Shape Design Sensitivity Analysis using the Boundary Element Method

Zhao, Zhiye

doi:10.1007/978-3-642-84382-2_4

Cited by 6 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus once the initial problem has been solved, ¢~ can be evaluated. It should be noted that different forms of constraints will lead to different formulations of ¢~, which can be derived using a material derivative method (Zhao 1990).…”

Section: = / U) Dr (13)mentioning

confidence: 99%

See 1 more Smart Citation

Shape design sensitivity analysis of kinematical boundaries

Zhao

1993

Structural Optimization

View full text Add to dashboard Cite

A new approach is used in this paper to derive the design sensitivity formulation with kinematical design boundaries. By employing the concept of the conventional finite difference approach, the variation of structural response due to change of the kinematic design boundary can be represented by the perturbed structure under a set of kinematical boundary conditions. Parameterization of the design variation with respect to the design variable enables us to transform the design sensitivity into the solutions of a boundary value problem with perturbation displacements on the design boundary. The perturbation diplacements can be evaluated from the stress and displacement fields of the initial problem. This approach can be treated as a special case of the general direct formulation, but the derivation using the finite difference procedure gives a strong physical meaning of the method, and the formulation derived provides an explicit form for design sensitivity calculation. Tim numerical implementation of this approach based on the boundary element method is discussed, and a few numerical examples are used to verify the proposed formulation.

show abstract

Section: = / U) Dr (13)mentioning

confidence: 99%

“…This alternative approach is called FDDM (finite difference displacement method) for simplicity. A similar procedure has also been applied to design sensitivity analysis with traction de-sign boundaries (Zhao 1990). …”

Section: Introductionmentioning

confidence: 97%

Shape design sensitivity analysis of kinematical boundaries

Zhao

1993

Structural Optimization

View full text Add to dashboard Cite

show abstract

An alternative approach to shape design sensitivity analysis

Zhao

Adey

1992

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA novel method is presented in this paper for calculating shape design sensitivity, which is based on the finite difference method (FDM). By analysing the numerical procedure of the FDM, the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known. The final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem, but under the perturbation loads. Therefore the new method does not require the calculation of the matrices of the perturbed structure, and is independent of the perturbation step. A numerical implementation of the finite difference load method (FDLM) is described in which the boundary element method is used to evaluate the structural response. The numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate.

show abstract