The direct determination of nonlinear displacements of arbitrarily supported shallow shells using mathematical programming techniques

Abstract

The nonlinear behavior of an asymmetrically loaded shallow shell of revolution with arbitrary edge conditions is investigated. The approach used in the present investigation is to obtain the displacement set which minimizes the finite-difference approximation of the shell potential energy by using mathematical programing techniques. In order to determine the mathematical programing technique which is most suitable for minimizing the shell potential several methods which have appeared in the literature are evaluated. These include the method of steepest descent, the conjugate gradient method, the variable metric method and the generalized Newton-Raphson procedure. A combination of the conjugate gradient method and the generalized Newton-Raphson procedure is found most suitable. Results of the present investigation are compared with published data for the buckling of a uniformly loaded clamped spherical cap. Additional results are presented which show the effect of changes in edge restraint and changes in shell geometry on the buckling pressure for uniformly loaded shallow shells.