A technique for evaluation of tank boiler stability by the variational method
Abstract
The paper is devoted to developing a technique for evaluation of the stability of the railway tank boiler shell under the action of outer overpressure due to vacuum inside the boiler. The tank boiler is represented as a cylindrical shell with bottoms in the form of membranes absolutely rigid in their plane. The technique is based on the application of the moment theory of shells, the Lagrange variational principle, the approximation of displacements in the form of double Fourier series and matrix operations. A critical state before the stability loss is under consideration. Taking into account the outer pressure, the additional potential energy of deformation is defined as the work of additional bending moments on curvature change deformations when there is a non-axisymmetric deformed state. In the resolving system of equations based on the condition of the total energy minimum, the additional potential energy contributes in the form of an additional stiffness matrix and the vector of the right-hand side is zero. Due to the orthogonality of trigonometric functions during integration, the system decays into individual harmonics. For each combination of the harmonics the problem of eigenvalues is solved; as a result, the critical values of the outer pressure are found, as well as the corresponding forms of stability loss. The developed technique was verified according to the FEM results. The stability of the petrol tank-car boiler shell was studied. It was established by the calculations that there is an additional value of the critical pressure that differs in an outward direction and in an unrealistically high level. An attempt is made to establish the physical meaning of the additional solution.