1b.…”

“…The naming and identification of toroidal pressure vessel parameters have varied significantly in the literature [8,. These terms are listed in Table 1 along with the appropriate naming and identification conventions adopted in this article.…”

“…R 0 [37] Major radius [8,37] Shell crown radius [42] Meridian radius [44] Bend/bending radius [35,36,38,39] Toroidal radius [45] Ring radius [46,47] r [mm] Cross-sectional radius a [8,31,32,41,42,48,49] x, y [44] r 0 [37] R 1 , R 2 [45] r 1 [50] R [43] Minor radius [37] Shell meridian radius [42] Toroid internal radius [42] Tube radius [35,36,38] Toroid tube radius [33,51,52] Toroidal shell radius [32] Meridian circle radius [48,49]…”

“…Relative bending radius [35][36][37] Aspect ratio [50] a [43,50] λ [33] ϕ [°] Hoop angle ss [41] u [37] θ [39] x 1 [46,47] Material coordinate [42] Parallel angular coordinate [36] Meridional angle [8,31,[35][36][37][38][39][40]50] Meridional coordinate [33,46,47,52] Co-latitude [51] Tangential angle [48,49]…”

“…Pressure vessels consisting of cylindrical bodies and domed heads are the traditional option for on-board gaseous fuel storage. However, they can be volumetrically inefficient and possess domed heads that are prone to over-design and a source of manufacturing difficulties [8,9]. Cylindrical pressure vessels can also suffer from stress concentrations in high curvature regions when their cross-sections deviate from traditional circular profiles [10].…”