Energy Method for the Calculation of High-Pier's Effective Length Factor at the Finished Stage

2013 ◽  
Vol 361-363 ◽  
pp. 1115-1118
Author(s):  
Peng Liu ◽  
Jie Rui ◽  
Bo Lei ◽  
Fei Zheng
Keyword(s):  
Boundary Conditions ◽  
Energy Method ◽  
Good Accuracy ◽  
Shape Function ◽  
Great Influence ◽  
Effective Length ◽  
Ideal Boundary ◽  
Effective Length Factor ◽  
High Pier ◽  
The One

This paper establishes the shape function of high-pier with non-ideal boundary conditions in the top and uses the energy method to calculate its critical load. Then its effective length factor is achieved by using Euler's formula. Further, the FEM and energy method are respect used to calculate the effective length factor of the engineering example and comparative analysis is carried on. Results show that: The non-ideal boundary conditions have great influence on the effective length factor and should be considered in the calculation. The result from the formula of energy method is nearly the same as the one from the FEM which demonstrates this method is of good accuracy to calculate the effective length factor of high-pier. In addition, it is also of great convenience in the design of high-piers.

A Calculation Method of High-Pier's Effective Length Factor Considering the Dead Weight

2013 ◽  
Vol 361-363 ◽  
pp. 1278-1283
Author(s):  
Peng Liu ◽  
Rui Zhi Wang ◽  
Fei Zheng ◽  
Qiong He
Keyword(s):  
Boundary Conditions ◽  
Calculation Method ◽  
Critical Force ◽  
Effective Length ◽  
Ideal Boundary ◽  
Dead Weight ◽  
Numerical Examples ◽  
First Order ◽  
Effective Length Factor ◽  
High Pier

Nowadays, uncertainty regarding the calculation method of effective length factor of high-pier has brought many inconveniences to the design of bridge. To solve the problem, this paper demonstrates the calculation method of effective length factor on the basis of Eulers formula considering both the influence of high-pier s dead weight and non-ideal boundary conditions on the critical force of first-order buckling. The influence of piers dead weight on effective length factor in the construction and finished stage are evaluated by numerical examples. Results show that: the effective length factor becomes smaller considering dead weight both in construction and finished stage. Moreover, high-piers dead weight causes more influence in the construction stage than finished stage which should be considered seriously in the design and construction.

Parameter Analysis on High-Pier's Effective Length Factor of Fabricated Beam Bridge

2013 ◽  
Vol 361-363 ◽  
pp. 1272-1277
Author(s):  
Peng Liu ◽  
Yong Jun Li ◽  
Fei Zheng ◽  
Jie Rui
Keyword(s):  
Critical Force ◽  
Parameter Analysis ◽  
Effective Length ◽  
Ideal Boundary ◽  
Dead Weight ◽  
First Order ◽  
Effective Length Factor ◽  
High Pier ◽  
The Stability ◽  
Beam Bridge

This paper illustrates the calculation method of effective length factor of the high-pier of fabricated beam bridge on the basis of Eulers formula by obtaining the critical force of first-order buckling according to the stability analysis. Engineering example is applied to calculate the effective length factor in the construction stage of fabricated beam bridge. Further, parameter analysis is used to study the variation of effective length factor and the influence of dead weight, non-ideal boundary conditions, the height and the radius of high-pier on it is evaluated. Results show that: there are many influencing factors acting on the effective length factor which cannot simply be represented by a fixed value and the calculation of the effective length factor should depend on the specific conditions of high-piers.

Experimental Investigation of Buckling Length of CFS Lipped Channel Beams under Restrained Boundary Conditions

2014 ◽  
Vol 984-985 ◽  
pp. 140-153
Author(s):  
R. Kandasamy ◽  
R. Thenmozhi
Keyword(s):  
Experimental Investigation ◽  
Boundary Conditions ◽  
Effective Length ◽  
Effective Length Factor ◽  
Buckling Length ◽  
Hot Rolled ◽  
Range Of Values ◽  
Code Provisions

