High order shape design sensitivity: an unified approach
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High order shape design sensitivity: an unified approachAuthor(s)
Date
1998Citation
Computational mechanics: new trends and applications (CD-ROM)
Abstract
[Abstract] Three basic analytical approaches have been proposed for the calculation
of sensitivity derivatives in shape optimization problems. The first approach is based
on differentiation of the discretized equations. The second approach is based on
variation of the continuum equations and on the concept of material derivative. The
third approach is based upon the existence of a transformation that links the material
coordinate system with a fixed reference coordinate system. This is not restrictive, since
such a transformation is inherent to FEM and BEM implementations.
In this paper we present a generalization of the latter approach on the basis of a generic
unified procedure for integration in manifolds. Our aim is to obtain a single, unified,
compact expression to compute arbitrarily high order directional derivatives, independently
of the dimension of the material coordinates system and of the dimension of
the elements. Special care has been taken on giving the final results in terms of easy-to-compute expressions, and special emphasis has been made in holding recurrence and
simplicity of intermediate operations. The proposed scheme does not depend on any particular
form of the state equations, and can be applied to both, direct and adjoint state
formulations. Thus, its numerical implementation in standard engineering codes should
be considered as a straightforward process. As an example, a second order sensitivity
analysis is applied to the solution of a 3D shape design optimization problem.
Keywords
Shape sensitivity
Sensitivity analysis
Shape optimization
Optimization
Integration in manifolds
Finite element method
Sensitivity analysis
Shape optimization
Optimization
Integration in manifolds
Finite element method
Description
4th World Congress on Computational Mechanics, 1998, Buenos Aires
ISBN
84-89925-15-1