Problems of Computational Mechanics Relate to Finite-Element Analysis of Structural Constructions

Abstract

The problems of computational mechanics, concerning with application of finite element analysis to structural constructions, are discussed. Our attention is addressed to medium-class software for personal computers with which structural constructions are usually analyzed. The complexity of a system and simplicity of its components, the large-scale of finite element problem, the heterogeneity of finite elements and its coupling, the estimation of correctness of finite element model, the problems of seismic analysis, the problem of indeterminacy and so on are the objective of this work.

Block Preconditioned Conjugate Gradient Method for Extraction of Natural Vibration Frequencies in Structural Analysis

“…The problems of structural mechanics often demonstrate the slow convergence due to using of different types of finite elements, thin-walled finite elements of floors, roofs and walls, considerable scattering of stiffness etc. [15]. Therefore, it is crucial to construct the effective preconditioning for accelerating of convergence of the PCG method.…”

About analysis of large problems of structural mechanics on multi-core computers

“…Расчетные модели современных многоэтажных зданий (чаще всего именно такие объекты порождают СЛАУ высокого порядка) часто являются плохо обусловленными вследствие наличия множества конечных элементов тонких пластин и оболочек, сопряжения разнотипных элементов (стержней, пластин, оболочек и объемных элементов), наличия жестких связей, упругих опор и т. д. [12]. Кроме того, из-за сложности геометрии контуров не всегда удается выдержать оптимальные соотношения сторон и оптимальные углы для конечных элементов пластин и оболочек.…”

Parallel Algorithms for Forward and Back Substitution in Linear Algebraic Equations of Finite Element Method

“…When dealing with problems of structural and solid mechanics by using finite element method, we have to solve systems of high-order linear algebraic equations with a sparse symmetric matrix. Direct methods are usually used to solve this class of problems, because most design models are poorly conditioned, which leads to slow convergence of iterative solvers [1], [2]. The solution of a system of linear algebraic equations, relying on the use of the direct method, consists of the following stages: matrix factorization and forward/back substitutions.…”

“…6 in(2). The degree of dependency of blocks V 2 and V 5 becomes equal to zero, and that of the block V 6 becomes equal to 2.…”