Abstract
This paper is concerned with a Newton ’s method for a kind of shape optimization problems. The first and the second variations of the object function are derived. These variations are discretized by introducing a set of boundary value problems in order to derive the second order numerical method. The boundary value problems are solved by the conventional finite element method. A simple numerical example is examined and shows the efficiency of the method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Cea, ‘Problems shape optimal design ’, in E. J. Haug and J. Cea (eds.), Optimization of Distributed Parameter Structures, vol.2, Sijthoff and Noordhoff, Alphen aan den Rijn, Holland, 1005–1048(1981).
J.-P. Zolesio, ‘The material derivative (or speed) method for shape optimization ’, ibd., 1152–1194 (1981).
N. Fujii, ‘Necessary conditions for a domain optimization problem in elliptic boundary value problems ’, SIAM J. Control and Optimization 24, 346–360(1986).
O. Pironneau, ‘On optimum problems in Stokes flow ’, J. Fluid Mech. 59, 117–128(1973)
O. Pironneau, ‘On optimum design in fluid mechnics ’, J. Fluid Mech. 64, 97–110(1974).
N. Fujii, ’second variation and its application in a domain optimization problem ’, Proceedings of the 4th IFAC Symposium on Control of Distributed Parameter Systems, Pergamon, 431–436(1986).
Y. Goto, N. Fujii and Y. Muramatsu, ’second order necessary optimality conditions for domain optimization problems with a Neumann problem ’, Proceedings of the 13th IFIP Conference on System Modelling and Optimization, in press (1988)
G. Polya, ‘Torsional rigidity, principal frequency, elctrostatic capacity and symmetrization ’, Quarterly Appl. Math. 6, 267–277 (1948).
O. Pironneau, Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, 1984.
J. P. Queau and Ph. Trompette, ‘Two-dimensional shape optimal design by the finite element method ’, Int. J. Num. Meth. Eng. 15, 1603–1612(1980).
G. Arumugam and O. Pironneau, ‘On the feasibility of riblets for airplane ’, Proceedings of the 13th IFIP Conference on System Modelling and Optimization, in press(1988).
N. Kikuchi, K. Y. Chung T. Torigaki and J. E. Taylor, ‘Adaptive finite element method for shape optimization of linear elastic structures ’, in J. A. Bennet and M. E. Botkin (eds.), The Optimal Shape, Plenum, New York, 139–169(1986).
C. A. Mota Soares and K. K. Choi, ‘Boundary elements in shape optimal design of structures ’, ibd., 199–231 (1986).
Ph. Trompette, J. L. Marcelin and C. Lallemaud, ‘Optimal shape design of axisymmetric structures ’, ibd., 283–295(1986).
C. A. Mota Soares (ed.), Computer Aided Optimal Design: Structural and Mechanical Systems, Springer-Verlag, Berlin, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 International Federation for Information Processing
About this paper
Cite this paper
Goto, Y., Fujii, N. (1989). A newton ’s method in a domain optimization problem. In: Simon, J. (eds) Control of Boundaries and Stabilization. Lecture Notes in Control and Information Sciences, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043356
Download citation
DOI: https://doi.org/10.1007/BFb0043356
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51239-4
Online ISBN: 978-3-540-46181-4
eBook Packages: Springer Book Archive