SUMMARYA novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested configurations. The applicability of the DMO method is demonstrated for fibre angle optimization of a cantilever beam and combined fibre angle and material selection optimization of a four-point beam bending problem and a doubly curved laminated shell.

In this article a novel method for structural optimization of laminated composite shell structures such as wind turbine blades is presented.The outer shape of a wind turbine blade is typically determined by aerodynamic considerations and therefore not subject to change. Furthermore, the thicknesses of the shell structures are also considered fixed. The design objective is chosen to be a global quantity such as maximum stiffness or lowest eigenfrequency with a constraint on the total mass, such that the cost of material can be considered. The design optimization method is based on ideas from multiphase topology optimization where the material stiffness (or density) is computed as a weighted sum of candidate materials, and the method is easy to implement in existing finite element codes. The potential of the method to solve the combinatorial problem of proper choice of material, stacking sequence and fibre orientation simultaneously for maximum stiffness or lowest eigenfrequency design is illustrated on both small test examples and a real-life main spar from a wind turbine blade.1. Analytical methods that rely on the closed-form formulation of an optimality criterion; see e.g. References 1 and 2. Pedersen 3 has used such methods to optimize 2D continua, beams and plates. However, for general shell problems the optimality criterion approaches have not yet been successfully applied.

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Abstract:The design problem of maximizing the lowest eigenfrequency or the buckling load factor of laminated composite shell structures is investigated using the socalled Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material, stacking sequence and fiber orientation simultaneously is illustrated for two multi-layered multi-material plate examples.

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