Boundary integral equation analysis in linear viscoelasticity: Variational and saddle point formulations
type: Item
instance of: scholarly article
title: Boundary integral equation analysis in linear viscoelasticity: Variational and saddle point formulations
zbMATH Open document ID: 0734.73084
DOI: 10.1007/BF00350613
published in: Computational Mechanics
publication date: 1991-01-01T00:00:00Z
review text: This interesting paper extends a formulation previously produced by the third author (for elasticity and inviscid plasticity problems) [e.g. Mech., Res. Commun. 10, 45-52 (1983; Zbl 0511.73090); with \textit{C. Polizzotto}, Comput. Methods Appl. Mech. Eng. 60, 175-194 (1987; Zbl 0602.73081); with \textit{G. Novati} and \textit{S. Sirtori}, Discretization methods in structural mechanics, Proc. IUTAM/IACM Symp., Vienna/Aust. 1989, 191-200 (1990; Zbl 0728.73086)] to viscoelasticity applications. In this context, the approach presented includes some advantageous aspects in comparison to the classical boundary element formulation for the title problem, such as symmetry of the final system of equations. The formulation, however, requires double integration as early Galerkin type formulations, but the complete Green's functions for the fundamental problem included in the appendix indicate the same order of singularities as the early elasticity implementation. The paper still lacks examples and comparisons with previous procedures, but represents a further step in the highly original line of action of this strong team of researchers.
Mathematics Subject Classification ID: 74S15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74Hxx
zbMATH DE Number: 4215512
zbMATH Keywords: symmetric, double integration boundary integral equation
zbMATH Keywords: time evolution of the boundary unknowns
zbMATH Keywords: min-max theorem
zbMATH Keywords: algebraic equations with symmetric coefficient matrix
zbMATH Keywords: time-dependent Green's functions
zbMATH Keywords: static and kinematic discontinuities
zbMATH Keywords: Stieltjes time-convolutions
zbMATH Keywords: variational characterizations of the boundary solutions
zbMATH Keywords: symmetric Galerkin BEM
author: Angelo Carini
author: M. Diligenti
author: G. Maier
reviewed by: J. C. F. Telles
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4215512