scholarly journals A Consistent Dynamic Finite Element Formulation For a Pipe Using Euler Parameters

1998 ◽  
Vol 5 (2) ◽  
pp. 111-117
Author(s):  
Ara Arabyan ◽  
Yaqun Jiang
Keyword(s):  
Mass Matrix ◽  
Three Dimensional ◽  
Element Formulation ◽  
Flexible Pipe ◽  
Euler Parameters ◽  
Rotation Rates ◽  
Large Rotations ◽  
Gyroscopic Effects ◽  
External Forces ◽  
Dynamic Loading Conditions

A pipe element developed earlier for the analysis of combined large bending and torsional deformations of blood vessels under static loading is extended to model behavior in the presence of large rotations and time-varying external forces. As in the case of the earlier element, the enhanced element supports ovalization and warping of its cross-section. The enhancements presented in this paper are comprised of a mass matrix and gyroscopic effects resulting from fast rotation rates and large deformations. The effectiveness of the element is demonstrated by two examples, which simulate the three-dimensional behavior of a highly flexible pipe under dynamic loading conditions.

A New Singularity-Free Formulation of a Three-Dimensional Euler-Bernoulli Beam Using Euler Parameters

2015 ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu ◽  
H. Ren
Keyword(s):  
Mass Matrix ◽  
Three Dimensional ◽  
Constraint Equation ◽  
Bernoulli Beam ◽  
Differential Algebraic Equation ◽  
Euler Parameters ◽  
Large Rotation ◽  
Current Formulation ◽  
Nodal Coordinates ◽  
Euler Bernoulli Beam

In this investigation, a new singularity-free formulation of a three-dimensional Euler-Bernoulli beam with large deformation and large rotation is developed. The position of the centroid line of the beam is integrated from its slope, which can be easily expressed by Euler parameters. The hyper-spherical interpolation function is used to guarantee that the normalization constraint equation of Euler parameters is always satisfied. Hence, each node of a beam element has only four nodal coordinates, which is significantly fewer than an absolute node coordinate formulation (ANCF) and the finite element method (FEM). Governing equations of the beam and constraint equations are derived using Lagrange’s equations for systems with constraints, which are solved by an available differential algebraic equation solver. The current formulation can be used to calculate the static equilibrium and dynamics of an Euler-Bernoulli beam under arbitrary concentrated and distributed forces. While the mass matrix is more complex than that in an absolute nodal coordinate formulation, the stiffness matrix and generalized forces are simpler, which is amenable for calculating the equilibrium of the beam. Several numerical examples are presented to demonstrate the performance of the current formulation. It is shown that the current formulation can achieve the same accuracy as the FEM and ANCF with a fewer number of coordinates.

Mean-Axis Conditions for Finite Elements Undergoing Large Rotations and Translations

1997 ◽  
Author(s):  
Venkata R. Sonti ◽  
Om P. Agrawal
Keyword(s):  
Finite Elements ◽  
Mass Matrix ◽  
Three Dimensional ◽  
The Body ◽  
Large Rotation ◽  
Mass Matrices ◽  
Large Rotations ◽  
The Individual ◽  
Rectangular Plate Element ◽  
Individual Mass

Abstract The mean-axis conditions for three types of finite elements that undergo large rotation and translation are derived. The cases include two Lagrangian planar elements (linear triangle and linear rectangle) and a three dimensional rectangular plate element. Each case includes two elements connected at the nodes. Three separate coordinate systems are used in describing the systems. The numerical values of different matrices including the mass matrix are presented for specific cases. It may be seen that the non-linear mass matrix is expressed in terms of a set of time-invariand matrices. The total mass matrix of the body i is obtained by assembling the individual mass matrices of the finite elements of body i.

