Pre-trained design optimization of variable stiffness composite cylinders modeled using Bézier curves

Coskun O., Türkmen H. S.

Structural and Multidisciplinary Optimization, vol.66, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s00158-022-03480-x
  • Journal Name: Structural and Multidisciplinary Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Keywords: Variable stiffness shell, Bezier curve, Buckling load, Strength, Optimization
  • Istanbul Technical University Affiliated: Yes


In this paper, a novel framework is proposed to optimize variable stiffness (VS) composite circular cylinders designed with the direct fiber path parameterization technique using cubic and quadratic Bézier curves as curvilinear fiber paths. The Bézier curves allow generating fiber paths with nonlinear angle variation, and they are defined by simple design variables such as segment/station angles and multipliers/curvatures. A finite element model of VS shells under pure bending with stiffness variation in circumferential direction due to axially shifted courses is implemented and optimized for maximum buckling load considering curvature and strength constraints. The proposed design optimization framework, called pre-trained multi-step/cycle surrogate-based optimization, is conducted in two steps using a non-dominated sorting genetic algorithm (NSGA-II). The framework leverages prior knowledge of the design space by using laminated VS shells with single ply definitions in the first step before performing the optimization of all VS plies in the second step. Four different stacking sequences are considered, consisting of all VS plies and partial VS plies in combination with unidirectional fibers. The VS composite shell modeled using cubic Bézier curves of constant curvature as the fiber path for all plies shows a 41% increase in buckling load compared to the reference quasi-isotropic composite cylindrical shell.