Effective length factor of CFS lipped channel beams subjected to flexure are given in AS/NSZ 4600, Euro code Part 1.3 and BS 5950, Part V taking into account their buckling phenomena. The coefficients are given for boundary conditions considering the effect of torsion and warping restraint. The effect of torsion and warping restraints is treated by defining the range of values for the coefficients. Lateral torsion buckling of the CFS beams greatly influences the effective length factors. 16 CFS lipped channel beams have been taken for the study with depth of 100mm, flange width 50mm and lip size varies from 10mm to 20mm.Experimental investigation has been carried out to verify the coefficients for the defined boundary conditions. The influence of flange width and lip size on the buckling length has been investigated. The results are compared with the Indian code provisions for hot rolled beams.

scholarly journals Electrically turning periodic structures in cholesteric layer with conical–planar boundary conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Oxana Prishchepa ◽  
Mikhail Krakhalev ◽  
Vladimir Rudyak ◽  
Vitaly Sutormin ◽  
Victor Zyryanov
Keyword(s):  
Boundary Conditions ◽  
Periodic Structures ◽  
Cholesteric Liquid Crystal ◽  
Growth Direction ◽  
Smooth Transition ◽  
Defect Structures ◽  
Optical Cell ◽  
Elastic Continuum ◽  
The One ◽  
Experimental Findings

AbstractElectro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by $$180^\circ$$ 180 ∘ . The $$U^+$$ U + and $$U^-$$ U - -defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of $$0\le \, V \le 1.3$$ 0 ≤ V ≤ 1.3  V during the process. Resulting orientation and distance between the lines don’t change under voltage. However, at $$V>1.3$$ V > 1.3  V $$U^+$$ U + -defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell’s center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

A Variational Approach to Loaded Ply Structures

2003 ◽  
Vol 9 (1-2) ◽  
pp. 175-185 ◽  
Author(s):  
G. H.M. Van Der Heijden ◽  
J. M.T. Thompson ◽  
S. Neukirch
Keyword(s):  
Boundary Conditions ◽  
Energy Method ◽  
Variational Approach ◽  
Energy Analysis ◽  
Numerical Results ◽  
Equilibrium Equations

We show how an energy analysis can be used to derive the equilibrium equations and boundary conditions for an end-loaded variable ply much more efficiently than in previous works. Numerical results are then presented for a clamped balanced ply approaching lock-up. We also use the energy method to derive the equations for a more general ply made of imperfect anisotropic rods and we briefly consider their helical solutions.

Contrast Study on the Radial Velocity of the Flow Field of the Hydrocyclones with Different Inlet Structures

2011 ◽  
Vol 339 ◽  
pp. 624-629
Author(s):  
Lian Cheng Ren ◽  
Zheng Liang ◽  
Jiang Meng ◽  
Lin Yang ◽  
Jia Lin Tian
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Radial Velocity ◽  
Axial Symmetry ◽  
Separation Efficiency ◽  
Great Influence ◽  
The Other ◽  
Contrast Study ◽  
The One ◽  
Tangential Inlet

On the base of numerical simulation and theoretical analysis, the flow field of a conventional single-tangential-inlet Hydrocyclone and a newly put forward axial-symmetry double-tangential-inlet hydrocyclone were contrasted. The study shows that the inlet structure of the Hydrocylone has a great influence on the radial velocity of the flow field in the hydrocyclone and that the radial velocity in the hydrocyclone with single-tangential-inlet is not symmetry about the axis of the hydrocyclone; and on the other hand the radial velocity in the hydrocyclone with axial-symmetry double-tangential-inlet is symmetry about the axis of the hydrocyclone. The magnitude of the radial velocity of the flow in the hydrocyclone with single-tangential-inlet is greater than that in the hydrocyclone with axial-symmetry double-tangential-inlet hydrocyclone, which means the hydrocyclone with axial-symmetry double-tangential-inlet has greater capability than the rival one with single-tangential inlet. The symmetry about the axis of the hydrocyclone of the radial velocity means the radial velocities in the place where the radio is the same are constant, which means the hydrocyclone has a great separation efficiency. The conclusion is that changing the conventional hydrocyclone into the one with axial-symmetry double-tangential-inlet structure can offer greater separation capability and efficiency.

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