3D isogeometric boundary element analysis and structural shape optimization for Helmholtz acoustic scattering problems

2021 ◽  
Vol 384 ◽  
pp. 113950
Author(s):  
Ahmed Mostafa Shaaban ◽  
Cosmin Anitescu ◽  
Elena Atroshchenko ◽  
Timon Rabczuk
Keyword(s):  
Shape Optimization ◽  
Boundary Element ◽  
Acoustic Scattering ◽  
Scattering Problems ◽  
Element Analysis ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Boundary Element Analysis ◽  
Acoustic Scattering Problems

Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems

1995 ◽  
Author(s):  
Steven J. Newhouse ◽  
Ian C. Mathews
Keyword(s):  
Boundary Element ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Error Estimator ◽  
Infinite Domain ◽  
Scattering Problems ◽  
Effective Form ◽  
Mesh Density ◽  
Acoustic Scattering Problems

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

A Relative-Stress Based Method for Structural Shape Optimization

2013 ◽  
Vol 327 ◽  
pp. 271-275 ◽  
Author(s):  
Zhi Xue Wu
Keyword(s):  
Shape Optimization ◽  
Optimization Method ◽  
Optimal Shape ◽  
Control Points ◽  
Stress Difference ◽  
Element Analysis ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Relative Stress ◽  
Dimensional Shape

A gradientless method for two-dimensional shape optimization is developed based on the magnitude of local relative-stress difference along the design boundary. The design boundary is modeled by using cubic splines, which are determined by a number of control points. The optimal shape of a design boundary with constant stress is achieved iteratively by moving control points consecutively (correspondingly, changing the shape of the design boundary) by an amount depending on the relative-stress difference between two neighboring boundary points. The key feature of the optimization method is that no arbitrary threshold stress is required. The result quality in terms of accuracy and efficiency are tested and discussed with several finite element analysis examples.

Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems

2020 ◽  
Vol 28 (4) ◽  
pp. 223-245
Author(s):  
Gabriel N. Gatica ◽  
Salim Meddahi
Keyword(s):  
Boundary Element ◽  
Acoustic Scattering ◽  
Rates Of Convergence ◽  
Boundary Element Methods ◽  
Scattering Problems ◽  
Combined Use ◽  
Virtual Element ◽  
2D And 3D ◽  
Element Method ◽  
Acoustic Scattering Problems

AbstractThis paper extends the applicability of the combined use of the virtual element method (VEM) and the boundary element method (BEM), recently introduced to solve the coupling of linear elliptic equations in divergence form with the Laplace equation, to the case of acoustic scattering problems in 2D and 3D. The well-posedness of the continuous and discrete formulations are established, and then Cea-type estimates and consequent rates of convergence are derived.

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