Lightweight design of variable-angle filament-wound cylinders combining Kriging-based metamodels with particle swarm optimization

Abstract

Variable-angle filament-wound (VAFW) cylinders are herein optimized for minimum mass under manufacturing constraints, and for various design loads. A design parameterization based on a second-order polynomial variation of the tow winding angle along the axial direction of the cylinders is utilized to explore the nonlinear steering-thickness dependency in VAFW structures, whereby the thickness becomes a function of the filament steering angle. Particle swarm optimization coupled with three Kriging-based metamodels is used to find the optimum designs. A single-curvature Bogner–Fox–Schmit–Castro finite element is formulated to accurately and efficiently represent the variable stiffness properties of the shells, and verifications are performed using a general purpose plate element. Alongside the main optimization studies, a vast analysis of the design space is performed using the metamodels, showing a gap in the design space for the buckling strength that is confirmed by genetic algorithm optimizations. Extreme lightweight while buckling-resistant designs are reached, along with non-conventional optimum layouts thanks to the high degree of thickness build-up tailoring.

Lightweight Design of Variable-Stiffness Cylinders with Reduced Imperfection Sensitivity Enabled by Continuous Tow Shearing and Machine Learning

“…The integration of K e K e K e and K G0 e K G0 e K G0 e over the finite element domains are performed numerically using standard Gauss-quadrature with 4 × 4 integration points per element. The authors verified that this amount of integration points leads to a converged behavior even for variable-stiffness filament-wound cylinders [40]. For each integration point, the local shell constitutive properties are calculated using the smeared approach proposed by Castro et al [36] based on a constant-volume constraint, verified against a discreet thickness modeling by Vertonghen and Castro [37].…”

“…In order to calculate the linear buckling load of the proposed variable-stiffness design, the single-curvature Bogner-Fox-Schmit-Castro (SC-BFSC) finite element is selected. First presented by Wang et al [40], the SC-BFSC element is based on the plate version presented by Castro and Jansen [24], which is a C1-contiguous and confirming element obtained by taking tensor products of cubic Hermite splines [41]. With 4 nodes per element and 10 degrees of freedom per node, the BFSC approximates the in-plane and out-of-plane displacements using third-order polynomials, leading to a fast convergence for cases with variable stiffness.…”

“…while providing estimates for the post-buckling stiffness b I , the mass, and the buckling load P critical . There are several boxplot diagrams presented in Figures 5-16, whose data are calculated following Equation (40). The results summarized in Tables 1-9 are also obtained by using Equation (40).…”

“…There are several boxplot diagrams presented in Figures 5-16, whose data are calculated following Equation (40). The results summarized in Tables 1-9 are also obtained by using Equation (40). As the sample points are randomly chosen in the design space, from the project perspective, it is important to identify the points along the frontier that offer a positive post-buckling stiffness, herein represented by the criteria b I > 0.…”

“…The minimum error, the median error, and the maximum error in the estimation of the b I , as evaluated by Equation (40), are shown in Table 7. The error dispersion of all Random Forest methods are compared in Figure 11.…”