Numerical Simulation on Combined Deformation of Tip-Loaded Cantilever Beam with Particle Flow Code

2011 ◽  
Vol 378-379 ◽  
pp. 31-34
Author(s):  
Yi Bo Xiong ◽  
Chun Ming Wang ◽  
Lu Peng
Keyword(s):  
Cantilever Beam ◽  
Axial Load ◽  
Beam Theory ◽  
Bending Moment ◽  
Transverse Load ◽  
Particle Flow ◽  
Particle Flow Code ◽  
Shear Stresses ◽  
Axial Tension ◽  
Theory Solution

In order to calculate the combined deformations of an Euler-Bernoulli cantilever beam subjected to bending moment, twisting moment, transverse load and axial load, particle flow code in 3 dimensions (PFC3D) is used with parallel bonds model. The computed deformations, including transverse deflections, rotations about axis, maximum normal and shear stresses, were compared with the analytical beam-theory solution in terms of axial tension, axial compression and none axial load, respectively. Between computed results and analytical beam-theory solution, the error bands are greater than 99.7% at the beam tip, while the error of the transverse deflection of the whole beam is less than 0.6%. So, the PFC3D is able to precisely simulate the combined deformation of cantilever beam, and this work has special reference to engineering calculations and designs when PFC is applied to model the mechanical behaviors of continuum materials.

scholarly journals Dynamic Response of Double Elastic Cantilever Beam Attributed to Variable Uniformly Distributed Load

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Wei He ◽  
Yanjing Wei
Keyword(s):  
Cantilever Beam ◽  
Double Layer ◽  
Structural Parameters ◽  
Load Condition ◽  
Beam Theory ◽  
Bending Moment ◽  
Heaviside Function ◽  
Electromagnetic Launch ◽  
Strength And Stiffness ◽  
Elastic Foundation Beam

Based on the double-layer elastic foundation beam theory, the rails and the wall plates of the electromagnetic launching device are modeled as a double-layer elastic cantilever foundation beam. After establishing the kinetic differential equation and setting the boundary condition of the cantilever beam, the displacement solution of double-layer elastic cantilever foundation beam under no load condition is obtained. Applying the Heaviside Function, the deflection equation of the upper and lower beam, the expression of the bending moment, and the stress are obtained. In the case of given motion parameters and structural parameters, the analytical solutions of the rail and the wall plate are calculated. The ANSYS numerical analysis is carried out under the same condition and the results of both solutions are in good agreement. The results can provide theoretical basis for the design of strength and stiffness of the electromagnetic launch device.

scholarly journals Stress Analysis of Suspended Pipe Partially Buried in Linear Elastic Soil

2016 ◽  
Vol 10 (1) ◽  
pp. 161-169
Author(s):  
Kun Huang ◽  
Xia Li ◽  
Yiheng Zhang
Keyword(s):  
Beam Theory ◽  
Bending Moment ◽  
Critical Length ◽  
Beam Model ◽  
Linear Elastic ◽  
Limit Value ◽  
Axial Tension ◽  
Calculation Results ◽  
Stress And Deformation ◽  
Elastic Soil

Based on the small deflection beam theory, bending equation with axial tension of suspended pipe partially buried in the linear elastic soil is established. And the corresponding boundary conditions are given according to the stress and deformation characteristics of suspended section and buried section. Then deflection equation for the suspended section is deduced. Afterwards, the stress and critical length of a suspended pipeline are calculated and analyzed. The results show that the tensile stress and bending stress on the endpoint of the suspended section meet the requirement of first strength theory and the critical suspended length is greater than the real suspended length, which is consistent with the actual situation. When the stiffness of soil tends to approach infinity, both the limit value of axial tension and endpoint bending moment agree well with the calculation results of fixed-fixed supported beam model.

Finite Element Modeling of Self-Loosening of Bolted Joints

2004 ◽  
Author(s):  
Ming Zhang ◽  
Yanyao Jiang ◽  
Chu-Hwa Lee
Keyword(s):  
Finite Element ◽  
Contact Pressure ◽  
Bending Moment ◽  
Shear Loading ◽  
Transverse Load ◽  
Fe Model ◽  
Bolted Joint ◽  
Cyclic Bending ◽  
Second Stage ◽  
Cyclic Bending Moment

A three-dimensional finite element (FE) model with the consideration of the helix angle of the threads was developed to simulate the second stage self-loosening of a bolted joint. The second stage self-loosening refers to the graduate reduction in clamping force due to the back-off of the nut. The simulations were conducted for two plates jointed by a bolt and a nut and the joint was subjected to transverse or shear loading. An M12×1.75 bolt was used. The application of the preload was simulated by using an orthogonal temperature expansion method. FE simulations were conducted for several loading conditions with different preloads and relative displacements between the two clamped plates. It was found that due to the application of the cyclic transverse load, micro-slip occurred between the contacting surfaces of the engaged threads of the bolt and the nut. In addition, a cyclic bending moment was introduced on the bolted joint. The cyclic bending moment resulted in an oscillation of the contact pressure on the contacting surfaces of the engaged threads. The micro-slip between the engaged threads and the variation of the contact pressure were identified to be the major mechanisms responsible for the self-loosening of a bolted joint. Simplified finite element models were developed that confirmed the mechanisms discovered. The major self-loosening behavior of a bolted joint can be properly reproduced with the FE model developed. The results obtained agree quantitatively with the experimental observations.

