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.

Effects of Friction on Post-Buckling Behavior and Axial Load Transfer in a Horizontal Well

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1104-1118 ◽  
Author(s):  
Guohua Gao ◽  
Stefan Miska
Keyword(s):  
Boundary Conditions ◽  
Critical Load ◽  
Axial Load ◽  
Load Transfer ◽  
Experimental Studies ◽  
Proper Solution ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Helical Buckling ◽  
Lateral Friction

Summary In this paper, the buckling equation and natural boundary conditions are derived with the aid of calculus of variations. The natural and geometric boundary conditions are used to determine the proper solution that represents the post-buckling configuration. Effects of friction and boundary conditions on the critical load of helical buckling are investigated. Theoretical results show that the effect of boundary conditions on helical buckling becomes negligible for a long pipe with dimensionless length greater than 5π Velocity analysis shows that lateral friction becomes dominant at the instant of buckling initiation. Thus, friction can increase the critical load of helical buckling significantly. However, once buckling is initiated, axial velocity becomes dominant again and lateral friction becomes negligible for post-buckling behavior and axial-load-transfer analysis. Consequently, it is possible to seek an analytical solution for the buckling equation. Analytical solutions for both sinusoidal and helical post-buckling configurations are derived, and a practical procedure for modeling of axial load transfer is proposed. To verify the proposed model and analytical results, the authors also conducted experimental studies. Experimental results support the proposed solutions.

CONCRETE-FILLED TUBULAR COLUMNS: PART 2 — COLUMN ANALYSIS

2004 ◽  
Vol 04 (04) ◽  
pp. 479-495 ◽  
Author(s):  
V. GAYATHRI ◽  
N. E. SHANMUGAM ◽  
Y. S. CHOO
Keyword(s):  
Equilibrium Equations ◽  
Beam Columns ◽  
Tubular Columns ◽  
Post Buckling ◽  
Updated Lagrangian Formulation ◽  
Combined Action ◽  
Newton Raphson ◽  
Experimental Values ◽  
Updated Lagrangian ◽  
Fibre Analysis

This paper is concerned with an analytical model for column analysis of concrete-filled tubular beam-columns subjected to the combined action of axial load and monotonic or cyclic bending. A method of segmentation is adopted in the analysis of beam-columns. The flexural and axial rigidities of the beam-column segments are derived from M–P–φ and M–P–ε relations obtained through fibre-analysis explained in Part 11 of the paper. Geometric and material nonlinearities are taken into account and incremental equilibrium equations are formulated based on an updated Lagrangian formulation. An incremental-iterative Newton–Raphson iteration technique is adopted to obtain the solution of the equations. The limitation of Newton–Raphson technique in approaching the limit points is overcome by using a generalized stiffness parameter, thereby tracing the post-buckling response. The accuracy of the model is verified by comparing the results with the experimental values available in published literature.

Buckling and Post-Buckling Behavior for Roof Strata in Longwall Mining

2012 ◽  
Vol 170-173 ◽  
pp. 751-754
Author(s):  
Qun Song ◽  
Zhi Lin Yang
Keyword(s):  
Longwall Mining ◽  
Main Roof ◽  
Equilibrium Path ◽  
Fracture Characteristics ◽  
Key Stratum ◽  
Buckling Behavior ◽  
Roof Stratum ◽  
Post Buckling ◽  
The Stability ◽  
Roof Strata

In accordance with the occurrence behavior of roof strata and the fracture characteristics of key stratum in shallow seam longwall mining, this paper studied the post-buckling behaviors of key roof stratum in the process of mining by using initial post-buckling theory, which derived a critical load and a breaking span of the main roof during the first weighting, determined the final subsidence for broken key stratum, and presented an application with the example of Daliuta 1203 face. The results indicate that the rock blocks a in are state of non-equilibrium after main roof breaking, the equilibrium path of main roof is unstable from breaking to final subsidence; thick unconsolidated layers above roof have effect on post-buckling behaviors of key stratum; the stability for bifurcation point equilibrium configuration and post-buckling equilibrium path of roof strata could be revealed and an effective method for determining displacement field of imperfection structure could be provided by using initial post -buckling theory.

scholarly journals Nonlinear Response of Graphite-Epoxy Composite Thin-Walled Structure under Elevated Thermal Environment

2011 ◽  
Vol 2-3 ◽  
pp. 865-869
Author(s):  
Yun Dong Sha ◽  
Fei Xu ◽  
Zhi Jun Gao
Keyword(s):  
Critical Temperature ◽  
Boundary Conditions ◽  
Nonlinear Response ◽  
Thermal Environment ◽  
Epoxy Composite ◽  
Complex Loading ◽  
Thin Walled Structures ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

