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.

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.

Large-deflection and post-buckling behavior of slender beam-columns with non-linear end-restraints

2011 ◽  
Vol 46 (1) ◽  
pp. 79-95 ◽  
Author(s):  
Carlos Vega-Posada ◽  
Mauricio Areiza-Hurtado ◽  
J. Dario Aristizabal-Ochoa
Keyword(s):  
Large Deflection ◽  
Beam Columns ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling

Post-buckling Behavior of Stiffened Cross-Ply Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 998-1000 ◽  
Author(s):  
M. Savoia ◽  
J. N. Reddy
Keyword(s):  
Axial Compression ◽  
Carrying Capacity ◽  
Shell Theory ◽  
Load Carrying Capacity ◽  
Imperfection Sensitivity ◽  
Buckling Modes ◽  
Geometric Imperfection ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Post Buckling

The post-buckling of stiffened, cross-ply laminated, circular determine the effects of shell lamination scheme and stiffeners on the reduced load-carrying capacity. The effect of geometric imperfection is also included. The analysis is based on the layerwise shell theory of Reddy, and the “smeared stiffener” technique is used to account for the stiffener stiffness. Nu cylinders under uniform axial compression is investigated to merical results for stiffened and unstiffened cylinders are presented, showing that imperfection-sensitivity is strictly related to the number of nearly simultaneous buckling modes.

The Elastic Instability of a Complete Spherical Shell

1962 ◽  
Vol 13 (2) ◽  
pp. 189-201 ◽  
Author(s):  
J.M.T. Thompson
Keyword(s):  
Spherical Shell ◽  
High Speed ◽  
Large Deflection ◽  
Elastic Shell ◽  
External Pressure ◽  
Maximum Pressure ◽  
Elastic Instability ◽  
Rotationally Symmetric ◽  
Post Buckling ◽  
Good Agreement

SummaryThe elastic instability of a complete spherical shell under uniform external pressure is studied experimentally and theoretically. The premature snapping of a thin elastic shell, made of polyvinyl chloride, is seen to be classical in nature. The experimental maximum pressure and pre-snapping bending deformation are correlated with the theoretical behaviour of an initially imperfect shell. The large deflection behaviour of a perfect shell is assessed experimentally, and the stable post-buckling states are observed to be rotationally symmetric. A fairly precise theoretical analysis of these states is performed, the use of a high-speed digital computer allowing a considerable advance over previous treatments. The experimental and theoretical post-buckling curves are in good agreement, yielding the first detailed correlation of post-snapping equilibrium states in the field of shell instability.

The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams

1987 ◽  
Vol 54 (3) ◽  
pp. 558-562 ◽  
Author(s):  
I. Sheinman ◽  
M. Adan
Keyword(s):  
Finite Difference ◽  
Shear Deformation ◽  
Nonlinear Differential Equations ◽  
Kinematic Model ◽  
Transverse Shear Deformation ◽  
Shear Effect ◽  
Laminated Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Post Buckling

A geometrical nonlinear theory of composite laminated beams is derived with the effect of transverse shear deformation taken into account. The theory is based on a high-order kinematic model, with the nonlinear differential equations solved by Newton’s method and a special finite-difference scheme. A parametric study of the shear effect involving several kinematic approaches was carried out for isotropic and anisotropic beams.

Characterization of Sheet Buckling Subjected to Controlled Boundary Constraints

2002 ◽  
Vol 124 (3) ◽  
pp. 493-501 ◽  
Author(s):  
Jian Cao ◽  
Xi Wang ◽  
Francis Joe Mills
Keyword(s):  
Hybrid Approach ◽  
Fem Analysis ◽  
Test Machine ◽  
Buckling Modes ◽  
Boundary Constraints ◽  
Numerical Predictions ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Strip Test

A wedge strip test is designed to study the onset and post-buckling behavior of a sheet under various boundary constraints. The device can be easily incorporated into a conventional tensile test machine and material resistance to buckling is measured as the buckling height versus the in-plane strain state. The design yields different but consistent buckling modes with easy changes of boundary conditions (either clamped or freed) and sample geometry. Experimental results are then used to verify a hybrid approach to buckling prediction, i.e., the combination of the FEM analysis and an energy-based analytical wrinkling criterion. The FEM analysis is used to obtain the stress field and deformed geometry in a complex forming condition, while the analytical solution is to provide the predictions less sensitive to artificial numerical parameters. A good agreement between experimental data and numerical predictions is obtained.

A Method for Analyzing Elastic Large Deflection Behavior of Perfect and Imperfect Plates With Partially Rotation-Restrained Edges

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Jeom Kee Paik ◽  
Do Kyun Kim ◽  
Hoseong Lee ◽  
Yong Lae Shim
Keyword(s):  
Large Deflection ◽  
Biaxial Loading ◽  
Torsional Rigidity ◽  
Nonlinear Behavior ◽  
Edge Condition ◽  
Biaxial Compression ◽  
Buckling Behavior ◽  
Deflection Analysis ◽  
Post Buckling ◽  
Loading Ratio

The edge condition of the plating in a continuous stiffened-plate structure is neither simply supported nor clamped because the torsional rigidity of the support members at the plate edges is neither zero nor infinite. In a robust ship structural design, it is necessary to accurately take into account the effect of the edge condition in analyses of plate behavior in terms of buckling and post-buckling behavior. The aim of this study is to develop a new method for analyzing the geometric nonlinear behavior (i.e., elastic large deflection or post-buckling behavior) of plates with partially rotation-restrained edges in association with the torsional rigidity of the support members and under biaxial compression. An analytical method was developed to solve this problem using the nonlinear governing differential equations of plates. The validity of the developed method was confirmed by comparison with nonlinear finite element method solutions with varying values for the torsional rigidity of the support members, plate aspect ratio, and biaxial loading ratio. The developed method was found to give reasonably accurate results for practical design purpose in terms of the large deflection analysis of plates with partially rotation-restrained edges, and it will be useful for the robust design of ship structures in association with buckling and ultimate strength of plates surrounded by support members.

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.

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