scholarly journals Wave Propagation in X-Section Piles for Low Strain Integrity Testing: Three-Dimensional Effects

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yanling Zhang ◽  
Yuming Fan ◽  
Zheng Li ◽  
Chenglong Wang ◽  
Xuanming Ding
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Propagation Characteristic ◽  
Scale Model ◽  
Geometrical Parameters ◽  
Response Characteristics ◽  
Dimensional Effects ◽  
Velocity Response

X-section cast-in-place concrete pile (referred to as XCC pile) has a different velocity response compared with circular section pile in the low strain testing due to the special cross section. Full-scale model tests of XCC pile were conducted to reveal the velocity response characteristics. The time-domain velocity responses on the pile top were obtained, which showed obvious three-dimensional effects because of the different high-frequency interferences. The test results were compared with the numerical results to validate the numerical model. Furthermore, numerical simulations were conducted to investigate the propagation characteristic of velocity waves along the longitudinal direction in the pile. The results indicated that the wave propagation was complicated as a result of the superposition of the incident wave and the reflected wave. The effects of the geometrical parameters of cross section on the three-dimensional effects of velocity responses were also studied. Three-dimensional effects would be more significant with a larger arc distance. However, the effects of arc angle were not obvious.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Three-dimensional cracked discs under anti-plane loading and effects of the boundary conditions

2015 ◽  
Vol 6 (4) ◽  
pp. 541-564 ◽  
Author(s):  
Filippo Berto ◽  
Alberto Campagnolo
Keyword(s):  
Boundary Conditions ◽  
Control Volume ◽  
Three Dimensional ◽  
Scale Model ◽  
Mode Iii ◽  
Coupled Modes ◽  
Present Contribution ◽  
Content Type ◽  
Dimensional Effects ◽  
Notch Tip

Purpose – Accordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions associated with the interaction between the V-notch tip and the material under the remotely applied loading conditions. This induces complex three-dimensional stress and displacement fields in the proximity of the notch tip, which are worthy of investigation. The paper aims to discuss these issues. Design/methodology/approach – Starting from Sih and Tang’s model, in the present contribution the authors propose some analytical expressions for the calculation of the strain energy density (SED) averaged over a control volume embracing the V-notch tip. The expressions vary as a function of the different boundary conditions. Dealing with the specific crack case, the results from the analytical frame are compared with those determined numerically under linear-elastic hypotheses, by applying different constraints to the through-the-thickness crack edges in three-dimensional discs subjected to Mode III loading. Free-free and free-clamped cases are considered. Findings – Due to three-dimensional effects, the application of a nominal Mode III loading condition automatically provokes coupled Modes (I and II). Not only the intensity of the induced modes but also their degree of singularity depend on the applied conditions on the crack flanks. The variability of local SED through the thickness of the disc is analysed by numerical analyses and compared with the theoretical trend. Originality/value – The capability of the SED to capture the combined three-dimensional effects is discussed in detail showing that this parameter is particularly useful when the definition of the stress intensity factors (SIFs) is ambiguous or the direct comparison between SIFs with odd dimensionalities is not possible.

scholarly journals Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
G. Giunta ◽  
S. Belouettar
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Approximation Order ◽  
Higher Order ◽  
Geometrical Parameters ◽  
Thin Walled ◽  
Three Dimensional Finite Element

This paper addresses a free vibration analysis of thin-walled isotropic beams via higher-order refined theories. The unknown kinematic variables are approximated along the beam cross section as aN-order polynomial expansion, whereNis a free parameter of the formulation. The governing equations are derived via the dynamic version of the Principle of Virtual Displacements and are written in a unified form in terms of a “fundamental nucleus.” This latter does not depend upon order of expansion of the theory over the cross section. Analyses are carried out through a closed form, Navier-type solution. Simply supported, slender, and short beams are investigated. Besides “classical” modes (such as bending and torsion), several higher modes are investigated. Results are assessed toward three-dimensional finite element solutions. The numerical investigation shows that the proposed Unified Formulation yields accurate results as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam.

