Design of a Bi-stable Airfoil with Tailored Snap-through Response Using Topology Optimization

Abstract

This study aims to harness the geometric non-linearity of structures to design a novel camber morphing mechanism for a bi-stable airfoil using topology optimization. The goal is to use snap-through instabilities to actuate and maintain the shape of the morphing airfoil. Topology optimization has been used to distribute material over the design domain and to tailor the nonlinear response of the baseline structure to achieve the desired bi-stable behavior. The large scale deformation undergone by the structure is modeled using a hyperelastic material model. The non-linear structural equilibrium equations are solved using arc-length and displacement-controlled Newton–Raphson (NR) analysis. Isoparamteric finite element evaluation is used for analyzing kinematic and deformation characteristics of the structure. The optimization problem is solved using a computationally efficient nonlinear optimization algorithm, the Method of Moving Asymptotes (MMA), with a Solid Isotropic Material Penalization (SIMP) scheme. The gradient information required for the optimization has been evaluated using an adjoint sensitivity formulation. Two different design domains, one with a structured quadrilateral mesh and other with an unstructured triangular mesh, are investigated and compared. The effect of different optimization parameters on the final optimized structure and its behavior has also been analyzed. The final result is a novel camber morphing mechanism without the disadvantages of increased weight and higher maintenance costs associated with conventional actuation mechanisms.