scholarly journals Dynamic Post-Buckling Behavior

2017 ◽  
Vol 17 (2) ◽  
pp. 131-150
Author(s):  
Ľuboš Šnirc ◽  
Alžbeta Grmanová ◽  
Ján Ravinger
Keyword(s):  
Residual Stresses ◽  
Linear Theory ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling ◽  
Non Destructive

Abstract Geometric non-linear theory has been used to describe the post-buckling behavior of slender web. Hamilton’s principle in increments has been used. Examples of dynamic post-bucking behavior of slender web loaded in compression are presented. Influence of residual stresses to frequency of slender web is a base for non-destructive method of investigation of structures.

Imperfection Sensitivity of Post-Buckling Behavior and Vibration Response in Pre- and Post-Buckled Regions of Nanoscale Plates Considering Surface Effects

2018 ◽  
Vol 10 (03) ◽  
pp. 1850027 ◽  
Author(s):  
Raheb Gholami ◽  
Reza Ansari
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Displacement Vector ◽  
Vibration Response ◽  
Hamilton’S Principle ◽  
Imperfection Sensitivity ◽  
Hamilton's Principle ◽  
External Work ◽  
Buckling Behavior ◽  
Post Buckling

This paper aims to investigate the imperfection sensitivity of the post-buckling behavior and the free vibration response under pre- and post-buckling of nanoplates with various edge supports in the thermal environment. Formulation is based on the higher-order shear deformation plate theory, von Kármán kinematic hypothesis including an initial geometrical imperfection and Gurtin–Murdoch surface stress elasticity theory. The discretized nonlinear coupled in-plane and out-of-plane equations of motion are simultaneously obtained using the variational differential quadrature (VDQ) method and Hamilton’s principle. To this end, the displacement vector and nonlinear strain–displacement relations corresponding to the bulk and surface layers are matricized. Also, the variations of potential strain energies, kinetic energies and external work are obtained in matrix form. Then, the VDQ method is employed to discretize the obtained energy functional on space domain. By Hamilton’s principle, the discretized quadratic form of nonlinear governing equations is derived. The resulting equations are solved employing the pseudo-arc-length technique for the post-buckling problem. Moreover, considering a time-dependent small disturbance around the buckled configuration, the vibrational characteristics of pre- and post-buckled nanoplates are determined. The influences of initial imperfection, thickness, surface residual stress and temperature rise are examined in the numerical results.

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

Stability and Vibration of Imperfect Column and Slender Web

2014 ◽  
Vol 969 ◽  
pp. 328-331
Author(s):  
Ľuboš Šnirc ◽  
Jan Ravinger
Keyword(s):  
Residual Stresses ◽  
Linear Theory ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Thin Walled Structures ◽  
Geometrical Imperfections ◽  
Thin Walled ◽  
Non Destructive ◽  
Structural Imperfections ◽  
Lagrange Description

Using the geometric non-linear theory (The Total Lagrange Description) in dynamics we can establish the problem of the natural vibration of the structure including the effects of the structural and geometrical imperfections. The incremental stiffness matrix can take into account the residual stresses (structural imperfections) and the geometrical initial displacements (geometrical imperfections) as well. The behaviour of columns, frames and thin-walled structures is sensitive to imperfections. This theory and results can be used as a base for the non-destructive method for the evaluation of the level of the load and the imperfections.

Pure Bending Test on a Box Girder With Low Panel’s Slenderness

2018 ◽  
Author(s):  
José Manuel Gordo ◽  
Carlos Guedes Soares
Keyword(s):  
Residual Stresses ◽  
Progressive Collapse ◽  
Bending Moment ◽  
Bending Test ◽  
Box Girder ◽  
Buckling Behavior ◽  
Linear Characteristic ◽  
Collapse Mode ◽  
Post Buckling ◽  
The Moment

The results of a four points bending test on a box girder are presented. The experiment is part of series of tests with similar configuration but different thickness, spacing between longitudinal stiffeners and span between frames. The present work refers to the stockiest plate box girder with a plate’s thickness of 4 mm and a span between frames of 800 mm. The experiment includes initial loading cycles allowing for residual stresses relief. It also includes a series of cycles close to collapse load allowing the analysis of linear characteristic at high levels of load. The moment curvature relationship is established for a large range of curvatures. The ultimate bending moment of the box is evaluated and compared with the first yield moment and the plastic moment allowing the evaluation of the efficiency of the structure. The post buckling behavior and collapse mode are characterized. Comparison of the experiment with a progressive collapse method is made taking into consideration the effect of residual stresses on envelop of the moment curvature curve of the structure.