Preliminary Parametric Assessment of a Bolted Endplate Joint under Combined Axial Force and Cyclic Bending Moment

2011 ◽  
Vol 255-260 ◽  
pp. 718-721
Author(s):  
Z.Y. Wang ◽  
Q.Y. Wang
Keyword(s):  
Finite Element Analysis ◽  
Axial Force ◽  
Seismic Design ◽  
Axial Load ◽  
Failure Modes ◽  
Bending Moment ◽  
Element Analysis ◽  
Cyclic Behaviour ◽  
Joint Behaviour ◽  
Steel Joints

Problems regarding the combined axial force and bending moment for the behaviour of semi-rigid steel joints under service loading have been recognized in recent studies. As an extended research on the cyclic behaviour of a bolted endplate joint, this study is performed relating to the contribution of column axial force on the cyclic behaviour of the joint. Using finite element analysis, the deteriorations of the joint performance have been evaluated. The preliminary parametric study of the joint is conducted with the consideration of flexibility of the column flange. The column axial force was observed to significantly influence the joint behaviour when the bending of the column flange dominates the failure modes. The reductions of moment resistance predicted by numerical analysis have been compared with codified suggestions. Comments have been made for further consideration of the influence of column axial load in seismic design of bolted endplate joints.

Vibration and Stability of an Elastic Beam Subjected to a Periodic Axial Load With Time-Dependent Displacement Excitation at Both Ends

1991 ◽  
Author(s):  
Xiao-Feng Wu ◽  
Adnan Akay
Keyword(s):  
Axial Load ◽  
Perturbation Technique ◽  
Harmonic Balance Method ◽  
Elastic Beam ◽  
Time Dependent ◽  
Transverse Load ◽  
Order Partial Differential Equation ◽  
Weighted Residual Method ◽  
Hill’S Equation ◽  
Hill's Equation

Abstract This paper concerns the transverse vibrations and stabilities of an elastic beam simultaneously subjected to a periodic axial load, a distributed transverse load, and time-dependent displacement excitations at both ends. The equation of motion derived from Bernoulli-Euler beam theory is a fourth-order partial differential equation with periodic coefficients. To obtain approximate solutions, the method of assumed-modes is used. The unknown time-dependent function in the assumed-modes method is determined by a generalized inhomogeneous Hill’s equation. The instability regions possessed by this generalized Hill’s equation are obtained by both the perturbation technique up to the second order and the harmonic balance method. The dynamic response and the corresponding spectrum of the transversely oscillating elastic beam are calculated by the weighted-residual method.

Effect of Dynamic Shear Force on Fastener Loosening in Assemblies

1997 ◽  
Author(s):  
Yubo Dong ◽  
Daniel P. Hess
Keyword(s):  
Cantilever Beam ◽  
Static Load ◽  
Nodal Line ◽  
Shear Stresses ◽  
Dynamic Shear ◽  
Bernoulli Beam ◽  
Cyclic Shear ◽  
Nodal Lines ◽  
Inertial Loading ◽  
Euler Bernoulli Beam

Abstract Placement and orientation of fasteners in assemblies is generally based on convenience or static load and strength considerations. Vibration and other dynamic loads can result in loosening of threaded product, particularly when cyclic shear stresses are present. This paper investigates the placement of a bolt and nut on a compound cantilever beam subjected to dynamic inertial loading. Calculations for an inertial loaded, cantilever, Euler-Bernoulli beam show that the dynamic shear stress is maximum near the dynamic nodal lines, and essentially vanishes near the anti-nodes. Experiments with a compound cantilever beam assembly with one fastener reveal that loosening occurs more readily when the bolt and nut are placed near a nodal line. Data presented include time to loosen, break-away torque, and acceleration level. The data shows that fastener integrity is maintained for longer periods of time and with lower tightening torques, when the bolt and nut are positioned away from nodal lines where shear stresses are lower, even though acceleration levels are higher.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

The Effect of Length: Diameter Ratio on Collapse of Casing

1984 ◽  
Vol 106 (2) ◽  
pp. 160-165 ◽  
Author(s):  
N. C. Huang ◽  
P. D. Pattillo
Keyword(s):  
Axial Load ◽  
External Pressure ◽  
Field Application ◽  
Diameter Ratio ◽  
Finite Cylinder ◽  
Oil Well ◽  
Steel Mill ◽  
Cross Sectional ◽  
Axial Tension ◽  
Collapse Resistance

This paper presents an analysis of the cross-sectional collapse of a cylinder of finite length loaded simultaneously by an axial tension (which may be zero) and external pressure. The calculation is based on Sanders’ nonlinear shell equations with plasticity introduced via the concept of effective stress from a uniaxial tension test. The finite cylinder is an appropriate model of oil well casing as it undergoes quality control testing in the steel mill where the edges of the cylinder are usually fixed in the case of nonzero axial load and free in the case of zero axial load. However, in field application, the length: diameter ratio of casing is such that the cylinder may be considered infinite. Guidelines contained herein permit prediction of the collapse resistance of field casing from the results of mill tests performed on short samples.

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