Bending of Superelastic Wires, Part II: Application to Three-Point Bending

1995 ◽  
Vol 62 (2) ◽  
pp. 466-470 ◽  
Author(s):  
B. T. Berg
Keyword(s):  
Numerical Procedure ◽  
Bending Moment ◽  
Numerical Results ◽  
Constitutive Relationship ◽  
Pure Bending ◽  
Three Point Bending ◽  
Rod Theory ◽  
Soft Loading ◽  
Loading And Unloading ◽  
The Relationship

The constitutive relationship between applied pure bending moment and the resulting curvature of a few superelastic alloy wires is applied to the three-point bending problem. Three-point bending experiments on hard and soft loading machines are described. The relationship between the applied deflection and the resulting force in three-point bending is calculated from a nonlinear Euler-Bernoulli rod theory. A numerical procedure used to solve the three-point bending problem for both loading and unloading is briefly described and numerical results are compared with experiment.

Bending of Superelastic Wires, Part I: Experimental Aspects

1995 ◽  
Vol 62 (2) ◽  
pp. 459-465 ◽  
Author(s):  
B. T. Berg
Keyword(s):  
Phase Region ◽  
Constitutive Relationship ◽  
Tension Stress ◽  
Bending Moments ◽  
Pure Bending ◽  
Three Point Bending ◽  
Strain Relationship ◽  
Niti Wires ◽  
Mixed Phase Region ◽  
Constant Moment

A pure-bending apparatus is used to measure the constitutive relationship between applied pure bending moments and the resulting curvatures of a few superelastic alloy wires. The sample nickel-titanium alloy (NiTi) wires change phase when ample bending moments are imposed. Like the material’s uniaxial tension stress-strain relationship, the measured moment-curvature relationship shows plateaus of constant moment and hysteresis. The bent shape is circular, except in the mixed phase region where it is composed of a phase mixture of circles. An example of the applications of the measured moment-curvature relations is presented in Part II of this paper where the three-point bending problem is considered.

Dynamic Fracture of a Beam or Plate in Plane Bending

1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann
Keyword(s):  
Crack Length ◽  
Dynamic Fracture ◽  
Crack Tip ◽  
Bending Moment ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Multiple Reflections ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Vibro-Stone Column Reinforcement Mechanism and Numerical Analysis

2012 ◽  
Vol 446-449 ◽  
pp. 1940-1943
Author(s):  
Yang Liu ◽  
Hong Xiang Yan
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Pore Pressure ◽  
Numerical Procedure ◽  
Numerical Results ◽  
Excess Pore Pressure ◽  
Stone Column ◽  
Reinforcement Mechanism ◽  
Consolidation Theory ◽  
Excess Pore

Numerical simulation of vibro-stone column is taken to simulate the installation of vibro-stone column. A relationship based on test is adopted to calculate the excess pore pressure induced by vibratory energy during the installation of vibro-stone column. A numerical procedure is developed based on the formula and Terzaghi-Renduric consolidation theory. Finally numerical results of composite stone column are compared single stone column.

Transverse Young's Moduli and Cell Shapes in Coniferous Early Wood

Holzforschung ◽  
2002 ◽  
Vol 56 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ugai Watanabe ◽  
Minoru Fujita ◽  
Misato Norimoto
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Bending Moment ◽  
Cell Models ◽  
Young’S Moduli ◽  
Cell Shapes ◽  
The Difference ◽  
Square Cells ◽  
Experimental Values ◽  
The Relationship

Summary The relationship between transverse Young's moduli and cell shapes in coniferous early wood was investigated using cell models constructed by two dimensional power spectrum analysis. The calculated values of tangential Young's modulus qualitatively explained the relationship between experimental values and density as well as the difference in experimental values among species. The calculated values of radial Young's modulus for the species having hexagonal cells agreed well with the experimental values, whereas, for the species having square cells, the calculated values were much larger than the experimental values. This result was ascribed to the fact that the bending moment on the radial cell wall of square cell models was calculated to be small. It is suggested that the asymmetrical shape of real wood cells or the behavior of nodes during ell deformation is an important factor in the mechanism of linear elastic deformation of wood cells.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

2021 ◽  
pp. 2-9
Author(s):  
M.V. Sukhoterin ◽  
◽  
A.M. Maslennikov ◽  
T.P. Knysh ◽  
I.V. Voytko ◽  
...  
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bending Moment ◽  
Partial Solution ◽  
Numerical Results ◽  
Cantilever Plate ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Beam Function

Abstract. An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

Investigation of the causes of damage to freight cars during disbanding on non-mechanized sorting slides and development of measures to prevent them

2021 ◽  
pp. 4-13
Author(s):  
S. V. Tankeev ◽  
◽  
A. E. Kolodin ◽  
V. B. Sverdlov ◽  
A. V. Nazarov ◽  
...  
Keyword(s):  
Low Power ◽  
Coefficient Of Friction ◽  
Damage Assessment ◽  
Laboratory Tests ◽  
Rolling Stock ◽  
Third Body ◽  
Normative Documents ◽  
The Coefficient Of Friction ◽  
Loading And Unloading ◽  
The Relationship

The damage assessment of freight cars during shunting and loading and unloading operations was made. The need to review the normative documents regulating the relationship between the owners of rolling stock, owners of non-public tracks and the carrier is noted. The reasons for formation of damage on the wheel pairs of freight cars when disbanding on low-power sorting slides are considered. The conditions for ensuring the deceleration of detachments on non-mechanized sorting slides without damaging the wheels are determined. The analysis of methods for ensuring braking on low-power slides is carried out. A method was chosen to ensure the wheel set rotation by introducing a third body between the rubbing surfaces during the braking of cars, which will take over a part of the resulting heat flow, reducing the temperature and increasing the coefficient of friction in the «wheel-rail» contact zone. A method is proposed to provide braking on the non-mechanized sorting slide during shoe braking by applying a friction compound to a non-working rail. Laboratory tests were carried out, which showed that the introduction of a friction additive can achieve the necessary coefficient of friction to comply with the standard parameters of deceleration of the car in the braking zone.

