Shape optimization of sound barriers using an isogeometric meshless method

The sound barrier is an important means to reduce noise caused by traveling vehicles on roads or railways. Structural design and optimization of the sound barrier can effectively reduce the use of materials and improve the noise reduction effect. In this paper, a new isogeometric singular boundary method is proposed and applied to the shape optimization of sound barriers. The geometric structure is accurately represented by using non-uniform rational B-splines. The acoustic shape sensitivity of the control points was calculated using the direct differentiation method and the adjoint variable method. After that, the method of moving asymptotes is adopted as an optimizer to search for the optimal layout of the design objective. In the numerical procedure, the shoelace formula is introduced to calculate the area of the closed structure, which only uses the discrete node information on the boundary. The proposed approach completely avoids the mesh division in the finite element method as well as the singular integral calculation in the boundary element method. More importantly, it can be seamlessly connected with the computer-aided design system for the subsequent treatment by engineers. Three numerical examples are provided to illustrate the accuracy and effectiveness of the proposed isogeometric method. This work provides a simple and effective way for the structural optimization design of sound barriers.