Post-buckling Behavior of Beams Under Contact Constraints

1994 ◽  
Vol 61 (4) ◽  
pp. 764-772 ◽  
Author(s):  
N. Adan ◽  
I. Sheinman ◽  
E. Altus
Keyword(s):  
Contact Surface ◽  
Moving Boundary ◽  
Initial Imperfection ◽  
Contact Forces ◽  
Arc Length ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Symmetric Response ◽  
Kinematic Approach ◽  
Good Agreement

An analytical model of the post-buckling behavior of a beam under contact constraints was derived. Experiments were carried out in order to characterize the various phenomenon involved in the problem. Two experiments with symmetric response with various contact surface and initial imperfection, and one experiment of asymmetric behavior were chosen for validation of the analytical results. The theory is based on a nonlinear kinematic approach and on the moving boundary procedure. The nonlinear equations are derived by the variational principle and solved through truncated approximating functions. A modification of an “arc-length” procedure was developed for solving the equation which incorporates the snapping effect. A comprehensive parametric study of the dominant parameters (distance between the beam and the contact surface, initial imperfections, contact location, magnitude of the contact forces, etc.) is carried out through numerical examples. Very good agreement with experimental results for the various phenomena involved in the problem was obtained for a clamped beam.

Post-Buckling Analysis of Heavy Columns with Application to Marine Risers

1985 ◽  
Vol 29 (03) ◽  
pp. 162-169
Author(s):  
Theodore Kokkinis ◽  
Michael M. Bernitsas
Keyword(s):  
Boundary Conditions ◽  
Small Strain ◽  
Equilibrium Path ◽  
Drilling Mud ◽  
Tubular Columns ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Combined Action ◽  
Raphson Iteration ◽  
Good Agreement

The post-buckling behavior of heavy tubular columns following static instability under the combined action of weight, tension/compression at the top, and fluid static pressure forces in the gravity field is studied. A two-dimensional nonlinear small-strain large-deflection model of the column is derived, consisting of an integrodifferential equilibrium equation and two end rotation conditions. The equation of equilibrium is discretized using a finite-element method. An approximate solution valid in the neighborhood of the bifurcation point and an incremental solution are used to determine the secondary equilibrium path. The results of both methods are corrected by Newton-Raphson iteration. Conditions for unstable initial post-buckling behavior and existence of limit points on the secondary equilibrium path are presented. The numerical solution is applied to the problem of the elastica and is found to be in good agreement with the analytical solution. The secondary equilibrium path for a 500-m-long (1640 ft) marine drilling riser is calculated for two sets of boundary conditions and various values of the drilling mud density. The effect of the drilling mud density and the boundary conditions on the riser's post-buckling behavior is discussed.

Post-buckling and Snap-Through Behavior of Inclined Slender Beams

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Jian Zhao ◽  
Jianyuan Jia ◽  
Xiaoping He ◽  
Hongxi Wang
Keyword(s):  
Large Deflection ◽  
Buckling Modes ◽  
Strongly Nonlinear ◽  
Elastic Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Slender Beams ◽  
Post Buckling ◽  
Inclined Beam ◽  
Good Agreement

Based on the geometrical nonlinear theory of large deflection elastic beams, the governing differential equations of post-buckling behavior of clamped-clamped inclined beams subjected to combined forces are established. By using the implicit compatibility conditions to solve the nonlinear statically indeterminate problems of elastic beams, the strongly nonlinear equations formulated in terms of elliptic integrals are directly solved in the numerical sense. When the applied force exceeds the critical value, the numerical simulation shows that the inclined beam snaps to the other equilibrium position automatically. It is in the snap-through process that the accurate configurations of the post-buckling inclined beam with different angles are presented, and it is found that the nonlinear stiffness decreases as the midpoint displacement is increased according to our systematical analysis of the inward relations of different buckling modes. The numerical results are in good agreement with those obtained in the experiments.

scholarly journals POST – BUCKLING BEHAVIOR OF STIFFENED CURVED PANEL USING ARC LENGTH METHOD

IJIREEICE ◽  
2021 ◽  
Vol 9 (10) ◽  
Author(s):  
Dr. Ganesh M ◽  
Karthick V ◽  
Krishna Kumar M S
Keyword(s):  
Arc Length ◽  
Buckling Behavior ◽  
Curved Panel ◽  
Post Buckling

Effect of Delamination on the Nonlinear Behavior of Composite Laminated Beams

1990 ◽  
Vol 112 (4) ◽  
pp. 393-397 ◽  
Author(s):  
I. Sheinman ◽  
M. Soffer
Keyword(s):  
Nonlinear Analysis ◽  
Laminated Composite ◽  
Nonlinear Behavior ◽  
Initial Imperfection ◽  
Load Carrying Capacity ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Geometrical Nonlinear ◽  
Laminated Composite Beams ◽  
Kinematic Approach

This paper presents a parametric study of the effect of delamination, and of initial imperfection, on the overall nonlinear behavior of laminated composite beams. The study is based on geometrical nonlinear analysis with the Von-Karman kinematic approach. It is shown that the bifurcation point provides not more than an indication of the buckling behavior, and that the full nonlinear analysis is needed for predicting the load-carrying capacity. It was also found that the delaminated beam is sensitive to initial imperfection.

Modeling of Tread Block Contact Mechanics Using Linear Viscoelastic Theory3

2008 ◽  
Vol 36 (3) ◽  
pp. 211-226 ◽  
Author(s):  
F. Liu ◽  
M. P. F. Sutcliffe ◽  
W. R. Graham
Keyword(s):  
High Speed ◽  
Slip Rate ◽  
Material Model ◽  
Contact Forces ◽  
Block Modeling ◽  
Rate Dependent ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
The Impact ◽  
Good Agreement

Abstract In an effort to understand the dynamic hub forces on road vehicles, an advanced free-rolling tire-model is being developed in which the tread blocks and tire belt are modeled separately. This paper presents the interim results for the tread block modeling. The finite element code ABAQUS/Explicit is used to predict the contact forces on the tread blocks based on a linear viscoelastic material model. Special attention is paid to investigating the forces on the tread blocks during the impact and release motions. A pressure and slip-rate-dependent frictional law is applied in the analysis. A simplified numerical model is also proposed where the tread blocks are discretized into linear viscoelastic spring elements. The results from both models are validated via experiments in a high-speed rolling test rig and found to be in good agreement.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

Appraisal of Allowable Loads by Simplified Rules

1986 ◽  
Vol 108 (2) ◽  
pp. 131-137
Author(s):  
D. Moulin
Keyword(s):  
Experimental Investigation ◽  
Plastic Region ◽  
Thin Structures ◽  
Geometric Imperfections ◽  
Buckling Behavior ◽  
Simplified Method ◽  
Post Buckling ◽  
Initial Geometric Imperfections ◽  
Fast Breeder Reactors ◽  
Breeder Reactors

This paper presents a simplified method to analyze the buckling of thin structures like those of Liquid Metal Fast Breeder Reactors (LMFBR). The method is very similar to those used for the buckling of beams and columns with initial geometric imperfections, buckling in the plastic region. Special attention is paid to the strain hardening of material involved and to possible unstable post-buckling behavior. The analytical method uses elastic calculations and diagrams that account for various initial geometric defects. An application of the method is given. A comparison is made with an experimental investigation concerning a representative LMFBR component.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

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