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.

Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem

1990 ◽  
Vol 43 (5S) ◽  
pp. S381-S388 ◽  
Author(s):  
N. N. Abboud ◽  
P. M. Pinsky
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Dispersion Analysis ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Boundary Operators

In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.

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.

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

Hierarchical models for the static analysis of three-dimensional sandwich beam structures

2015 ◽  
Vol 133 ◽  
pp. 1284-1301 ◽  
Author(s):  
G. Giunta ◽  
S. Belouettar ◽  
H. Nasser ◽  
E.H. Kiefer-Kamal ◽  
T. Thielen
Keyword(s):  
Static Analysis ◽  
Hierarchical Models ◽  
Three Dimensional ◽  
Sandwich Beam ◽  
Beam Structures

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

Effective Shear Area in One Dimensional Ship Hull Finite Element Models to Predict Natural Frequencies of Vibration

2013 ◽  
Author(s):  
Osvaldo Pinheiro de Souza e Silva ◽  
Severino Fonseca da Silva Neto ◽  
Ilson Paranhos Pasqualino ◽  
Antonio Carlos Ramos Troyman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Numerical Results ◽  
Computational Method ◽  
Scale Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Area

This work discusses procedures used to determine effective shear area of ship sections. Five types of ships have been studied. Initially, the vertical natural frequencies of an acrylic scale model 3m in length in a laboratory at university are obtained from experimental tests and from a three dimensional numerical model, and are compared to those calculated from a one dimensional model which the effective shear area was calculated by a practical computational method based on thin-walled section Shear Flow Theory. The second studied ship was a ship employed in midshipmen training. Two models were made to complement some studies and vibration measurements made for those ships in the end of 1980 decade when some vibration problems in them were solved as a result of that effort. Comparisons were made between natural frequencies obtained experimentally, numerically from a three dimensional finite element model and from a one dimensional model in which effective shear area is considered. The third and fourth were, respectively, a tanker ship and an AHTS (Anchor Handling Tug Supply) boat, both with comparison between three and one dimensional models results out of water. Experimental tests had been performed in these two ships and their results were used in other comparison made after the inclusion of another important effect that acts simultaneously: the added mass. Finally, natural frequencies experimental and numerical results of a barge are presented. The natural frequencies numerical results of vertical hull vibration obtained from these approximations of effective shear areas for the five ships are finally discussed.

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