Undestructive determination of the buckling load of an elastic bar

AIAA Journal ◽  
1970 ◽  
Vol 8 (12) ◽  
pp. 2274-2276 ◽  
Author(s):  
MENAHEM BARUCH
Keyword(s):  
Buckling Load ◽  
Elastic Bar

Determination of the Buckling Load of Struts with Successive Approximations

1943 ◽  
Vol 47 (387) ◽  
pp. 103-105
Author(s):  
J. Ratzersdorfer
Keyword(s):  
Differential Equation ◽  
Compressive Force ◽  
Buckling Load ◽  
Moment Of Inertia ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Exact Determination ◽  
The Moment ◽  
Image Position

In cases of tapered struts with hinged or built-in ends where the exact determination of the buckling load is complicated it may be useful to apply a method of successive approximations.Let us first consider a bar of the length l with hinged ends under the action of the compressive force P. The differential equation of the bending line becomeswhere v is the deflection at the section u, v with the moment of inertia I (u) and E is Young's modulus. At the ends of the bar the deflection v is equal to zero (Fig. I).

scholarly journals Buckling of nanobeams and nanorods with cracks

2019 ◽  
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Piecewise Constant ◽  
Cracklike Defects ◽  
General Method

Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

scholarly journals DETERMINATION OF THE CRITICAL BUCKLING LOADS OF EULER COLUMNS USING STODOLA-VIANELLO ITERATION METHOD

2018 ◽  
Vol 30 (3) ◽  
Author(s):  
Ofondu I.O. ◽  
Ikwueze E.U. ◽  
Ike C.C.
Keyword(s):  
Iteration Method ◽  
Longitudinal Axis ◽  
Rayleigh Quotient ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Relative Errors ◽  
Fixed End

The Stodola-Vianello iteration method was implemented in this work to determine the critical buckling load of an Euler column of length l with fixed end (x = 0) and pinned end (x = l), where the longitudinal axis is the x-direction.The critical buckling loads were found to be variable, depending on the x-coordinate. Integration and the Rayleigh quotients were used to find average buckling coefficients. First iteration gave relative errors of 4% using integration and 2.5% using Rayleigh quotient.Second iteration gave average relative errorsless than 1% for both the integration and the Rayleigh quotients. Better estimates of the critical buckling loads were obtained using the Rayleigh quotient in the Stodola-Vianello’s iteration.

scholarly journals Stability of nanobeams and nanoplates with defects

2021 ◽  
Vol 25 (2) ◽  
pp. 221-238
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Critical Stress ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Physical Parameters ◽  
Axial Loads ◽  
Critical Buckling Load ◽  
Support Conditions ◽  
The Impact

The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.

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