Analysis of Membranes Stretched Over a Unilateral Support
The main objective of the present. paper is to find the equilibrium configuration of membranes of various shapes, stretched over a plane frame, in the vicinity of a rigid, two-dimensional profile which supplies unilateral constraints to its deflections. The problem is considered under the following conditions: (i) the membrane is subjected to assigned, constant tension forces and to transversal loads; (ii) boundary conditions of the membrane are given by zero displacements along the contour of the frame; (iii) the deformations are small; (iv) the contact is frictionless and reactions are assumed to be vertical.
References
G. DUVANT and J. L. LIONS, Les inequations en mecanique et physique, Dunod, Paris, 1972.
P. VILLAGGIO, Monodimensional solids with constrained solutions, Meccanica, 2, 1, 1967.
P. VILLAGIO, Comparison properties for solutions of unilateral problems, Meccanica, 13, 1, 1978.
L. CORRADI and G. MAIER, A matrix theory of elastic-locking structures, Meccanica, 4, 4, 1969.
G. MAIER, Mathematical programming methods in elastoplastic analysis, Variational methods in engineering, Proc. Int. Conf. 2, Southampton, Univ. Press, 1973.
P. D. PANAGIOTOPOULOS, Convex analysis and unilateral static problems, lngenieur Archiv, 75, 1976.
A. CANNAROZZl and A. TRALLI, Probiermi di vinocolamento monolatero negli spostamenti di sistemi discreti, 3rd Nat. Congr. of Itatian Assoc. for Theoretical and Applied Mechanics; Cagliari, 1976.
L. BINDA, R. CONTRO, Unilateral contact problems for cables, Engineering Structures, 1, 1979.
C. W. CRYER, The solution of a quadratic programming problem using systematic overrelaxtition, SIAM J. Control, 9, 1971.
O. L. MANGASARIAN, Solution of linear complementarity problems by linear programming, Comp. Sciences Technical Report N. 257, Comp. Sc. Dep., Univ. Wisconsin, 1975.