Large Scale Optimization of Compression Loaded Composite Structures

The size of wind turbines has increased dramatically in the last decade, and today a standard wind turbine blade has a length between 40 and 60 meters. These high performance, multi-material structures are lightweight and may exhibit maximum tip displacements of up to about 25% of the length before they fail due to local buckling on the compressive side of the blade. Thus, in order to improve the structural performance the design objective is to increase the buckling load factor, taking weight considerations into account. This paper deals with this design problem for wind turbine blades specifically, but the methodology can be applied to any laminated multi-material composite shell structure.

The outer shape of a wind turbine blade is determined by aerodynamic considerations and therefore in general not subject to change. These structures consist of stiff fiber reinforced polymers such as Glass or Carbon Fiber Reinforced Polymers (GFRP/CFRP) together with foam and different types of wood stacked in a number of layers and bonded together by a resin. The design problem is then to determine the best stacking sequence by proper choice of material and fiber orientation of each FRP layer in order to obtain the desired structural performance.

For complicated geometries like wind turbine blades this is a very challenging design problem that calls for use of sophisticated structural optimization tools, and in this paper the so-called Discrete Material Optimization (DMO) approach is used. The DMO method is based on ideas from multi-phase topology optimization where the material stiffness (or density) is computed as a weighted sum of candidate materials. In this way the discrete problem of choosing the best material (with the right orientation) is converted to a continuous formulation where the design variables are the scaling factors (or weight functions) on each candidate material. The method has been successfully applied for compliance problems using as many as 13 candidate materials at each point and several hundred thousands of design variables in total, see [

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The analysis of the compression loaded multi-material composite structure is based on a linearized buckling problem for the undeformed geometry. Layered shell finite elements are used for the analysis, and the sensitivities of the buckling load factor are determined analytically. Multiple eigenvalues are taken into account, and the optimization problem is solved using the Method of Moving Asymptotes. Several examples involving thousands of design variables will illustrate the potential of the approach for buckling optimized designs of multi-material composite structures.