The geometrically nonlinear analysis of antimetrically loaded shallow spherical shells

The present study deals with the non-linear analysis of clamped shallow spherical shellssubjected to antimetrical distributed load acting vertically downward and changing withheight. In our case, -like most of the shell problems- numerical methods have been employedin solving the set of partial differential equations which are in strongly non-linear form. First,the partial differential shell equations have been converted to ordinary differential equationsby Kantorovich method. Next, the ordinary differential equations have been transformed toalgebraic equations with the help of finite difference method. Finally, the set of non-linearalgebraic equations have been solved by Newton-Raphson method. The critical load isdetermined for various parameters for perfect and imperfect shells including both symmetricaland asymmetrical initial imperfections. The diagrams of stress resultants and load-displacement graphs have been sketched and numerical comparisons have been carried out.Keywords: Shallow spherical shells, finite difference method, Newton method, non-linearequations.JURY:Prof. Dr. R. Faruk YÜKSELER (Supervisor) Date : 15.12.2005Prof. Dr. Surkay AKBAROV Page : 103Prof. Dr. Reha ARTANProf. Dr. Uğur GÜVENProf. Dr. Mehmet Hakkı OMURTAG