Composite materials thin-walled structures are widely used as skin panel in flight vehicles in recent years. These structures will encounter severe complex loading conditions, which may be a combination of mechanical, aerodynamic, thermal and acoustic loads. Thin-walled structures subjected to this kind of loadings will exhibit nonlinear response; as a result, fatigue failure will occur. High temperature may cause large thermal deflection and stress, for some special conditions, may cause thermal buckling. Once the thermal buckling appears, the stiffness will change correspondingly, it will cause significant influence on the dynamic response and fatigue failure. Accordingly, it is important to research the nonlinear response of this kind of structures under elevated thermal environment. Nonlinear response and thermal pre-buckling/post-buckling behavior of a Graphite-Epoxy composite plate subjected to server thermal loading is numerically investigated in this paper. A composite laminated plate with clamped-clamped boundary conditions is chosen as simulated body, nonlinear finite element model is developed using the first-order shear deformable plate theory, Von Karman strain-displacement relations, and the principle of virtual work. The thermal load is assumed to be a steady-state with different predefined temperature distribution. The thermal strain is stated as an integral quantity of the thermal expansion coefficient with respect to temperature. Then the modes of the plate are analyzed, the nature frequencies and modal shapes are obtained. The critical temperature of buckling is calculated. The static nonlinear equations of motions are solved by the Newton-Raphson iteration technique to obtain the thermal post-buckling deflection. The Riks method is used to analyze static post-buckling behavior. In the numerical examples, four types of situations are studied, which include i) the buckling behaviors for different initial imperfections, ii) the buckling behaviors for different thickness to width ratios, and iii) The buckling behaviors for different width to length ratios; The critical temperature, the static thermal post-buckling deflection and the load to displacement relation are presented respectively. The influences of different boundary conditions on the buckling behaviors of the plate are achieved as well. The simulation method and results presented in this paper can be valuable references for further analysis of the nonlinear responses of thin-walled structures under complex loading conditions.

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 THERMAL POST-BUCKLING OF SLENDER ELASTIC RODS WITH DIFFERENT BOUNDARY CONDITIONS

2006 ◽  
Vol 5 (2) ◽  
pp. 50
Author(s):  
R. F. Solano ◽  
M. A. Vaz
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Different Boundary Conditions ◽  
Linear Ordinary Differential Equations ◽  
Linear Elastic ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling ◽  
Complex Boundary

This paper presents mathematical formulation, critical buckling temperature and analytical and numerical solutions for the thermal post-buckling behavior of slender rods subjected to uniform thermal load. The material is assumed to be linear elastic, homogeneous and isotropic. Furthermore, large displacements are considered hence the formulation is geometrically non-linear. Three different boundary conditions are assumed: (i) double-hinged non-movable, (ii) hinged non-movable at one end, whereas at the other end longitudinal displacement is constrained by a linear spring, and (iii) double-fixed non-movable. The governing equations are derived from geometrical compatibility, equilibrium of forces and moments, constitutive equations and strain-displacement relation, yielding a set of six first-order non-linear ordinary differential equations with boundary conditions specified at both ends, which constitutes a complex boundary value problem. The buckling and post-buckling solutions are respectively accomplished assuming infinitesimal and finite rotations. The results are presented in non-dimensional graphs for a range of temperature gradients and different values of slenderness ratios, and it is shown that this parameter governs the rod post-buckling response. The influence of the boundary conditions is evaluated through graphic results for deformed configuration, maximum deflection, maximum inclination angle and maximum curvature in the rod.

A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells

1988 ◽  
Vol 55 (3) ◽  
pp. 611-617 ◽  
Author(s):  
R. Schmidt ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Plate Theory ◽  
Small Strain ◽  
Present Theory ◽  
Shell Structures ◽  
Governing Equations ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Principle Of Virtual Displacements

A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Ka´rma´n type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

A REVIEW OF THE INSTABILITY PROBLEM FOR FRAME STRUCTURES

2001 ◽  
Vol 01 (02) ◽  
pp. 181-194 ◽  
Author(s):  
QIANG XUE ◽  
JOHN L. MEEK
Keyword(s):  
Limit Point ◽  
Limit State ◽  
Beam Theory ◽  
Point Of View ◽  
Equilibrium Path ◽  
Small Deflection ◽  
Non Linear ◽  
Post Buckling ◽  
Work Done ◽  
Raphson Iteration

This paper presents large deflection, post-buckling analysis of plane and spatial elastic frames from a dynamic point of view. A co-rotational formulation combined with small deflection beam theory with the inclusion of the effect of axial force is adopted. A constant arc length method combined with the modified Newton–Raphson iteration method and the extrapolation technique to improve the convergence behaviour are employed to trace the non-linear equilibrium path up to the limit point. The change in the sign of the incremental work done is used to determine the occurrence of a limit point. As the limit state being examined is passed, the previous converged solution is adopted to start the non-linear dynamic analysis based on the average acceleration of the Newmark algorithm with a slow rate of load increment and in order to trace the post-buckling load-deflection path. As a result, the snap through problem is overcome without decreasing the external load. Numerical examples are presented to demonstrate the performance of the method.

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.

Sign in / Sign up

Export Citation Format

Share Document