More Effective Numerical Methods for Analyzing Thermomechanical Processes in the Components of Equipment in a Nuclear Power Plant

Abstract

An increase in the efficiency of the finite-element algorithm for solving the problems of calculating the stress-strain state of the structural elements of a nuclear power system with a complicated three-dimensional geometry is examined. The construction of the finite-element models of such elements, which adequately reflect the structural features, makes it necessary to solve enormous systems of linear algebraic equations. For this it is suggested that iteration methods based on the method of conjugate gradients with preconditioning of the matrix on the basis of incomplete Holesski decomposition be used. Modifications of methods for constructing the preconditioning matrix are developed, the efficiency of the basic and modified algorithms is investigated for the example of a calculation of the stress-strain state of a IR-8 pipe panel. It is shown that the models which describe in detail the geometry and structural features of the objects studied make it possible in certain cases to decrease the conservatism of the normative estimates.