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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**W. Prager and J. E. Taylor,*Problems of optimal structural design*, J. Appl. Mech.**35**, 102-106 (1968)**[2]**W. S. Hemp,*Optimum Structures*, Oxford University Press, Bath, 1973**[3]**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)**[4]**R. L. Benedict,*Maximum stiffness design for elastic bodies in contact*, J. Mech. Design**104**, 825-830 (1981)**[5]**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**[6]**J. Céa and K. Malanowski,*An example of a max-min problem in partial differential equations*, SIAM J. Control**8**, 305-316 (1970)**[7]**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)**[8]**N. Kikuchi and J. T. Oden,*Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods*, SIAM, Philadelphia, 1988**[9]**S. Kesavan,*Topics in Functional Analysis and Applications*, Wiley, New Delhi, 1989**[10]**I. Ekeland and R. Temam,*Convex Analysis and Variational Problems*, North-Holland, Amsterdam, 1976**[11]**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)**[12]**A. Klarbring and L.-E. Andersson,*On a Class of Limit States of Frictional Joints*, LiTH-IKP-R-740, Linköping, 1993**[13]**Ky Fan,*Sur un théorème minimax*, C. R. Acad. Sci. Paris**259**, 3925-3928 (1964)**[14]**M. Sion,*On general minimax theorems*, Pacific J. Math.**8**, 171-176 (1958)**[15]**J. Céa,*Optimization--Theory and Algorithms*, Tata Institute of Fundamental Research, Bombay, 1978**[16]**A. Klarbring, J. Petersson, and M. Rönnqvist,*Truss topology optimization involving unilateral contact*, J. Optim. Theory Appl.**87**, no. 1, 1-31 (1995)

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
73K40,
49N55

Retrieve articles in all journals with MSC: 73K40, 49N55

Additional Information

DOI:
https://doi.org/10.1090/qam/1402408

Article copyright:
© Copyright 1996
American Mathematical Society