TEST EXAMPLE OF CALCULATION OF THIN-WALLED STRUCTURES WITH TRUNCATED CONICAL SHELL

Problems related to axisymmetric deformation of a truncated conical shell of constant thickness under the effect of a constant pressure are encountered when calculating the linear stress-deformed state of shell structures used in the nuclear fuel cycle within the framework of a model of the Kirchhoff‐Love parameters. In practice, an analytic solution of such boundary-value problems leads to certain mathematical difficulties related to integration of one of the two differential decision equations, which is of fourth order, reduced to second order by means of a complex transformation. The differential decision equations for a truncated conical shell obtained following Meisner were transformed without any reduction in order to a new form more convenient for practical integration by means of infinite power series. The solution found in terms of power series was tested in compiling a test example of a calculation of the parameters of a deformed annular apparatus one of whose platforms is in the form of a truncated conical shell. The test example contains the results of an analytic solution of the above boundary-value problem and finite-element modeling using the CAN program. The error of the calculated stresses is estimated for an analytic solution, making it possible to consider the solution as a standard for comparison. Problems related to axisymmetric deformation of a truncated conical shell of constant thickness under the effect of a constant pressure are encountered in calculations of the linear stress-deformed state of shell structures used in the nuclear fuel cycle within the framework of a model of the Kirchhoff‐Love parameters. In practice, an analytic solution of such boundary-value problems leads to certain mathematical difficulties related to integration of one of the two differential decision equations, which is of fourth order, reduced to second order by means of a complex transformation [1, 2]. The differential decision equations for a truncated conical shell obtained following Meisner [3] (Fig. 1), which constitutes a special case of a shell of revolution, were transformed without reducing the order to a form more convenient for practical integration by means of infinite power series under the condition c > 1 and ⏐n⏐ < 0.5: