scholarly journals Nonlinear Modeling of Cables with Flexural Stiffness

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Walter Lacarbonara ◽  
Arnaud Pacitti
Keyword(s):  
Finite Difference ◽  
Nonlinear Modeling ◽  
Continuation Method ◽  
Normal Modes ◽  
Bending Moment ◽  
Flexural Stiffness ◽  
Weak Formulation ◽  
Static Responses ◽  
Quasistatic Regime ◽  
Extensible Cables

A geometrically exact formulation of cables suffering axis stretching and flexural curvature is presented. The dynamical formulation is based on nonlinearly viscoelastic constitutive laws for the tension and bending moment with the additional constitutive nonlinearity accounting for the no-compression condition. A continuation method, combined with a mixed finite-difference spatial discretization, is then employed to path-follow the static responses of cables subject to forces or support displacements. These computations, conducted in the quasistatic regime, are based on cables with linearly elastic material behaviors, whereas the nonlinearity is in the geometric stiffness terms and the no-compression behavior. The finite-difference results have been confirmed employing a weak formulation based on quadratic Lagrangian finite elements. The influence of the flexural stiffness on the nonlinear static responses is assessed comparing the results with those obtained for purely extensible cables. The properties of the frequencies of the linear normal modes of cables with flexural stiffness are also investigated and compared with those of purely extensible cables.

Comparison Of Finite-Difference And Analytic Microwave Calculation Methods

1996 ◽  
Vol 430 ◽  
Author(s):  
F. I. Friedlander ◽  
H. W. Jackson ◽  
M. Barmatz ◽  
P. Wagner
Keyword(s):  
Finite Difference ◽  
Numerical Evaluation ◽  
Normal Modes ◽  
Materials Processing ◽  
Calculation Methods ◽  
Power Absorption ◽  
Microwave Cavities ◽  
Analytic Expressions ◽  
Lossy Dielectric ◽  
Electromagnetic Solver

AbstractNormal modes and power absorption distributions in microwave cavities containing lossy dielectric samples were calculated for problems of interest in materials processing. The calculations were performed both using a commercially available finite-difference electromagnetic solver and by numerical evaluation of exact analytic expressions. Results obtained by the two methods applied to identical physical situations were compared. Our studies validate the accuracy of the finite-difference electromagnetic solver. Relative advantages of the analytic and finitedifference methods are discussed.

scholarly journals CALCULATION OF THE BENDING ELEMENTS WITH ALLOWANCE FOR THE PHYSICAL NONLINEARITY OF THE STRAIN

2016 ◽  
Vol 1 (12) ◽  
pp. 58-64
Author(s):  
Шишов ◽  
Ivan Shishov ◽  
Рязанов ◽  
Maksim Ryazanov ◽  
Рощина ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Bending Moment ◽  
Physical Nonlinearity ◽  
Deflection Curve ◽  
Physical Strain ◽  
Concrete Condition ◽  
The Finite Difference Method ◽  
Limiting Value ◽  
Small Spacing

An algorithm of the reinforced binding elements calculation with allowance for the physical strain of concrete and reinforcement has been suggested. The three linear diagram of the concrete condition and the two linear of the tensile reinforcement that correspond to the recommended norms in Russia have been used. The task has been solved by the method of linear approximation. The finite difference method has been used at each approximation that allows to define the beam rigidity individually for each dot j =1,2 , dotted on the beam with some small spacing. A method of determining the deflection curve bending, the bending moment, the rigidity as well as the compression areas of the reinforcement suitable for any deformation of the concrete most tensile fabric from 0 to limiting value ε_b2 has been suggested. A solution for the continuous three-span beam has also been introduced.

Effective flexural stiffness of slender structural concrete columns

2008 ◽  
Vol 35 (4) ◽  
pp. 384-399 ◽  
Author(s):  
Timo K. Tikka ◽  
S. Ali Mirza
Keyword(s):  
Reinforced Concrete ◽  
Full Range ◽  
Strain Curve ◽  
Bending Moment ◽  
Concrete Columns ◽  
Flexural Stiffness ◽  
Column Length ◽  
Stress Strain Curve ◽  
Structural Concrete ◽  
Composite Steel

The CSA A23.3 standard permits the use of a moment-magnifier approach for the design of slender reinforced concrete and composite steel–concrete columns. This approach is strongly influenced by the effective flexural stiffness (EI), which varies due to the nonlinearity of the concrete stress–strain curve and the cracking along the column length, among other factors. The EI equations given in the CSA standard are approximate when compared with the EI values computed from the axial load – bending moment – curvature relationships. This study was conducted to determine the influence of a full range of variables on EI used for the design of slender reinforced concrete and composite steel–concrete columns, and also to examine the existing CSA EI equations. Over 27 000 isolated concrete columns, each with a different combination of specified variables, in symmetrical single-curvature bending were simulated to generate the stiffness data. Two new design equations to compute EI of structural concrete columns were then developed from the simulated stiffness data and are proposed as an alternative to the existing CSA design equations for EI.

