Open AccessABOUT CONTEMPORARY APPROACHES TO REDUCTION OF COMPUTATIONAL DIMENSION OF PROBLEMS OF STRUCTURAL ANALYSIS WITHIN FINITE ELEMENT METHOD
Author(s) -
Alexander M. Belostotsky,
Pavel А. Akimov,
Dmitry S. Dmitriev
Publication year - 1970
Publication title -
international journal for computational civil and structural engineering
Language(s) - English
Resource type - Journals
eISSN - 2588-0195
pISSN - 2587-9618
DOI - 10.22337/1524-5845-2017-13-3-19-33
Subject(s) - finite element method , reduction (mathematics) , stiffness matrix , dimension (graph theory) , degrees of freedom (physics and chemistry) , matrix (chemical analysis) , mass matrix , dimensionality reduction , computer science , mixed finite element method , mathematics , structural engineering , algorithm , geometry , engineering , materials science , physics , artificial intelligence , pure mathematics , quantum mechanics , neutrino , nuclear physics , composite material
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.