Direct approach to the minimization of the maximal stress over an arch structure

Journal of Optimization Theory and Applications

Volumn 97, Issue 3, 1998, Pages 551-578

  Habbal, A ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Mechanical structures; Nonsmooth analysis; Shape optimization; Shell theory

Indexed keywords

COMPUTATION THEORY; COST BENEFIT ANALYSIS; SHAPE OPTIMIZATION;

ARCH STRUCTURES; DIRECT APPROACH; LINEAR ELASTIC; MAXIMAL STRESS; MECHANICAL STRUCTURES; MINIMISATION; NON-SMOOTH ANALYSIS; SHAPE-OPTIMIZATION; SHELL THEORY; THIN SHELL THEORY;

ARCHES;

EID: 0032362640     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022685908429     Document Type: Article

References (31)

1. MYSLINSKI, A., and SOKOLOWSKI, J., Nondifferentiable Optimization Problems for Elliptic Systems, SIAM Journal on Control and Optimization, Vol. 23, pp. 632-648, 1985.
2. HABBAL, A., Theoretical and Numerical Study of Nonsmooth Shape Optimization Applied to the Arch Problem, Mechanics of Structures and Machines, Vol. 20, pp. 93-117, 1992.
3. ROUSSELET, B., Shape Optimization of Structures with Pointwise State Constraints, Control of Partial Differential Equations, Edited by A. Bermudez, Springer Verlag, Berlin, Germany, pp. 255-264, 1987.
4. BENDSOE, M. P., and TAYLOR, J. E., An Interpretation for Minmax Structural Design Problems Including a Method for Relaxing Constraints, International Journal of Solids and Structures, Vol. 20, pp. 301-314, 1984.
5. AUBERT, P., Thickness Optimization of a Geometrically Nonlinear Arch at Limit Points, Applied Mathematics and Computer Science, Vol. 6, pp. 101-117, 1996.
6. COX, S. J., Extremal Eigenvalue Problems for the Laplacian, Recent Advances in PDE, Edited M. A. Herrero and E. Zuazua, Masson, Paris, France, pp. 37-53, 1994.
7. OVERTON, M. L., and COX, S. J., On the Optimal Design of Columns against Buckling, SIAM Journal on Mathematical Analysis, Vol. 23, pp. 287-325, 1992.
8. HEMP, W., Optimum Structures, Clarendon Press, Oxford, England, 1973.
9. VENKAYYA, V., Structural Optimization: A Review and Some Recommendations, International Journal of Numerical Methods in Engineering, Vol. 13, pp. 205-228, 1978.
10. MOTA SOARES, C., Computer Aided Optimal Design: Structural and Mechanical Systems, Springer Verlag, Berlin, Germany, 1987.
11. SANDERS, J. L., and BUDIANSKY, B., On the Best First-Order Linear Shell Theory, Progress in Applied Mechanics, W. Prager Anniversary Volume, Macmillan, New York, New York, pp. 129-140, 1967.
12. DESTUYNDER, P., A Classification of Thin Shell Theories, Acta Applicandae Mathematicae, Vol. 4, pp. 15-63, 1985.
13. BREZIS, H., Analyse Fonctionnelle: Théorie et Applications, Masson, Paris, France, 1983.
14. CIARLET, P. G., The Finite-Element Method for Elliptic Problems, North-Holland, Amsterdam, Holland, 1980.
15. ZEINE, O. M., Contributions Theoriques en Optimisation et Modelisation des Structure, PhD Thesis, Université de Nice-Sophia Antipolis, Nice, France, 1995.
16. ROUSSELET, B., BENEDICT, R., and CHENAIS, D., Design Sensitivity for Arch Structures, Journal of Optimization Theory and Applications, Vol. 58, pp. 225-239, 1988.
17. CARTAN, H., Cours de Calcul Differentiel, Hermann, Paris, France, 1967.
18. CLARKE, F. H., Optimization and Nonsmooth Analysis, Wiley, New York, New York, 1983.
19. LEMARÉCHAL, C., Nondifferentiable Optimization, Nonlinear Optimization, Edited by L. C. W. Dixon, E. Spedicato, and G. P. Szego, Birkhauser, Basel, Switzerland, pp. 149-199, 1980.
20. LEMARÉCHAL, C., A View of Line Searches, Optimization and Optimal Control, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 30, pp. 59-78, 1981.
21. STRODIOT, J. S., LEMARÉCHAL, C., and BIHAIN, A., On a Bundle Algorithm for Nonsmooth Optimization, Nonlinear Programming 4, Edited by O. L. Mangasarian, G. L. Meyer, and S. M. Robinson, Academic Press, New York, New York, pp. 245-282, 1981.
22. MIFFLIN, R., Semismooth and Semiconvex Functions in Constrained Optimization, SIAM Journal on Control and Optimization, Vol. 15, pp. 959-972, 1977.
23. KIWIEL, K. C., Proximity Control in Bundle Methods for Convex Nondifferentiable Optimization, Mathematical Programming, Vol. 46, pp. 105-122, 1990.
24. HIRIART-URRUTY, J. B., and LEMARÉCHAL, C., Convex Analysis and Minimization Algorithms, I and II, Springer Verlag, Berlin, Germany, 1993.
25. SCHRAMM, H., and ZOWE, J., A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results, SIAM Journal on Optimization, Vol. 2, pp. 121-152, 1992.
26. LIONS, J. L., and MAGENES, E., Problèmes aux Limites Non-Homogènes et Applications, Dunod, Paris, France, 1968.
27. CEA, J., Optimization: Theory and Algorithms, Springer Verlag, Berlin, Germany, 1978.
28. DEBOOR, C., A Practical Guide to Splines, Applied Mathematics and Sciences, Springer Verlag, Berlin, Germany, 1985.
29. DUCATEL, Y., and BERNADOU, M., Approximation of General Arch Problems by Straight Beam Elements, Numerische Mathematik, Vol. 40, pp. 1-29, 1982.
30. HABBAL, A., Optimisation Nondifferentiable de Formes d'Arches, PhD Thesis, Université de Nice-Sophia Antipolis, Nice, France, 1990.
31. CHENAIS, D., Discrete Gradient and Discretized Continuum Gradient in Shape Optimization of Shells, Mechanics of Structures and Machines, Vol. 22, pp. 73-115, 1994.