Analysis of Internal Force and Deformation for Pit Retaining Structure by Considering the Interaction of Pile Stiffness

2013 ◽  
Vol 838-841 ◽  
pp. 397-401
Author(s):  
Ming Li ◽  
Ren Wang Liang
Keyword(s):  
Finite Difference ◽  
Engineering Design ◽  
Axial Force ◽  
Influence Factors ◽  
Bending Moment ◽  
Internal Force ◽  
Equivalent Stiffness ◽  
Deep Excavation ◽  
Retaining Structure ◽  
Design Software

In this paper, taking one deep excavation engineering as an example, modeling by the FLAC3D finite difference software, combining with the Lizheng deep excavation supporting design software, taking the equivalent stiffness of combination pile as 2.300-4.789(10-2m3), and analyzing the pile body bending moment, anchor axial force and pit deformation by considering interaction of pile stiffness. In addition, in this paper the influence factors of pile stiffness has been discussed, and provides a reference for the engineering design.

Numerical Analysis of Stabilization of Slopes Overlying Bedrock Using Piles and Effect of Socketed Length of Pile on Stability

2014 ◽  
Vol 580-583 ◽  
pp. 424-431 ◽  
Author(s):  
Mudthir Bakri ◽  
Yuan You Xia ◽  
Hua Bing Wang
Keyword(s):  
Numerical Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Shear Force ◽  
Factor Of Safety ◽  
Bending Moment ◽  
Computer Code

Piles are used widely for stabilization of landslides. To stabilize a slope settled on bedrock with piles the required factor of safety must be checked, and pile should be designed properly. Piles should be socketed into firm rock to prevent uprooting or overturning .In this research it is aimed to look into the socketed length of pile in bedrock. Therefore the parameters that affect the factor of safety of slope/pile system such as location, length, spacing and diameter of piles are analyzed. The effect of socketed length of pile in rock on pile behavior is investigated by plotting the shear force and bending moment diagrams along pile. The optimal pile position is found to be located slightly upper of the middle of the slope. The minimum socketed length after which the factor of safety will be remained constant is found to be 0.12L where L is pile length.FLAC3D computer code based on finite difference method is used to simulate the slope/pile system.

scholarly journals Stable wide‐angle Fourier finite‐difference downward extrapolation of 3‐D wavefields

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 872-882 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
Finite Difference ◽  
Continuation Method ◽  
Phase Error ◽  
Azimuthal Anisotropy ◽  
Laplacian Operator ◽  
Lateral Velocity ◽  
Data Set ◽  
Frequency Dependent ◽  
Reference Velocity ◽  
Velocity Variations

I present an unconditionally stable, implicit finite‐difference operator that corrects the constant‐velocity phase‐shift operator for lateral velocity variations. The method is based on the Fourier finite‐difference (FFD) method. Contrary to previous results, my correction operator is stable even when the medium velocity has sharp discontinuities, and the reference velocity is higher than the medium velocity. The stability of the new correction enables the definition of a new downward‐continuation method based on the interpolation of two wavefields: the first wavefield is obtained by applying the FFD correction starting from a reference velocity lower than the medium velocity; the second wavefield is obtained by applying the FFD correction starting from a reference velocity higher than the medium velocity. The proposed Fourier finite‐difference plus interpolation (FFDPI) method combines the advantages of the FFD technique with the advantages of interpolation. A simple and economical procedure for defining frequency‐dependent interpolation weight is presented. When the interpolation step is performed using these frequency‐dependent interpolation weights, it significantly reduces the residual phase error after interpolation, the frequency dispersion caused by the discretization of the Laplacian operator, and the azimuthal anisotropy caused by splitting. Tests on zero‐offset data from the SEG‐EAGE salt data set show that the FFDPI method improves the imaging of a fault reflection with respect to a similar interpolation scheme that uses a split‐step correction for adapting to lateral velocity variations.

