Acoustic Finite Element Analysis of Coupled Cavities Having Bulk-Reacting Absorbing Materials

1995 ◽  
Author(s):  
A. Qian ◽  
R. S. Ballinger
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Propagation Speed ◽  
Acoustic Medium ◽  
Element Formulation ◽  
Element Analysis ◽  
One Dimensional ◽  
Cavity Structure ◽  
Absorbing Material ◽  
Complex Propagation

Abstract This research presents the finite element formulation of a bulk-reacting sound absorbing material for use in interior cavity solutions. The bulk properties of the absorbing material are represented by complex density and complex propagation speed. Coupling between the vibrating cavity structure and the acoustic medium is considered. The continuity of sound pressure and the particle velocity at the interface between the acoustic domains having different properties is satisfied. Two case studies, a one-dimensional duct and a three-dimensional cavity, are considered. Analytical solutions and experimental results are compared to the finite element results. Excellent agreement has been achieved.

Mixed Finite Element Analysis of Elastomeric Butt-Joints

2005 ◽  
Vol 129 (1) ◽  
pp. 11-18 ◽  
Author(s):  
P. A. Kakavas ◽  
G. I. Giannopoulos ◽  
N. K. Anifantis
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Poisson Ratio ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Butt Joint ◽  
Element Formulation ◽  
Butt Joints ◽  
Element Analysis ◽  
Strain Energy Density Function

This paper presents a mixed finite element formulation approximating large deformations observed in the analysis of elastomeric butt-joints. The rubber has been considered as nearly incompressible continuum obeying the Mooney/Rivlin (M/R) strain energy density function. The parameters of the model were determined by fitting the available from the literature uniaxial tension experimental data with the constitutive equation derived from the M/R model. The optimum value of the Poisson ratio is adjusted by comparing the experimentally observed diametral contraction of the model with that numerically obtained using the finite element method. The solution of the problem has been obtained utilizing the mixed finite element procedure on the basis of displacement/pressure mixed interpolation and enhanced strain energy mixed formulation. For comparison purposes, an axisymmetric with two-parameter M/R model and a three-dimensional (3D) with nine-parameters M/R model of the butt-joint are formulated and numerical results are illustrated concerning axisymmetric or general loading. For small strains the stress and/or strain distribution in the 2D axisymmetric butt-joint problem was compared with derived analytical solutions. Stress distributions along critical paths are evaluated and discussed.

Development of A Three-Dimensional Membrane Element for the Finite Element Analysis of Tires

1991 ◽  
Vol 19 (1) ◽  
pp. 23-36 ◽  
Author(s):  
K. Ishihara
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Computing Time ◽  
Three Dimensional ◽  
Complex Nature ◽  
Element Formulation ◽  
Membrane Element ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Modeling Strategy

Abstract A three-dimensional membrane element was developed for the finite element analysis of tires. In general, the three-dimensional finite element analysis of tires uses a lot of computing time because of the complex nature of the problem. Major sources of complexity are, for example, nonlinearities in kinematics, material properties, boundary conditions, and the multilayer structure which is inherent to the tire. One of the ways to overcome this situation can be in the modeling strategy. This paper describes an approach where the cord-rubber composite components of the tire are modeled by membrane elements. The number of nodes required in the tire model using this strategy is considerably reduced, without any loss of accuracy, compared with models in which only ordinary solid elements are used. The nonlinear finite element formulation, numerical examples, and a comparison of the results with those obtained from models using solid elements and experimental values are given in the paper.

scholarly journals A static analysis of three-dimensional sandwich beam structures by hierarchical finite elements modelling

2017 ◽  
Vol 21 (7) ◽  
pp. 2382-2410 ◽  
Author(s):  
Gabriele De Pietro ◽  
Gaetano Giunta ◽  
Salim Belouettar ◽  
Erasmo Carrera
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Free Parameter ◽  
Three Dimensional ◽  
Sandwich Beam ◽  
Element Approximation ◽  
Element Formulation ◽  
Linear Quadratic ◽  
Beam Structures ◽  
One Dimensional

A static analysis of three-dimensional sandwich beam structures using one-dimensional modelling approach is presented within this paper. A family of several one-dimensional beam elements is obtained by hierarchically expanding the displacements over the cross-section and letting the expansion order a free parameter. The finite element approximation order over the beam axis is also a formulation free parameter (linear, quadratic and cubic elements are considered). The principle of virtual displacements is used to obtain the problem weak form and derive the beam stiffness matrix and equivalent load vectors in a nuclear, generic form. Displacements and stresses are presented for different load and constraint configurations. Results are validated towards three-dimensional finite element solutions and experimental results. Sandwich beams present a three-dimensional stress state and higher-order models are necessary for an accurate description. Numerical investigations show that fairly good results with reduced computational costs can be obtained by the proposed finite element formulation.

scholarly journals Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

2021 ◽  
Vol 5 (3) ◽  
pp. 132
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Algebraic Equations ◽  
State Representation ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Infinite State

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

scholarly journals A coupled thermo-hydro-mechanical finite element formulation of one-dimensional beam elements for three-dimensional analysis

2018 ◽  
Vol 104 ◽  
pp. 29-41 ◽  
Author(s):  
Klementyna A. Gawecka ◽  
David M. Potts ◽  
Wenjie Cui ◽  
David M.G. Taborda ◽  
Lidija Zdravković
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
One Dimensional ◽  
Beam Elements

Finite Element Analysis of Nanoscale Thermal Measurements of Superlattices

2002 ◽  
Vol 739 ◽  
Author(s):  
Jason R. Foley ◽  
C. Thomas Avedisian
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Heat Flow ◽  
Three Dimensional ◽  
Simulated Data ◽  
Element Formulation ◽  
Finite Element Code ◽  
Arbitrary Geometry ◽  
Element Analysis ◽  
Thermal Measurements

ABSTRACTA finite element analysis applicable to two- and three-dimensional heat flow in samples of arbitrary geometry and composition is presented for use in a thermal wave experiment. The finite element formulation is summarized, including the use of symmetry to simplify the problem, and the governing differential equations for the heat transport are found to be in the form of the Helmholtz equation for the specific case of a modulated heat source. Simulated data for a Nb/Si superlattice is calculated using the finite element code and is shown to agree with predictions from an analytical model, validating the approach taken.

Sign in / Sign up

Export Citation Format

Share Document