Abstract
The problem of shape optimal design for multiply-connected elastic bars in torsion is formulated and solved numerically. A variational formulation for the equation is presented in a Sobolëv space setting and the material derivative idea of Continuum Mechanics is used for the shape design sensitivity analysis. The finite element method is used for a numerical solution of the variational state equation and is integrated into an iterative optimization algorithm. Numerical results are presented for both simply- and doubly-connected bars, with prescribed bounds on admissible location of both inner and outer boundaries.
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References
Sokolnikoff, I.S., Mathematical Theory of Elasticity, McGraw-Hill, New York, (1956).
Polya, G., and Weinstein, A., "On the Torsional Rigidity of Multiply Connected Cross-Sections", Ann. of Math, 52, 154–163, (1950).
Banichuk, N.V., "Optimization of Elastic Bars in Torsion", Int. J. Solids Struct., 12, 275–286, (1976).
Kurshin, L. M., and Onoprienko, P.N., "Determination of the Shapes of Doubly-Connected Bar Sections of Maximum Torsional Stiffness", Prik. Math. Mech. (English translation Appl. Mathematics and Mechanics, PMM), 40, 1078–1084, (1976).
Dems, K., "Multiparameter Shape Optimization of Elastic Bars in Torsion", Int. J. Num. Meth. Engng., 15, 1517–1539, (1980).
Aubin, J.P., Applied Functional Analysis, Wiley-Interscience, New York, (1979).
Zolesio, J.P., "The Material Derivative (or speed) Method for Shape Optimization", Optimization of Distributed Parameter Structures, Vol. II, (ed, E.J. Haug and J. Cea) Sitjthoff-Noordhoff, Rockville, Md., 1089–1151, (1981).
Haug, E.J., Choi, K.K., and Komkov, V., Structural Design Sensitivity Analysis, Academic Press, New York, (1984).
Cea, J., "Problems of Shape Optimal Design", Optimization of Distributed Paramemter Structures, Vol. II. (ed. E.J. Haug and J. Cea) Sitjthoff-Noordhoff, Rockville, Md., 1005–1048, (1981).
Rousselet, B., and Haug, E.J., "Design Sensitivity Analysis of Shape Variation", Optimization of Distributed Parameter Structures, Vol. II, (ed. E.J. Haug and J. Cea) Sijthoff-Noordhoff, Rockville, Md., 1397–1442, (1981).
Choi, K.K., Haug, E.J., Hou, J.W., and Sohoni, V.N., "Pshenichny's Linearization Method for Mechanical System Optimization", Trans, ASME, J. Mech. Design, to appear (1984).
Pshenichny, B.N., and Danilin, Y.M., Numerical Methods in Extremal Problems, Mir, Moscow, (1978).
Zienkiewicz, O.C., The Finite Element Method in Engineering Science, (the second expanded edition), McGraw Hill, London, 1971.
Diaz, A.R., Kikuchi N. and Taylor J.E., Optimal Design Formulation for Finite Element Grid Adaptation, in this volume.
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© 1984 Springer-Verlag
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Hou, J.W., Haug, E.J., Benedict, R.L. (1984). Shape optimization of elastic bars in torsion. In: Komkov, V. (eds) Sensitivity of Functionals with Applications to Engineering Sciences. Lecture Notes in Mathematics, vol 1086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073068
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DOI: https://doi.org/10.1007/BFb0073068
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