A boundary-perturbation finite element approach for shape optimization

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 4, 2000, Pages 801-819

  Givoli, Dan ^a   Demchenko, Tatyana ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Boundary perturbation; Finite element; Helmholtz equation; Scattering; Shape optimization

Indexed keywords

ACOUSTIC WAVE SCATTERING; LINEAR EQUATIONS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

BOUNDARY PERTURBATION; HELMHOLTZ EQUATION;

FINITE ELEMENT METHOD;

EID: 0034135280     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000210)47:4<801::AID-NME798>3.0.CO;2-P     Document Type: Article

References (27)

1. Bendsoe MP. Optimization of Structural Topology, Shape and Material. Springer: Berlin, 1995.
2. Phan AV, Mukherjee S, Mayer JRR. Stresses, stress sensitivities and shape optimization in two-dimensional linear elasticity by the boundary contour method. International Journal for Numerical Methods in Engineering 1998; 42:1391-1407.
3. Yamazaki K, Shibuya K, Sensitivity analysis of nonlinear material and its application to shape optimization. AIAA Journal 1998; 36:1113-1115.
4. Lutz T, Wagner S. Drag reduction and shape optimization of airship bodies. Journal of Aircraft 1998; 35:345-351.
5. Aubert P, Rousselet B. Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities. International Journal for Numerical Methods in Engineering 1998; 42:15-48.
6. Le Riche R, Cailletaud G. A mixed evolutionary/Heuristic approach to shape optimization. International Journal for Numerical Methods in Engineering 1998; 41:1463-1484.
7. Morse PM, Feshbach H. Methods of Theoretical Physics. McGraw-Hill: New York, 1953; 1052-1060.
8. Stoker JJ. Water Waves. Interscience Publ: New York, 1957.
9. Komata M. A generalized perturbation theory applicable to reactor boundary changes. Nuclear Science and Engineering 1977; 64:811-822.
10. Van Dyke M. Perturbation Methods in Fluid Mechanics. Parabolic Press: Stanford, 1975; 13-14.
11. Parnes R. The boundary perturbation method in elastostatics: investigation of higher order effects and accuracy of solutions. Journal of Theoretical and Applied Mechanics 1987; 6:295-314.
12. Parnes R. A BPM solution for elliptic plates subjected to eccentric loads. Intrenational Journal of Solids and Structures 1988; 24:761-776.
13. Givoli D, Elishakoff I. Stress concentration at a nearly circular hole with uncertain irregularities. ASME Journal of Applied Mechanics 1992; 59:S65-S71.
14. Bruno OP, Reitich F. Calculation of electromagnetic scattering via boundary variation and analytic continuation. Applied Computers Electromagnetics Society Journal 1996; 11:17-31.
15. Givoli D. Scattering matrix of a nearly circular cylinder. Wave Motion 1999; 30:239-251.
16. Lomakin VA. Concentration of stresses near a surface with rapidly oscillating irregularities. Prikladna Mekhanika 1968; 4:1-8 (English translation: Soviet Applied Mechanics 1968; 4:1-4).
17. Lomakin VA. Concentration of stresses near a surface with rapidly oscillating irregularities. Prikladna Mekhanika 1968; 4:1-8 (English translation: Soviet Applied Mechanics 1968; 4:1-4).
18. Lekhinitskii SG. An approximate method for analyzing the stresses in an elastic anisotropic plate around a distorted circular hole, Inzhenernyi Sbornik 1953; 17:1-28 (in Russian).
19. Lekhinitskii SG. Anisotropic Plates. Gordon and Breach Science Publ: New York, 1968 (English translation from the 1957 Russian edition).
20. Kubenko VD, Nemish YuN, Shnerneko Kl, Shul'ga NA. Perturbation method in boundary value problems of the mechanics of deformable bodies. Prikladna Mekhanika 1982; 18:3-20 (English translation: Soviet Applied Mechanics 1982; 18:955-970).
21. Kubenko VD, Nemish YuN, Shnerneko Kl, Shul'ga NA. Perturbation method in boundary value problems of the mechanics of deformable bodies. Prikladna Mekhanika 1982; 18:3-20 (English translation: Soviet Applied Mechanics 1982; 18:955-970).
22. Givoli D, Elishakoff I, Stavsky Y. A boundary-perturbation finite-element method for plane elasticity problems. Computer Methods in Applied Mechanics and Engineering 1992; 96:45-63.
23. Hughes TJR. The Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1987.
24. Givoli D. A direct approach to the finite element solution of elliptic optimal control problems. Numerical Methods in Partial Differential Equations 1999; 15:371-388.
25. Givoli D, Rand O. Minimization of the thermoelastic deformation in space structures undergoing periodic motion. AIAA Journal of Spacecraft and Rockets 1995; 32:662-669.
26. Bender CM, Orszag SA. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill: New York, 1978.
27. Givoli D, Doukhovni I. Finite element-quadratic programming approach for contact problems with geometrical nonlinearity. Computers and Structures 1996; 61:31-41.