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.

Analytical study of thermal buckling and post-buckling behavior of composite beams reinforced with SMA by Reddy Bickford theory

2021 ◽  
pp. 1045389X2110116
Author(s):  
Mahshad Fani ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Composite Structures ◽  
Volume Fraction ◽  
Thermal Buckling ◽  
Constitutive Law ◽  
Beam Deflection ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling

Shape memory alloys are used in composite structures due to their shape memory effect and phase transformation. The recovery force of the shape memory alloy improves the post-buckling behavior of the structure. In this study, the thermal buckling and post-buckling of Shape Memory Alloy (SMA) hybrid composite laminated beam subjected to uniform temperature distribution is investigated. To this purpose, considering Von-Karman non-linear strain terms for large deformation, the non-linear equations of SMA reinforced beam based on Reddy Bickford theory have been derived. Besides, the recovery stress of the restrained SMA wires during martensitic transformation was calculated based on the one-dimensional constitutive law of the Brinson’s model. A numerical solution using Galerkin’s method has been presented for solving the nonlinear partial differential equations to obtain the critical buckling temperature and transverse deformation of the beam in the post-buckling region in both symmetric and anti-symmetric layups. The effect of SMA volume fraction, pre-strain, the boundary condition of the beam, stacking sequence, and its geometric properties have been studied. The results show that even by adding a small amount of SMA to the composite, the critical buckling temperature increases significantly, and the beam deflection decreases. Besides, using this theory has an evident effect on the anti-symmetric layup, especially for the thick beams.

A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings

2016 ◽  
Vol 52 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Amlan Paul ◽  
Debabrata Das
Keyword(s):  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Temperature Rise ◽  
Functionally Graded ◽  
Buckling Load ◽  
Uniform Temperature ◽  
Buckling Behavior ◽  
Non Linear ◽  
Graded Material ◽  
Post Buckling

In the present work, the non-linear post-buckling load–deflection behavior of tapered functionally graded material beam is studied for different in-plane thermal loadings. Two different thermal loadings are considered. The first one is due to the uniform temperature rise and the second one is due to the steady-state heat conduction across the beam thickness leading to non-uniform temperature rise. The governing equations are derived using the principle of minimum total potential energy employing Timoshenko beam theory. The solution is obtained by approximating the displacement fields following Ritz method. Geometric non-linearity for large post-buckling behavior is considered using von Kármán type non-linear strain-displacement relationship. Stainless steel/silicon nitride functionally graded material beam is considered with temperature-dependent material properties. The validation of the present work is successfully performed using finite element software ANSYS and using the available result in the literature. The post-buckling load–deflection behavior in non-dimensional plane is presented for different taperness parameters and also for different volume fraction indices. Normalized transverse deflection fields are presented showing the shift of the point of maximum deflection for various deflection levels. The results are new of its kind and establish benchmark for studying non-linear thermo-mechanical behavior of tapered functionally graded material beam.

Buckling of Long Thin Plates under Residual Stresses with Application to Strip Rolling

2014 ◽  
Vol 611-612 ◽  
pp. 221-230 ◽  
Author(s):  
Kekeli Kpogan ◽  
Michel Potier-Ferry
Keyword(s):  
Experimental Data ◽  
Finite Elements ◽  
Residual Stresses ◽  
Thin Plates ◽  
Continuous Annealing ◽  
Deflection Curve ◽  
Strip Rolling ◽  
Buckling Mode ◽  
Buckling Behavior ◽  
Post Buckling

We present a simplified numerical method which can be used to predict efficiently the response of long thin plates under effects of residual stresses induced by production process such as rolling or continuous annealing. The principle consists in assuming harmonic buckling mode along the sheet length, and we consider Koiter-Budiansky post-buckling theory to compute the stress-deflection curve. In this way, only the width of the sheet has to be discretized by 1D finite elements. The size and shape of the flatness defects can be predicted efficiently and for a large number of cases. Various types of residual stresses and loadings can be accounted for. In particular, we will see the influence of the global traction on the buckling and post-buckling behavior. The numerical results are compared with experimental data and full numerical computations

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