Application of the method of spline-collocations to the solution of dynamic and static problems for structurally inhomogeneous cylindrical shells

Abstract

The method of spline collocation, in contrast to the use of double trigonometric series for the approximation of the displacements of points of the middle surface of a shell, allows us to significantly expand the class of applied problems and, in some cases, to obtain more accurate numerical results. For example, by reducing the grid spacing along the length of the shell in places, where it is supported by circular edges, or by varying the location of concentrated masses, we can reduce the order of the resolving system of algebraic equations with the same accuracy of the results obtained. The ability to change the boundary conditions at the transverse edges of the shell makes it possible to evaluate their influence on the characteristics of the stressstrain state. Note that the splinecollocation method was mainly used to study the stressstrain state of shells with slowly varying stiffness and geometric parameters along the coordinate, where the spline approximation of the solution is used. Here, the method is used for shells with a substantially nonuniform structure. In the method of calculating the static and dynamic stressstrain state and natural frequencies of the ribbed multilayer orthotropic cylindrical shells with attached masses, the method based on the splinecollocation, and the method of decomposition of a solution in eigenoscillations, the solution were tested by the wellknown example. Using numerical examples, the practical convergence of displacements, forces, and moments depending on the number of collocation points has been investigated. It should be noted that the solution of the problem uses the theory of shells and rods based on the S.P. Timoshenko shift model. The described method of studying the problems of the statics and dynamics of cylindrical closed multilayer shells with structural and technological features (stiffening ribs, attached concentrated masses) under arbitrary boundary conditions is implemented using the developed software.