Ship Hull Bottom Slamming

1995 ◽  
Vol 117 (4) ◽  
pp. 252-259 ◽  
Author(s):  
P. Rassinot ◽  
A. E. Mansour
Keyword(s):  
Normal Modes ◽  
Bending Moment ◽  
Simple Expression ◽  
Ship Hull ◽  
Hydrodynamic Load ◽  
Maximum Value ◽  
Strip Theory ◽  
The Impact ◽  
Increasing Function ◽  
Free Beam

A method is presented to evaluate the hull bending moment due to bottom slamming. Theoretical explanations and updates are given to the commonly used empirical results, and some observations are made on slamming. An energy approach combined with a strip theory is used to get the hydrodynamic load, and to analyze the effects of the forward velocity. Impacts of simple bodies are simulated numerically to describe these loads. The ship hull is represented as a nonuniform free-free beam, and its response is decomposed into normal modes; only the contribution of the first one is kept. In a numerical example, the bending moment during the impact is determined. It is shown that its value when the impact is over is much harder to predict. The maximum value of the bending moment, however, occurs during the impact, and is an increasing function of the vertical velocity, as expected. A simple expression is given for it.

scholarly journals Application of the Electronic Differential Analyzer to the Oscillation of Beams, Including Shear and Rotary Inertia

1955 ◽  
Vol 22 (1) ◽  
pp. 13-19
Author(s):  
C. E. Howe ◽  
R. M. Howe
Keyword(s):  
Transverse Shear ◽  
Normal Modes ◽  
Bending Moment ◽  
Accurate Method ◽  
Rotary Inertia ◽  
Lateral Vibration ◽  
Wide Range ◽  
Modes Of Vibration ◽  
Set Up ◽  
Differential Analyzer

Abstract The equations for normal modes of lateral vibration of beams are set up on the electronic differential analyzer. Beam deflections due to transverse shear and rotary-inertia forces are included. The differential analyzer is shown to be a fast and accurate method for solving the problem. Analyzer outputs include mode shape, slope, bending moment, and shear force along the beam. Curves showing the normal-mode frequencies for the first three modes of vibration of a uniform free-free beam are presented for a wide range of transverse shear and rotary-inertia parameters. The electronic differential analyzer also is utilized to solve the problem of lateral vibration of nonuniform beams.

scholarly journals MÉTODO DE DIFERENCIAS FINITAS PARA UN PROBLEMA DE VALOR DE FRONTERA UNIDIMENSIONAL

2019 ◽  
pp. 5-8
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problem ◽  
Difference Method ◽  
Sparse Matrices ◽  
Boundary Value ◽  
Bending Moment ◽  
One Dimensional ◽  
Dimensional Boundary ◽  
The One

MÉTODO DE DIFERENCIAS FINITAS PARA UN PROBLEMA DE VALOR DE FRONTERA UNIDIMENSIONAL THE FINITE- DIFERENCE METHOD FOR A ONE-DIMENSIONAL BOUNDARY-VALUE PROBLEM Luis Jaime Collantes Santisteban, Samuel Collantes Santisteban DOI: https://doi.org/10.33017/RevECIPeru2006.0011/ RESUMEN En este trabajo se considera el problema de valor de frontera unidimensional dado en (1). Se aproxima la solución del problema mediante el método de diferencias finitas suponiendo que la función c(x) es no negativa sobre 0,1, lo que permite establecer la convergencia del método de aproximación. El uso del método de diferencias finitas, a la vez, involucra la solución de sistemas de ecuaciones lineales con matrices muy ralas, cuyos ceros están posicionados de una manera remarcable. Dichas matrices son de tipo tridiagonal. Para la solución de dichos sistemas se ha utilizado el método de Thomas. Palabras clave: problema de valor de frontera unidimensional, diferencias finitas, matriz tridiagonal, método de Thomas, momento flexionante. ABSTRACT In this work the one-dimensional boundary-value problem given in (1) is considered. The solution of the problem by means of finite-difference method comes near supposing that the function c(x) is nonnegative on 0,1, which allows to establish the convergence of the considered method of approximation. The use of the finite-difference method, in turn, involves the solution of linear systems with very sparse‟ matrices, whose zeros are arranged in quite remarkable fashion. These matrices are of tridiagonal type. For the solution of these systems the Thomas‟ method has been used. Keywords: one-dimensional boundary-value problem, finite-difference, tridiagonal matrix, Thomas‟ method, bending moment.

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