Approximate dynamic responses in random media
type: Item
instance of: scholarly article
title: Approximate dynamic responses in random media
zbMATH Open document ID: 0815.73080
published in: Acta Mechanica
publication date: 1994-01-13T00:00:00Z
review text: Complex stochastic algorithms are reduced by a stationary iterative strategy which is styled after \textit{B. A. Boley} [Q. Appl. Math. 14, 249- 257 (1956)]. Primary solutions of the thermo-elasto-dynamic system are computed for uncoupled problems. For wave propagation problems and steady harmonic responses, the lumped mass matrix representation is found to be adequate to detect random fluctuations about the mean values. The possibility of transforming stochastic problems under random loading is examined. One-dimensional finite element analysis is done for shear and bending problems of beams using the concept of equivalent random loading. Then, the stochastic differential equations are rederived for self- adjoint cases. Deterministic computer programs for dynamic problems are applied in stochastic finite element analysis with some modifications. Stochastic boundary element and stochastic finite element are formulated. The operator equation for the mean field is constructed after J. B. Keller's idea [\textit{J. B. Keller}, Proc. Symp. Appl. Math. 16, 145-170 (1964; Zbl 0202.467); ibid. 13, 227-246 (1962; Zbl 0108.147)]. The smoothing assumption permits the flux field to be deterministic for a set of deterministic model displacements. The proposed finite element technique combines methods given by \textit{V. I. Tatarski} [Wave propagation in turbulent medium (1961; Zbl 0114.419)]. The formulation may be applied to unbounded media as well, e.g. to foundation-structure interaction problems.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74J99
Mathematics Subject Classification ID: 74H50
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74S15
zbMATH DE Number: 482331
zbMATH Keywords: stationary iterative strategy
zbMATH Keywords: thermo-elasto-dynamic system
zbMATH Keywords: lumped mass matrix representation
zbMATH Keywords: equivalent random loading
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: operator equation
zbMATH Keywords: foundation-structure interaction
author: Gautam Dasgupta
reviewed by: J. Murzewski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 482331