Numerical methods for second-order shape sensitivity analysis with applications to heat conduction problems
✍ Scribed by Gene J. -W. Hou; Jeenson Sheen
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 1002 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
In this paper, two linite-element-based schemes for second-order shape sensitivity analysis are presented. In the first formulation, the AV-DD method, the first-order shape sensitivity equation is derived and expressed in terms of state and adjoint variables. The resultant equation is then directly differentiated to obtain the second-order shape sensitivity equation. In the second formulation, the DD-AV method, the functional of concern is differentiated twice to yield the second-order sensitivity equation in which the second-order shape derivatives can be eliminated by introducing a proper adjoint equation. A thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes. It is shown that both methods yield identical results, though the DD-AV method is computationally more efficient.