REFINED BEAM THEORIES BASED ON A UNIFIED FORMULATION

2010 ◽  
Vol 02 (01) ◽  
pp. 117-143 ◽  
Author(s):  
ERASMO CARRERA ◽  
GAETANO GIUNTA
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Cross Sections ◽  
Order Approximation ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Approximation Order ◽  
Form Solution ◽  
Geometrical Parameters ◽  
Beam Theories

This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.

scholarly journals Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120384 ◽  
Author(s):  
Simon N. Gaulter ◽  
Nicholas R. T. Biggs
Keyword(s):  
Cross Section ◽  
Turning Point ◽  
Harmonic Wave ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Interior Layer ◽  
Oscillatory Behaviour ◽  
Trapped Modes ◽  
Trapped Mode ◽  
Time Harmonic

In this paper, we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying ‘bulge’, symmetric in the longitudinal direction. Extending previous research carried out in the two-dimensional case, we first use a WKBJ-type ansatz to identify the possible quasi-mode solutions that propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-off regions. We note that the expansions are non-uniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-off regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x =0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

Experimental and Theoretical Study of Three-Dimensional Effects on Vertical Wave-in-Deck Forces

2009 ◽  
Author(s):  
Rolf Baarholm
Keyword(s):  
Model Test ◽  
Three Dimensional ◽  
Water Entry ◽  
Scale Model ◽  
Two Dimensional ◽  
Wave Impact ◽  
Dimensional Effects ◽  
Von Karman ◽  
Von Kármán ◽  
Water Exit

In order to validate theory for computing wave-in-deck loads of offshore platforms, a small scale model test campaign of wave impact on an idealized platform deck is performed at Towing Tank no. II at MARINTEK. The main objectives of the tests were to assess three-dimensional effects and to better understand the effect transverse and longitudinal structural members have on the fluid flow. The emphasis in the present paper is to demonstrate the three-dimensional effects. Model tests of the same structure were performed for both two-dimensional and three-dimensional flow conditions. The model test results show that three-dimensional effects significantly reduce the wave-in-deck loads. In particular, for the water exit phase, the vertical force is almost halved due to three-dimensional effects. Two different two-dimensional methods are used to study water impact on the deck: one method is based on a generalization of Wagner’s impact theory while the latter is a simple von Karman approach. Moreover, a three-dimensional correction is introduced. Comparisons show that the Wagner based method yields good results for the water entry phase, but it overestimates the water exit force and underestimates the duration of the wave-in-deck event. The von Karman type approach underestimates the water entry force.

A Simple Method for the Design of Supersonic Nozzles of Arbitrary Cross Section Shape

2020 ◽  
Author(s):  
N. Boughazi ◽  
A. Haddad
Keyword(s):  
Cross Section ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Simple Method ◽  
Supersonic Nozzles ◽  
De Laval Nozzle

Abstract A simple approach for the design of supersonic nozzles of complex 3D shapes is presented. The Method of characteristics is primarily applied to compute the axisymmetric flow field of the supersonic section of the de-Laval nozzle. Two-dimensional simulations are performed for the axisymmetric flow fields. The 3D configuration is then generated from the desired exit axisymmetric cross-sectional shape chosen through tracing its geometrical parameters back.to the throat. Elliptical, corrugated and two-dimensional wedge nozzles were designed using this approach. Preliminary results show a smooth geometrical transition from the throat to the exit cross section. Further three-dimensional analyses of the obtained geometries along with cold flow testing constitute the next steps to be performed.

ANALYSIS OF THIN-WALLED BEAMS VIA A ONE-DIMENSIONAL UNIFIED FORMULATION THROUGH A NAVIER-TYPE SOLUTION

2011 ◽  
Vol 03 (03) ◽  
pp. 407-434 ◽  
Author(s):  
G. GIUNTA ◽  
F. BISCANI ◽  
S. BELOUETTAR ◽  
E. CARRERA
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Approximation Order ◽  
Geometrical Parameters ◽  
Type Solution ◽  
Dimensional Finite Element ◽  
Thin Walled ◽  
Three Dimensional Finite Element ◽  
Beam Theories

A unifying approach to formulate several axiomatic theories for beam structures is addressed in this paper. A N-order polynomials approximation is assumed on the beam cross-section for the displacement unknown variables, N being a free parameter of the formulation. Classical beam theories, such as Euler–Bernoulli's and Timoshenko's, are obtained as particular cases. According to the proposed unified formulation, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The linear static analysis of thin-walled beams is carried out through a closed form, Navier-type solution. Simply supported beams are, therefore, presented. Box, C- and I-shaped cross-sections are accounted for. Slender and deep beams are investigated. Bending and torsional loadings are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and the loading conditions.

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