Isogeometric shape optimization for widening band gaps of periodic composite plates

This paper presents an isogeometric shape optimization methodology to widen the band gap of periodic com-posite plates by smoothly optimizing its thickness profile. To save the computational cost, two NURBS surfaces are used in the isogeometric optimization method. While a fine NURBS surface (analysis mesh) is used for modeling the band gap of periodic composite plates within the isogeometric analysis (IGA) framework, a coarser NURBS design surface, i.e., the design mesh, is employed to describe the periodic plate thickness profile exactly and the position of control points are taken as optimal thickness variables. The particle swarm optimization (PSO) algorithm is adopted to solve the constrained dynamic maximization problems. On the other hand, the level set method and triangular domain integration technique are employed to describe the two-phase material interface of periodic composite plates. Numerical examples are provided to validate the accuracy and reliability of the present method. The numerical results showed that the present method can provide an accurate analysis and smooth plate thickness profile in the optimization process. The band gap of periodic composite plates is maximized effectively by the design of the plate thickness profile using the present optimization approach.