A New Singularity-Free Formulation of a Three-Dimensional Euler–Bernoulli Beam Using Euler Parameters

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu ◽  
H. Ren
Keyword(s):  
Mass Matrix ◽  
Three Dimensional ◽  
Constraint Equation ◽  
Bernoulli Beam ◽  
Differential Algebraic Equation ◽  
Euler Parameters ◽  
Current Formulation ◽  
Nodal Coordinates ◽  
Distributed Forces ◽  
Euler Bernoulli Beam

In this investigation, a new singularity-free formulation of a three-dimensional Euler–Bernoulli beam with large deformations and large rotations is developed. The position of the centroid line of the beam is integrated from its slope, which can be easily expressed by Euler parameters. The hyperspherical interpolation function is used to guarantee that the normalization constraint equation of Euler parameters is always satisfied. Each node of a beam element has only four nodal coordinates, which are significantly fewer than those in an absolute node coordinate formulation (ANCF) and the finite element method (FEM). Governing equations of the beam and constraint equations are derived using Lagrange's equations for systems with constraints, which are solved by a differential-algebraic equation (DAE) solver. The current formulation can be used to calculate the static equilibrium and linear and nonlinear dynamics of an Euler–Bernoulli beam under arbitrary, concentrated, and distributed forces. While the mass matrix is more complex than that in the ANCF, the stiffness matrix and generalized forces are simpler, which is amenable for calculating the equilibrium of the beam. Several numerical examples are presented to demonstrate the performance of the current formulation. It is shown that the current formulation can achieve the same accuracy as the ANCF and FEM with a fewer number of coordinates.

A Finite Element Formulation for the Dynamic Analysis of Machine Components Fabricated From Composite Materials

1992 ◽  
Author(s):  
A. Semos ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Element Formulation ◽  
Reinforced Composite ◽  
External Forces ◽  
Three Dimensional Space

Abstract In this paper finite element procedures are presented for analyzing the elastic-dynamic behavior of mechanical components fabricated from fiber-reinforced composite materials. An arbitrarily laminated composite plate element is created which allows the analysis of components that are moving in three dimensional space. The five D.O.F. per node static model of S. C. Panda and R. Natarajan is used as a basis for the derivation of the dynamic model. The elemental equations of motion are derived from Hamilton’s Principle. The formulation considers the total kinetic and strain energies of the moving element, together with the work due to bending, caused by the transversely acting external forces, as well as that due to the foreshortening of the element, caused by axially applied loads.

scholarly journals Experimental and Numerical Investigation about Small Clearance Journal Bearings under Static Load Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Carlo Alberto Niccolini Marmont Du Haut Champ ◽  
Fabrizio Stefani ◽  
Paolo Silvestri
Keyword(s):  
Three Dimensional ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Small Scale ◽  
Test Rig ◽  
Small Clearance ◽  
Dimensional Simulation ◽  
Dynamic Loading Conditions ◽  
Static And Dynamic Loading ◽  
Good Agreement

The aim of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., microgas turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed and the performance of its bearings was investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial rotor kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for thermoelasto-hydrodynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this paper, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RKs, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results.

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

Integrity Assessment of Damaged Flexible Pipe Cross-Sections

2014 ◽  
Author(s):  
Guomin Ji ◽  
Bernt J. Leira ◽  
Svein Sævik ◽  
Frank Klæbo ◽  
Gunnar Axelsson ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Computer Code ◽  
Flexible Pipe ◽  
Dynamic Stresses ◽  
Integrity Assessment ◽  
Residual Capacity ◽  
Nonlinear Finite Element Model

This paper presents results from a case study performed to evaluate the residual capacity of a 6″ flexible pipe when exposed to corrosion damages in the tensile armour. A three-dimensional nonlinear finite element model was developed using the computer code MARC to evaluate the increase in mean and dynamic stresses for a given number of damaged inner tensile armor wires. The study also includes the effect of these damages with respect to the associated stresses in the pressure spiral. Furthermore, the implications of a sequence of wire failures with respect to the accumulated time until cross-section failure in a probabilistic sense are addressed.

Consistent Hydrodynamic Mass for Parallel Prismatic Beams in a Fluid-Filled Container

1984 ◽  
Vol 106 (3) ◽  
pp. 270-275
Author(s):  
J. F. Loeber
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Incompressible Fluid ◽  
Finite Element Methods ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Beam Length ◽  
Step Process ◽  
Beam Bending

In this paper, representation of the effects of incompressible fluid on the dynamic response of parallel beams in fluid-filled containers is developed using the concept of hydrodynamic mass. Using a two-step process, first the hydrodynamic mass matrix per unit (beam) length is derived using finite element methods with a thermal analogy. Second, this mass matrix is distributed in a consistent mass fashion along the beam lengths in a manner that accommodates three-dimensional beam bending plus torsion. The technique is illustrated by application to analysis of an experiment involving vibration of an array of four tubes in a fluid-filled cylinder.

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