Abstract
The optimal shape design of a two dimensional body on a rigid foundation is analyzed. The problem is how to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that a certain energy integral (total potential energy, for example) will be minimized. It is assumed that the material of the body is elastic. Some remarks will be given concerning the design of an elastic perfectly plastic body. Numerical examples will be given.
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References
BendsSe, M.P., Olhoff, N. and Sokolowski, J.: Sensitivity analysis of problems of elasticity with unilateral constraints, J. Struct. Mech. 13 (2), 1985, pp. 201–222.
Benedict, R., Sokolowski, J. and Zolesio, J.P.: Shape optimization for contact problems, In System Modelling and Optimization, P. Toft-Cristensen (ed.), LN Control and Information Sciences, Vol. 59, Springer Verlag, 1984, pp. 790–799.
Haslinger, J., Hor6k, V. and Neittaanmäki, P.: Shape optimization in contact problem with friction. - Numer. Funct. Anal. and Optimiz., 1986, to appear.
Haslinger, J. and Neittaanmäki, P.: On the existence of optimal shapes in contact problems. Numer. Funct. Anal. and Optimiz., Vol. 7, No. 3–4, 1984, pp. 107–124.
Haslinger, J. and Neittaanmäki, P.: Shape optimization of an elastic body in contact with rigid foundation, in Proc. 2nd Int. Confr. on Variational Methods in Engineering (Ed. C.A. Brebbia), Springer Verlag, 1985, pp. 6–31–6–4o.
Haslinger, J. and Neittaanmäki, P.: On the existence of optimal shapes in contact problems - perfectly plastic bodies, Univ. Jyväskylä, Dept. Math., Preprint 42, 1986, Comput. Mech., to appear.
Haslinger, J. and Neittaanmäki, P.: Shape optimization in contact problems. Approximation and numerical realization, to appear.
Haslinger, J., Neittaanmäki, P., Kaarna, A. and Tiihonen, T.: Optimal shape control of the domain in unilateral boundary value problems. Part I. Abstract setting and Dirichlet-Signorini problem. Part II. Design of an elastic body. Lappeenranta University of Technology, Dept. Physics and Mathematics, Reports 4–5, 1986.
Haslinger, J., Neittaanmäki, P. and Tiihonen, T.: Shape optimization of an elastic body in contact based on penalization of the state inequality, Apl. Math., 31 (1986), pp. 54–77.
Haug, E.J. and Cea, J. (ed.): Optimization of distributed parameter structures, Nato Advances Study Institute Series, Series E, Alphen aan den Rijn: Sijthoff & Noordhoff, 1981.
Pironneau, O.: Optimal shape design for elliptic systems, Springer Series in Computational Physics, Springer Verlag, New York, 1984.
Sokolowski, J. and Zolesio, J.P.: Shape sensitivity analysis of elastic struc-tures, The Danish Center of Applied Mathematics and Mechanics, Report No. 289, 1984.
Zolesio, J.P.: The material derivative (or speed) method for shape optimiza-tion, in [10], pp. 1089–1150.
Zolesio, J.P.: Shape controlability of free boundaries, as [2], pp. 354–361.
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Haslinger, J., Neittaanmäki, P., Tiihonen, T. (1986). Shape Optimization in Contact Problems. 1. Design of an Elastic Body. 2. Design of an Elastic Perfectly Plastic Body. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007544
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DOI: https://doi.org/10.1007/BFb0007544
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