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Efficient treatment of stress singularities in poroelastic wave based models using special purpose enrichment functions

Elke Deckers, +3 more
- 01 Jun 2011 - 
- Vol. 89, Iss: 11, pp 1117-1130
TLDR
In this article, the authors discussed the application of the Wave Based Method for the particular case that stress singularities are present in corners of the poroelastic domain and proposed a suitable set of enrichment functions to extend the conventional set of expansion functions.
About: 
This article is published in Computers & Structures.The article was published on 2011-06-01 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Finite element method & Asymptotic analysis.

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The wave based method: An overview of 15 years of research

Elke Deckers, +9 more
- 01 Jun 2014 - 
TL;DR: An overview of the current state of the art of the Wave Based Method, a comparison of the properties of the wave functions and element-based prediction techniques, application areas, extensions to the method such as hybrid and multi-level approaches and the most recent developments are given.
Journal ArticleDOI

On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach

Karel Vergote, +3 more
- 01 Jun 2011 - 
TL;DR: This paper proposes a framework for coupling Trefftz-based deterministic models with statistical SEA models, and the recently developed and computationally more efficient Wave Based Method (WBM) is being used.
Journal ArticleDOI

An efficient Wave Based Method for solving Helmholtz problems in three-dimensional bounded domains

Bert Van Genechten, +10 more
- 01 Jan 2012 - 
TL;DR: In this article, the authors discuss the use of the Wave Based Method for the analysis of time-harmonic three-dimensional interior acoustic problems, which is an alternative deterministic technique which is based on the indirect Trefftz approach.
Journal ArticleDOI

A modal-based reduction method for sound absorbing porous materials in poro-acoustic finite element models

Romain Rumpler, +2 more
- 08 Nov 2012 - 
TL;DR: An original modal reduction technique, involving real-valued modes computed from a classical eigenvalue solver is proposed to reduce the size of the problem associated with the porous media, suited for homogeneous porous layers.
Journal ArticleDOI

The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media

Jean-Daniel Chazot, +2 more
- 14 Feb 2014 - 
TL;DR: An extension of the Partition of Unity Finite Element Method to the numerical simulation of Biot's waves in poroelastic materials is presented and it is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.
References
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Journal ArticleDOI

Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range

Maurice A. Biot
- 01 Mar 1956 - 
TL;DR: In this article, a theory for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid is developed for the lower frequency range where the assumption of Poiseuille flow is valid.
Journal ArticleDOI

Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials

J.‐F. Allard, +1 more
- 01 May 1994 - 
TL;DR: In this paper, the authors present a method for estimating the effective density and the bulk modulus of open cell foams and fibrous materials with cylindrical porous layers. But the authors do not consider the effect of noise on the propagation of sound.
Book

Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions

Parry Moon, +1 more
TL;DR: In this article, the vector Helmholtz equation was used to describe the transformation in the complex plane of eleven coordinate systems, including three differential equations, and three differentially varying functions.

Ein Gegenstuck zum Ritzschen Verfahren

E. Trefftz
Book

Advanced Engineering Mathematics

Michael D. Greenberg
TL;DR: In this paper, the authors present a review of partial fraction expansions of differential algebraic expressions, as well as a discussion of the existence and uniqueness of solutions of systems of linear algebraic equations.
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A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

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- 15 Jan 2011 - 

Trefftz-Based Methods for Time-Harmonic Acoustics

Bert Pluymers, +3 more
- 17 Aug 2007 - 

An efficient wave based prediction technique for plate bending vibrations

Caroline Vanmaele, +2 more
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- 06 Jul 1999 - 
Frequently Asked Questions (1)
Q1. What are the contributions in "Efficient treatment of stress singularities in poroelastic wave based models using special purpose enrichment functions" ?

This paper discusses the application of the Wave Based Method for the particular case that stress singularities are present in corners of the poroelastic domain. Based on an asymptotic analysis, the paper derives a criterion to predict the presence of stress singularities and proposes a suitable set of enrichment functions to extend the conventional set of expansion functions. The beneficial effect of incorporating these functions on the convergence of the Wave Based Method is illustrated by means of a numerical validation study.