On stiffness maximization of variable thickness sheet with unilateral contact
Author:
J. Petersson
Journal:
Quart. Appl. Math. 54 (1996), 541-550
MSC:
Primary 73K40; Secondary 49N55
DOI:
https://doi.org/10.1090/qam/1402408
MathSciNet review:
MR1402408
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Abstract: The problem of maximizing the stiffness of a linearly elastic sheet, in unilateral contact with a rigid frictionless support, is considered. The design variable is the thickness distribution, which is subject to an isoperimetric volume constraint and upper and lower bounds. The bounds may vary over the domain of the sheet, and the lower one is allowed to be zero, hence giving the possibility of obtaining topology information about an optimal design.
W. Prager and J. E. Taylor, Problems of optimal structural design, J. Appl. Mech. 35, 102–106 (1968)
W. S. Hemp, Optimum Structures, Oxford University Press, Bath, 1973
M. P. Rossow and J. E. Taylor, A finite element method for the optimal design of variable thickness sheets, AIAA Journal 11, 1566–1568 (1973)
R. L. Benedict, Maximum stiffness design for elastic bodies in contact, J. Mech. Design 104, 825–830 (1981)
M. Bendsøe, A. Diaz, and N. Kikuchi, Topology and generalized layout optimization of elastic structures, Topology Design of Structures, edited by M. P. Bendsøe and C. A. Mota Soares, Kluwer Academic Plublishers, Dordrecht, 1993, pp. 159–205
J. Céa and K. Malanowski, An example of a max-min problem in partial differential equations, SIAM J. Control 8, 305–316 (1970)
M. P. Bendsøe, On obtaining a solution to optimization problems for solid, elastic plates by restriction of the design space, J. Struct. Mech. 11, 501–521 (1984)
N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988
S. Kesavan, Topics in Functional Analysis and Applications, Wiley, New Delhi, 1989
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976
W. Achtziger, M. P. Bendsøe, A. Ben-Tal, and J. Zowe, Equivalent displacement based formulations for maximum strength truss topology design, Impact Comp. Sci. Engrg. 4, 315–345 (1992)
A. Klarbring and L.-E. Andersson, On a Class of Limit States of Frictional Joints, LiTH-IKP-R-740, Linköping, 1993
Ky Fan, Sur un théorème minimax, C. R. Acad. Sci. Paris 259, 3925–3928 (1964)
M. Sion, On general minimax theorems, Pacific J. Math. 8, 171–176 (1958)
J. Céa, Optimization—Theory and Algorithms, Tata Institute of Fundamental Research, Bombay, 1978
A. Klarbring, J. Petersson, and M. Rönnqvist, Truss topology optimization involving unilateral contact, J. Optim. Theory Appl. 87, no. 1, 1–31 (1995)
W. Prager and J. E. Taylor, Problems of optimal structural design, J. Appl. Mech. 35, 102–106 (1968)
W. S. Hemp, Optimum Structures, Oxford University Press, Bath, 1973
M. P. Rossow and J. E. Taylor, A finite element method for the optimal design of variable thickness sheets, AIAA Journal 11, 1566–1568 (1973)
R. L. Benedict, Maximum stiffness design for elastic bodies in contact, J. Mech. Design 104, 825–830 (1981)
M. Bendsøe, A. Diaz, and N. Kikuchi, Topology and generalized layout optimization of elastic structures, Topology Design of Structures, edited by M. P. Bendsøe and C. A. Mota Soares, Kluwer Academic Plublishers, Dordrecht, 1993, pp. 159–205
J. Céa and K. Malanowski, An example of a max-min problem in partial differential equations, SIAM J. Control 8, 305–316 (1970)
M. P. Bendsøe, On obtaining a solution to optimization problems for solid, elastic plates by restriction of the design space, J. Struct. Mech. 11, 501–521 (1984)
N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988
S. Kesavan, Topics in Functional Analysis and Applications, Wiley, New Delhi, 1989
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976
W. Achtziger, M. P. Bendsøe, A. Ben-Tal, and J. Zowe, Equivalent displacement based formulations for maximum strength truss topology design, Impact Comp. Sci. Engrg. 4, 315–345 (1992)
A. Klarbring and L.-E. Andersson, On a Class of Limit States of Frictional Joints, LiTH-IKP-R-740, Linköping, 1993
Ky Fan, Sur un théorème minimax, C. R. Acad. Sci. Paris 259, 3925–3928 (1964)
M. Sion, On general minimax theorems, Pacific J. Math. 8, 171–176 (1958)
J. Céa, Optimization—Theory and Algorithms, Tata Institute of Fundamental Research, Bombay, 1978
A. Klarbring, J. Petersson, and M. Rönnqvist, Truss topology optimization involving unilateral contact, J. Optim. Theory Appl. 87, no. 1, 1–31 (1995)
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Article copyright:
© Copyright 1996
American Mathematical Society
