AXIALLY-SYMMETRICAL DEFORMATION OF THIN SHELLS OF REVOLUTION MADE OF A NONLINEARLY ELASTIC-MATERIAL

Approximate elasticity relations are derived for the axially symmetric deformation of a thin shell of revolution made of a non-linearly elas tic material using the three-dimensional equations of the theory of el asticity. The deformations are assumed to be of the order of a small p arameter which is proportional to the square root of the dimensionless thickness of the shell. Terms of the second order of smallness with r espect to the deformations are retained in the elasticity relations, a s a result of which the equations obtained have an error of the order of the dimensionless thickness of the shell, which is customary in the Linear theory of shells. The Kirchhoff-Love hypotheses are satisfied only in the first approximation. The axial compression of a shell, ass uming that one of the extreme parallels can freely slide along a plane of support, which is perpendicular to the axis of revolution, is cons idered as an example. A formula is obtained for the limiting load, whi ch physically and geometrically takes account of nonlinear effects in the first approximation. (C) 1997 Elsevier Science Ltd. All rights res erved.