existence; masonry dam; hydrostatic pressure; penalty method; convergence; shape optimization; weight minimization; finite elements
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
 G. Anzellotti: A class of non-coercive functionals and masonry-like materials
. Ann. Inst. H. Poincaré 2 (1985), 261-307. MR 0801581
 S. Bennati A. M. Genai C. Padovani: Trapezoidal gravity dams in pure compression. CNUCE - C.N.R., Internal Rep. C88-22, May 1988.
 S. Bennati M. Lucchesi: The minimal section of a triangular masonry dam. Мессаniса J. Ital. Assoc. Theoret. Appl. Mech. 23 (1988), 221-225.
 M. Giaquinta G. Giusti: Researches on the equilibrium of masonry structures
. Arch. Rational Mech. Anal. 88 (1985), 359-392. MR 0781597
 I. Hlaváček: Optimization of the shape of axisymmetric shells
. Apl. Mat. 28 (1983), 269-294. MR 0710176
 I. Hlaváček: Inequalities of Korn's type, uniform with respect to a class of domains
. Apl. Mat. 34 (1989), 105-112. MR 0990298
| Zbl 0673.49003
 I. Hlaváček R. Mäkinen: On the numerical solution of axisymmetric domain optimization problems
. Appl. Math. 36 (1991), 284-304. MR 1113952
 J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies. An Introduction
. Elsevier, Amsterdam, 1981. MR 0600655
 O. Pironneau: Optimal Shape Design for Elliptic Systems
. Springer-Verlag, New York, 1983. MR 0725856