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.

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.

Flexible Riser Top Connection Analysis With I-Tube Interface and Bending Hysteresis Effect

2019 ◽  
Author(s):  
Yangye He ◽  
Hailong Lu ◽  
Murilo Augusto Vaz ◽  
Marcelo Caire
Keyword(s):  
Kinematic Hardening ◽  
Bending Moment ◽  
Element Model ◽  
Beam Model ◽  
Flexible Riser ◽  
Nonlinear Bending ◽  
Cross Sectional ◽  
Irregular Wave ◽  
Global Dynamic ◽  
Curvature Distribution

Abstract The flexible riser top connection to the floating production platform is a critical region for fatigue lifetime (re)assessment. The interface with the I-tube and its curved sleeve combined with the gap between the riser and bend stiffener may lead to different curvature distribution when compared to the traditional modeling approach that considers the bend stiffener attached to the pipe. For a more accurate top connection assessment, the flexible riser bending hysteresis can also be directly incorporated in the global dynamic analysis helping to reduce curvature amplitude and lifetime prediction conservatism. This work investigates a 7” flexible riser-bend stiffener top connection with I-tube interface by performing irregular wave global dynamic analyses with the OrcaFlex package and considering a nonlinear bending moment vs curvature riser behavior obtained from a detailed cross sectional model developed in Abaqus. OrcaFlex curvature distribution results are also compared with a quasi-static finite element model that uses an elasto-plastic formulation with kinematic hardening to represent riser hysteresis through an equivalent beam model. A good curvature distribution correlation is observed for both top connection models (OrcaFlex x Abaqus) in the bend stiffener area with reduced amplitudes when riser bending hysteresis is considered.

Laminated pipe bends of mixed wall construction subjected to an in-plane bending moment

1989 ◽  
Vol 24 (3) ◽  
pp. 127-138 ◽  
Author(s):  
R Kitching ◽  
D R Hose
Keyword(s):  
Fourier Series ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Bending Moment ◽  
Numerical Results ◽  
Pipe Bend ◽  
Simple Method ◽  
Composite Pipe ◽  
Wall Construction ◽  
Plane Bending

Some of the ways in which the analysis of laminated composite pipe bends may differ from that of isotropic pipe bends are highlighted. The possible difference between effective bending and tensile moduli is recognised and its influence investigated over a range of bend geometries. A simple method for estimation of the influence of transverse shear terms on the performance of such a pipe bend under in-plane bending is presented, together with numerical results from the analysis. The range of geometries over which these terms may be important is discussed. The analysis is presented in a form which is readily implemented on a microcomputer, and suitable expressions for evaluation of appropriate Fourier series integrals are developed.

scholarly journals AERODYNAMIC ANALYSIS OF A ROLLING WRAPAROUND FIN PROJECTILE IN SUPERSONIC FLOW

2012 ◽  
Vol 19 ◽  
pp. 276-282 ◽  
Author(s):  
JUNG-YOUNG KIM ◽  
SUNG-IN CHO ◽  
IN LEE ◽  
HYOUNG-JIN NA ◽  
SANG-YOUNG JUNG
Keyword(s):  
Supersonic Flow ◽  
Euler Equation ◽  
Three Dimensional ◽  
Numerical Results ◽  
Experimental Results ◽  
Coordinate Frame ◽  
Experiment Data ◽  
Roll Damping ◽  
Time Marching ◽  
Supersonic Region

In this paper, the roll characteristics of a rolling wraparound fin projectile have been investigated in supersonic region. Computation of the flowfield was performed using a time-marching, three-dimensional Euler equation in a body fixed rotating coordinate frame. First, the roll producing moment coefficients of a projectile were obtained from the flowfiled solution at various Mach numbers and compared with the experimental and numerical results. They showed favorable agreement with experimental results in magnitude and sign. Next, the roll damping moment coefficients of a rolling wraparound fin were computed and compared with correlation based on experiment data. The correlation gave a somewhat larger value in magnitude than the present computation. However, the computed values agreed well with correlation in the trend.

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.

A Theoretical Study of the Elastic Behavior of Two Normally Intersecting Cylindrical Shells

1969 ◽  
Vol 91 (3) ◽  
pp. 563-572 ◽  
Author(s):  
J. W. Hansberry ◽  
N. Jones
Keyword(s):  
Cylindrical Shell ◽  
Theoretical Study ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Pressure Vessels ◽  
Numerical Results ◽  
Elastic Behavior ◽  
Cylinder Diameter ◽  
Plane Transverse

A theoretical study has been made into the elastic behavior of a joint formed by the normal intersection of a right circular cylindrical shell with another of larger diameter. The wall of the larger cylinder is assumed to remain open inside the joint in order to give an arrangement which is encountered frequently in pressure vessels or pipeline intersections. An external bending moment which acts in the plane of the joint is applied to the nozzle cylinder and is equilibriated by moments of half this magnitude applied to either end of the parent cylinder. A solution for this loading has been obtained by assuming antisymmetric distributions of certain stresses across a plane transverse to the joint. The analysis presented is believed to be valid for nozzle to cylinder diameter ratios of less than 1:3. Numerical results are given for a number of cases having radius ratios of 1:10 and 1:4.

