Buckling analysis of homogeneous or composite I-beams using a 1D refined beam theory built on Saint Venant's solution

2018 ◽  
Vol 127 ◽  
pp. 822-831 ◽  
Author(s):  
Fares Naccache ◽  
Rached El Fatmi
Keyword(s):  
Beam Theory ◽  
Buckling Analysis ◽  
Refined Beam Theory

Matrix Method for Buckling Analysis of Frames Based on Hencky Bar-Chain Model

2019 ◽  
Vol 19 (08) ◽  
pp. 1950093 ◽  
Author(s):  
W. H. Pan ◽  
C. M. Wang ◽  
H. Zhang
Keyword(s):  
Matrix Method ◽  
Structural Changes ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Chain Model ◽  
Bernoulli Beam ◽  
Various Boundary Conditions ◽  
End Restraint ◽  
Euler Bernoulli Beam ◽  
General Frames

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams

2019 ◽  
Vol 57 ◽  
pp. 175-191 ◽  
Author(s):  
Wafa Adda Bedia ◽  
Mohammed Sid Ahmed Houari ◽  
Aicha Bessaim ◽  
Abdelmoumen Anis Bousahla ◽  
Abdelouahed Tounsi ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Strain Gradient ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Beam Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Strain Gradient Theory ◽  
Beam Model ◽  
Nonlocal Strain Gradient

In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton’s principle. Analytical solutions for the bending and buckling analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending buckling of nanobeams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory. The results obtained are found to be accurate. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and buckling behaviour of nanobeams, but also comparable with the other shear deformation theories which contain more number of unknowns

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