Gradient-based shape optimization of induction welding coil for thermoplastic composites via level-set method

One of the advantages of thermoplastic over thermoset-based polymer composites is the ability to join parts by locally melting and re-solidifying the polymer to form cohesive bonds, alternatively to mechanical fasteners or adhesives. Interest in thermoplastic composites for use in primary structures of aircraft has grown exponentially in the past decade, thanks to the advancements in cohesive joining technologies to reduce structural weight, airframe cost, and enable high-rate production. One of the cohesive joining technologies of interest for thermoplastic composite is welding based on induction heating using an alternating EM field created by running an alternating current through a coil. The best coil design depends on the material to be welded, especially on the type of thermoplastic material and the laminate stacking sequence used and the geometry of the joint. This study focuses on shape optimization of induction welding coils, which are a critical factor in a welding process. A hybrid boundary element/edge-based finite element method is used to solve the Maxwell equations and resolve eddy currents induced in thermoplastic composite laminates. Level-set method is employed for the parameterization of the induction coil design. The coil shape is updated based on the shape sensitivities calculated through the adjoint variable method. To demonstrate the effectiveness of the proposed optimization framework, several numerical studies are performed, and some important geometric characteristics of the optimized coils are observed.