High Order Shape Design Sensitivity: A Unified Approach
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High Order Shape Design Sensitivity: A Unified ApproachAuthor(s)
Date
2000Citation
Computer methods in applied mechanics and engineering, vol. 188, n. 4 (Aug. 2000), p. 681-696
Abstract
[Abstract] Three basic analytical approaches have been proposed for the calculation of sen-
sitivity derivatives in shape optimization problems. The first approach is based on
differentiation of the discretized equations [1-3]. The second approach is based on
variation of the continuum equations [1,4,5] and on the concept of material deriva-
tive. The third approach [6] 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 imple-
mentations.
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 deriva-
tives, 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
Editor version
ISSN
0045-7825