Shape And Topology Optimization Based On Isogeometric Boundary Element Method In Acoustics

Nowadays,noise control is a research topic that has attracted much attention in engineering.Designing acoustic structures by using shape and topology optimization methods has been proven to be an effective approach for noise reduction.Before optimization,developing an accurate numerical method to predict the acoustic field is quite important.The boundary element method(BEM)is much suitable for the external acoustic problem with a large domain or an infinite domain since the fundamental solution of BEM can satisfy the radiation boundary condition at infinity.Moreover,structural optimization needs to repeatedly perform the update of structural geometry and calculation of the physical field,which makes the communication between the two fields quite frequent and brings great difficulties to the traditional modeling and discretization methods.Isogeometric analysis(IGA),which utilizes the non-uniform rational B-splines(NURBS)to approximate structural geometries and physical fields at the same time,can accomplish mesh division of the model automatically and integrate the process of geometry design and physical analysis;therefore,IGA provides great convenience and flexibility for structural optimization design.Furthermore,since the BEM only needs the discretization of structural boundaries,it can be naturally combined with the IGA that normally employs NURBS to construct curves and surfaces,namely forming IGA BEM.In this dissertation,being aimed at important engineering problems such as sound barriers,submarines,and phononic crystal-like periodic structures,further research is carried out on the computational accuracy and efficiency problems of IGA BEM.Several acoustic shape and topology optimization approaches are proposed,and the main contents and contributions of this dissertation include the four following aspects:An IGA BEM is proposed for three-dimensional(3D)doubly-periodic multilayered acoustic structures.First,the interface between adjacent acoustic media is constructed by the NURBS surface,and the acoustic transmission boundary condition is considered;thus,the reflection and transmission of acoustic waves on the interface can be analyzed.Furthermore,the boundary value problem for the structure can be solved by imposing the quasi-periodic boundary condition on the unit cell.The Ewald method is utilized to solve the convergent problem of periodic Green’s function and its normal derivative,which significantly improves the computational efficiency.Finally,by polar coordinate system conversion and moving the collocation points on the boundary of parametric space to reasonable positions,the singular integrals can be calculated exactly,and the calculation of singular integral for elements in adjacent cells is needless.A shape optimization approach is proposed for 3D doubly-periodic multilayered acoustic structures by using IGA BEM.Based on the shape perturbation assumption and the adjoint variable method(AVM),the shape derivative formula of the three-dimensional multi-layered acoustic structure is derived.Further,the shape sensitivities of each control point for three directions can be obtained by isogeometric discretization of the shape derivatives.The adjoint equation that only needs to be computed once is also formulated by the doubly-periodic IGA BEM,which can remarkably accelerate the calculation for shape sensitivities with numerous design variables.Finally,according to shape sensitivities,the shape optimization for the 3D doublyperiodic multi-layered structure is realized by the method of moving asymptotes,which is also applied to the interface design of the multi-layered sound absorbing material.A multimaterial topology optimization approach is developed for acoustic design based on the IGA BEM and piecewise constant level set(PCLS)method.A new topology optimization approach is developed to design the distribution of multiple sound absorbing materials(SAM)on the structural surface to reduce the sound pressure in the reference area.First,an efficient IGA BEM is proposed by combining multi-patched discretization and CPU parallel design,and a submarine model entirely composed of NURBS surfaces is built for optimization design.Secondly,various SAM domains are expressed by PCLS,and the sensitivity formula of the objective function is derived by the AVM.Finally,we propose a novel penalty coefficient formula and the ordered volume constraint algorithm to improve the PCLS,which can achieve controlling volume fractions of multiple materials.For design domains with different materials volumes,the objective function can always converge stably.An efficient approach of combined shape and SAM topological distribution optimization is proposed for sound barriers based on IGA BEM.In this dissertation,the combined optimization method,which can realize the simultaneous optimization of the structural shape and the SAM distribution on structural surfaces,is developed on the basis of IGA BEM.The objective function is set as the sum of squares of sound pressure amplitudes in the reference plane,and the sensitivity is derived by the direct differentiation method or AVM.The NURBS control point that can change the geometry flexibly is set as the shape design variable,while the artificial density of the integral element is set as the topology design variable,in which the SIMP method is used to achieve the optimization design of the SAM distribution on the surface of the sound barrier.In addition,four different iteration schemes of shape and topology are proposed,and the optimization effect and computational efficiency are compared to obtain an excellent one.