A compliance approximation method applied to variable stiffness composite optimisation

Abstract

A way to approximate the compliance of composites for optimisation is described. A two-level approximation scheme is proposed inspired by traditional approximation concepts such as force approximations and convex linearisation. In level one, an approximation in terms of the reciprocal in-plane stiffness matrix is made. In level two, either the lamination parameters, or the nodal fibre angle distribution are used as design variables. A quadratic approximation is used to build the approximations in terms of the fibre angles. The method of conservative, convex separable approximations is used for the optimisation. Conservativeness is guaranteed by adding a convex damping function to the approximations. Two numerical examples, one optimisng the compliance of a plate clamped on the left, loaded downwards on the bottom right, another one optimising the compliance of a plate loaded with a shear force and a moment show the computational efficiency of the proposed optimisation algorithm.

A Review on Topology Optimization Strategies for Additively Manufactured Continuous Fiber-Reinforced Composite Structures

“…The LPs framework is briefly discussed for completeness on available parameterization schemes. Still, interested readers can refer to the review by Albazzan et al [139] and recent work on the TO of laminates in the following citations [140][141][142][143].…”

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

“…[28][29][30][31][32] Multistep and multi-objective optimization of laminated composite circular cylindrical shells under hydrostatic pressure using genetic algorithm (GA) and developed non-dominated sorting genetic algorithm (NSGA-II) were presented in recent years. [33][34][35][36][37] Peeters et al 38,39 described a two-level approach for variable stiffness composites and notified to the fiber placement defects in buckling analysis and optimization. Miller and Ziemiański 40 optimized dynamic behavior in addition to buckling load for laminated composite cylindrical shell.…”

Optimal design and manufacture of variable stiffness laminated continuous fiber reinforced composites

“…Recent efforts have started utilizing topology optimization to couple microstructure optimization with macroscale material layout design 20,21,40,[62][63][64][65] . The fiber path to be optimized is usually parametrized by use of discrete nodal or elemental fiber angles directly 61,[66][67][68] , by a family of curves (the curves were used to define either the fiber orientations or paths e.g., linear curves, Bezier curves, Lagrange polynomials) [69][70][71][72][73][74][75] , lamination parameters [76][77][78][79][80][81][82] and polar lamination parameters 83 . When using a family of curves, a manufacturable fiber layout is readily available, but this restricts the design space.…”

“…When fiber angles are available (either directly from optimization or through lamination parameters), a post-processing step is utilized to determine the fiber paths or layout. One commonly used approach is the streamline methodology where fiber paths are obtained from the streamlines of the optimized fiber angle field 65,67,79,81,82,84 . However, this does not guarantee uniform fiber distribution and thus could lead to unwanted overlaps or gaps when AFP/ATL techniques are used to realize the optimized structures.…”