Optimal Design of the Cyclically Symmetrical Structure Under Static Load

Abstract

A method is proposed for solving the problems of optimal design of cyclically symmetric structures under static loading, which has been tested on critical structural elements of hydraulic turbines. One of the basic problems in the design of hydraulic turbines is considered, namely, ensuring their strength and reliability under continuous operation under the influence of a static loading. The problem of optimal design of the initial and modified covers of a rotary-blade hydraulic turbine operating in the normal mode has been solved. A Kaplan turbine cover is a complex spatial structure consisting of thin-walled elements. Therefore, the finite element method is used for the calculation to most fully take into account the design features and the spectrum of external influences acting during operation. As the initial design, covers with an initial and modified hole in the rib were selected. The geometric parameters of the cover are modified to minimize the cover weight. The thicknesses of structural elements are taken as design variables. The minimum and maximum thicknesses, as well as maximum stress intensity values are limited. The objective function is the cover weight. The problem of optimal design is solved with the help of the gradient method using a finite-difference analogue of a gradient of the objective function. The distribution of axial displacements and stress intensity in the original and modified cover design during normal operation was obtained. It was found that the mass of the cover structure was reduced by 30%, and the rolled stock thickness range was downsized by five positions, which is significant in the manufacture of a new design. In this case, the stress values in the optimal structure during the modification of the hole in the ribs did not exceed the admissible values. The proposed approach will subsequently be applied to the analysis of elements of aircraft structures.