A weighted least squares approach for the design of adaptive aerodynamic structures subjected to an out-of-plane transformation

An optimal design framework for adaptive wind turbine blades is presented. A mathematical framework establishes the topology of actuators and material compliance. These parameters are selected to adapt the blade twist distribution into a range of prescribed blade configurations. Our previous work established the ideal twist distribution configurations. The distributions improve the aerodynamic efficiency for a range of wind speeds in which the system operates at partial production. Within this range the nonlinear blade twist distribution changes in relation to the speed. The possibility of producing adaptively compliant structures is becoming increasingly possible with innovative materials and additive manufacturing (AM) processes. Our overarching goal is to create a comprehensive design infrastructure that integrates manufacturing and materials innovation with the complex needs of adaptive structures. This work proposes a method through which the ideal twist distribution can be actualized in structural implementation. The implementation involves a modular blade composed of flexible sections whose twist is modulated by actuators along the blade. Each flexible blade section is composed of two contiguous segments, each with a different torsional stiffness defined by a stiffness ratio. The stiffness variation within each section allows the blade to assume a nonlinear twist distribution when actuated. Errors relative to an ideal twist distribution are minimized by optimizing the stiffness ratios and twist actuator locations. The optimization is completed using a weighted least squares approach that allows the blade designer to bias blade performance toward different operating conditions. A quadratic weighting scheme that penalizes twist errors toward the blade tip is found to result in a higher power coefficient than other weighting schemes.