Boundary homogenization and boundary shape optimization for a cylinder

2005 ◽  
pp. 37-49
Author(s):  
Alain Brillard
Keyword(s):  
Shape Optimization ◽  
Boundary Shape

Numerical Considerations in Structural Component Shape Optimization

1985 ◽  
Vol 107 (3) ◽  
pp. 334-339 ◽  
Author(s):  
R. J. Yang ◽  
K. K. Choi ◽  
E. J. Haug
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Shape Optimization ◽  
Structural Component ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Test Problems ◽  
Material Derivative ◽  
Boundary Shape ◽  
Component Shape

A unified design sensitivity analysis theory and a linearization method of optimization are employed for structural component shape optimization. A material derivative method for shape design sensitivity analysis, using the variational formulation of the equations of elasticity and the finite element method for numerical analysis, is used to calculate derivatives of stress and other structural response measures with respect to boundary shape. Alternate methods of boundary shape parameterization are investigated, through solution of two test problems that have been treated previously by other methods: a fillet and a torque arm. Numerical experiments with these examples and a variety of finite element models show that component shape optimization requires careful selection of boundary parameterization, finite element model, and finite element grid refinement techniques.

Shape Optimization of Acoustic Enclosures Based on a Wavelet–Galerkin Formulation

2015 ◽  
Vol 07 (01) ◽  
pp. 1550009 ◽  
Author(s):  
S. Zhang ◽  
L. Cheng
Keyword(s):  
Shape Optimization ◽  
Sound Pressure ◽  
General Procedure ◽  
Sound Field ◽  
Boundary Shape ◽  
Rectangular Enclosure ◽  
Entire Boundary ◽  
Orthogonal Property ◽  
Acoustic Enclosures ◽  
Fitting Ability

The problem of the shape optimization of acoustic enclosures is investigated in this paper. A general procedure, comprising a Wavelet–Garlerkin formulation and a so-called vertex-driven shape optimization is proposed to deal with the general problem of internal sound field prediction and the optimization of the boundary shape. It is shown that, owing to the compactly supported orthogonal property and the remarkable fitting ability, Daubechies Wavelet can be used as a global basis to approximate the unknown sound field on a relatively large interval globally instead of piecewise approximation like most of element based methods do. This feature avoids meshing the boundary of the enclosure, although vertex points are needed to define the boundary shape, whose positions keep updating during the shape optimization process. A rectangular enclosure is used as benchmark to assess and validate the proposed formulation, by investigating the influence of some key parameters involved in the formulation. It was shown that the sound pressure along the entire boundary of the rectangular enclosure can be accurately approximated without meshing. The same enclosure with an inner rigid acoustic screen is then used to reduce the sound pressure level within a chosen area through optimizing the shape of the screen, which shows the remarkable potentials of the proposed approach as a shape optimal tool for inner sound field problems.

Integrated topology and boundary shape optimization of 2-D solids

1991 ◽  
Vol 87 (1) ◽  
pp. 15-34 ◽  
Author(s):  
Martin Philip Bendsøe ◽  
Helder Carrico Rodrigues
Keyword(s):  
Shape Optimization ◽  
Boundary Shape
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