On Nonlinear Bending of a Plate Strip

1965 ◽  
Vol 87 (4) ◽  
pp. 406-412
Author(s):  
P. E. Wilson
Keyword(s):  
Stress Corrosion ◽  
Maximum Stress ◽  
Direct Application ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Experimental Results ◽  
Nonlinear Bending ◽  
Plate Strip ◽  
Stress States

Ends of an initially straight plate strip are rotated 90 deg. Using nonlinear bending theory, the maximum stress is obtained as a function of the half-distance between the rotated ends of the strip. Numerical results are presented in nondimensional form, and the theoretical solution is shown to compare favorably with experimental results. Information given here has a direct application to stress states in a stress corrosion specimen.

scholarly journals Flexural Behavior of Innovative Posttensioned Composite Beams with Corrugated Steel Webs

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xiang Li ◽  
Tao Yang ◽  
Yongbing Zhang ◽  
Yun Zhang ◽  
Taosheng Shen
Keyword(s):  
Yield Strength ◽  
Bending Moment ◽  
Composite Beams ◽  
Considerable Effect ◽  
Steel Tube ◽  
Numerical Results ◽  
Flexural Behavior ◽  
Steel Tubes ◽  
Depth Ratio ◽  
Ultimate Load Carrying Capacity

Steel-concrete composite beams with corrugated steel webs (CSWs) usually have concrete flanges that are prone to crack under tension, and an innovative posttensioned composite beam (IPCB) with CSWs has been proposed previously to overcome this shortcoming. Here, an IPCB with CSWs is manufactured and submitted to a flexural test to investigate its flexural behavior, based on which finite element (FE) models with different parameters are developed and analyzed using the ANSYS software. The effects of the span-to-depth ratio, concrete compressive strength, initial effective prestress, width of the upper concrete flange, and yield strength of the steel tubes on the flexural behavior of the IPCBs with CSWs are discussed. Numerical results show that the span-to-depth ratio of the beam and the yield strength of the steel tube have a considerable effect on the ultimate load-carrying capacity of the IPCB, which increases by 48.2% when the depth of the CSWs is increased from 240 to 400 mm and by 21.8% when the yield strength of the steel tubes is increased from 295 to 395 MPa. The plane-section assumption is unsuitable for IPCBs. Almost all the unbonded posttensioning strands in the beams yield for the specimens at ultimate state. The normal stress is distributed unevenly across the width of the upper concrete flange, and the maximum shear lag coefficient is 1.17. Based on the numerical results, a calculation method is established to evaluate the bending moment resistance of an IPCB with CSWs. Comparison shows that the theoretical results in accordance with the proposed method agree well with the numerical results.

Effectiveness of Stoppers and Shock Absorber Devices in Mitigating Earthquake Damage to Curved Viaducts with Steel Bearing Supports

2015 ◽  
Vol 09 (04) ◽  
pp. 1550011 ◽  
Author(s):  
Qin Tian ◽  
Toshiro Hayashikawa ◽  
Wei-Xin Ren ◽  
Xing-Wen He
Keyword(s):  
Shock Absorber ◽  
Bending Moment ◽  
Earthquake Damage ◽  
Numerical Results ◽  
Large Displacements ◽  
Conventional Steel ◽  
Roller Bearings

Viaducts with steel bearings are subject to damage during earthquakes. Damage to conventional steel bearings could cause viaduct decks to collapse. This study attempts to prevent large displacements by installing steel stoppers at both sides of roller bearings. Shock absorber devices (SADs) are also installed between roller bearings and stoppers to reduce pounding forces. The study then explores the effectiveness of different stopper gaps and SADs installed between roller bearings and stoppers in mitigating viaduct damage. The effectiveness of stoppers without and with SADs is also investigated. The pounding forces between roller bearings and stoppers, the displacements on the tops of piers, the displacements of superstructures, and the bending moment–curvature relationship at pier bases are evaluated accordingly. Numerical results reveal that earthquake damage to viaducts with small stopper gaps is not significant. The application of SADs is also found to significantly mitigate viaduct damage.

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