METHOD OF COMPENSATING LOADS FOR SHALLOW SHELLS. VIBRATION AND STABILITY PROBLEMS
Based on the integral representation of the displacements functions through Green's functions, the author proposed a method to solve the system of differential equations of the given problem. The equations were solved approximately by reducing to algebraic equations by finite difference techniques in Samarsky scheme. Some examples are given for calculation of eigenvalues of shallow shell vibration problem, which are compared with results received by Onyashvili using Galerkin method.
... method. Introduction The stability and vibration problems of shallow shells have been studied by many scientists , . The usual approaches for those problem were based on the partial differential equations of high order with unknown functions being displacement w and stress Ø functions. Integrating these equations by analytical method usually are too difficult because of the high order of the differential equations even if for bending problems . On the base of the integral representation of displacement functions through Green functions the author has proposed a numerical method for solving the differential equations of the problem. These equations were solved approximately after producing them into linear algebraic equations by finite difference technique.