The Nonlinear Bending of Thin Circular Rods

1956 ◽  
Vol 23 (1) ◽  
pp. 7-10
Author(s):  
H. D. Conway
Keyword(s):  
Euler Equation ◽  
Bending Moment ◽  
Numerical Results ◽  
Nonlinear Bending

Abstract Two examples of the nonlinear bending of thin circular rods are discussed using the Bernoulli-Euler equation, which states that the change of curvature of a rod is proportional to the bending moment producing it. Numerical results are presented.

Required Linepipe Properties for High Strain Applications and Possible Resolution by Pipe Manufacturing Technology

2008 ◽  
Author(s):  
Hitoshi Asahi ◽  
Eiji Tsuru
Keyword(s):  
Tensile Strain ◽  
Compressive Strain ◽  
Bending Moment ◽  
Uniaxial Tensile ◽  
Buckling Behavior ◽  
Strain Limit ◽  
Bent Pipe ◽  
Uniaxial Tensile Stress ◽  
The Relationship ◽  
Pipe Manufacturing

Application of strain based design to pipelines in arctic or seismic areas has recently been recognized as important. So far, there has been much study performed on tensile strain limit and compressive strain limit. However, the relationship between bending buckling (compressive strain limit) and tensile strain limit has not been discussed. A model using actual stress strain curves suggests that the tensile strain limit increases as Y/T rises under uniaxial tensile stress because a pipe manufacturer usually raises TS instead of lowering YS to achieve low Y/T. Under bending of a pipe with a high D/t, an increase in compressive strain on intrados of a bent pipe at the maximum bending moment (ε-cp*) improves the tensile strain limit because the tensile strain limit is controlled by the onset of buckling or ε-cp* which is increased by lowering Y/T. On the other hand, under bending of a pipe with a low D/t, the tensile strain limit may not be influenced by improvement of buckling behavior because tensile strain on the extrados is already larger than the tensile limit at ε-cp*. Finally, we argue that the balance of major linepipe properties is important. Efforts other than the strict demands for pipe properties are also very important and inevitable to improve the strain capacity of a pipeline.

Three-Dimensional Finite Element Analysis of Pipe Flange Connections: The Case of Using Compressed Asbestos Sheet Gasket

2002 ◽  
Author(s):  
Tomohiro Takaki ◽  
Toshimichi Fukuoka
Keyword(s):  
Contact Pressure ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Bending Moment ◽  
Elastic Interaction ◽  
Bearing Surface ◽  
Element Analysis ◽  
Bolt Stress ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The most important factor for the leakage problem of pipe flange connections is considered to be contact pressure distribution at the gasket bearing surface in service. In this study, the mechanical behaviors of the pipe flange connection are evaluated using FEM as a three-dimensional contact problem, in which a gasket is modeled as a nonlinear one-dimensional gasket element. Here, the contact pressure distributions at the gasket bearing surface and the variations of the bolt stress are estimated under uniform bolt preloads or nonuniform ones due to the elastic interaction during bolting up. The numerical procedure proposed here can successively deal with the processes of bolt-up, applying inner pressure and applying bending moment. The analytical objects are pipe flanges specified in JIS B 2238 with compressed asbestos sheet gaskets being inserted. The validity of the numerical method is ascertained by experiment.

scholarly journals Sensitivity analysis of a municipal wastewater treatment plant model

2019 ◽  
Vol 252 ◽  
pp. 05010
Author(s):  
Paweł Król ◽  
Alberto Gallina ◽  
Michał Lubieniecki ◽  
Tadeusz Uhl ◽  
Tadeusz Żaba
Keyword(s):  
Wastewater Treatment ◽  
Municipal Wastewater ◽  
Treatment Process ◽  
Biological Process ◽  
Treatment Plant ◽  
Numerical Procedure ◽  
Municipal Wastewater Treatment ◽  
Wastewater Treatment Process ◽  
Plant Model ◽  
The Relationship

Waste management is a crucial process to keep the environment in wholesome conditions. The environmental impact of solid waste and wastewater is reduced through construction of appropriate disposal installations. The objective of wastewater treatment in biological reactors is to control the process of biomaterial growth by aerating the sewage content. The process is complex, as depending on a plenty of parameters. In the last decades an effective numerical model, called the Activated Sludge Model (ASM), has been proposed for describing the biological process. The ASM is implemented in the Benchmark Simulation Model (BSM) that simulates the whole wastewater treatment process. The most important parameters in ASM are the kinetic and stoichiometric coefficients. The former describes rate-concentration dependence. The latter characterises the relationship between the components of chemical reactions taking place in the cleaning process. Above parameters are determined by on-site calibration and their importance is relevant during the development of numeric models. This paper aims to examine the influence of kinetic and stoichiometric parameters on the wastewater treatment process of a plant in Płaszów, Kraków. The analysis is carried out by a sample-based numerical procedure. It highlights the ASM parameters playing a major role in the treatment process. Results obtained from the analysis are important for future validation and optimisation processes.

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