ABOUT CONTEMPORARY APPROACHES TO REDUCTION OF COMPUTATIONAL DIMENSION OF PROBLEMS OF STRUCTURAL ANALYSIS WITHIN FINITE ELEMENT METHOD

Abstract

At present, as is known, there are many methods of reduction of computational dimension of problems of structural analysis within finite element method (FEM), including the reduction of the dimensions of the mass matrix and the stiffness matrix of the finite element model (to bring them, for example, in accordance with the “structural health monitoring” (or “test”) model of the object, which degrees of freedom are determined by the places of installation of accelerometers. In this respect, the following approaches are considered in this paper (with the corresponding analysis of the advantages and disadvantages): the Gaian reduction method, the IRS
(Improved Reduced System) reduction method and the dynamic reduction method. In addition, the so-called static finite element method for seismic analysis of underground structures, based on the substructuring technique, is considered.