Effect of warping shape on buckling of circular and rectangular columns under axial compression

Ma, Weili; Jiang, Zi-Cheng; Li, Xian-Fang

doi:10.1016/j.apm.2020.08.003

Cited by 9 publications

(2 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus in what follows it is convenient to take

f\left(z\right)

as an odd function with

f\left(0\right) =0

. There are a large number of functions to satisfy such conditions [37]. For example, the warping shape

f(z)

may be chosen as a variety of functions including polynomials, trigonometric functions, exponential functions, and so forth, some of which are listed in Table 1.…”

Section: Theoretical Formulationmentioning

confidence: 99%

Higher‐order effect of axial force on free vibration and buckling of functionally graded sandwich beams

Sun,

2024

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

This paper presents a novel higher‐order shear deformation beam theory for analyzing the stability and free vibration of functionally graded (FG) sandwich beams with emphasis on the effect of higher‐order moment (HOM) and cross‐sectional warping. The governing equation of axially loaded FG sandwich beams is derived from three‐dimensional equations of the theory of elastic waves in bodies with homogeneous initial stresses. The characteristic equations for typical end conditions are obtained exactly. The numerical results of the natural frequencies and critical loads are calculated and verified for special cases by comparing them with the existing solutions. The effects of gradient index, core thickness, HOM, and warping shapes on the natural frequencies and critical buckling loads are elucidated for different slenderness ratios and end constraints.

show abstract

“…Thus in what follows it is convenient to take

f\left(z\right)

as an odd function with

f\left(0\right) =0

. There are a large number of functions to satisfy such conditions [37]. For example, the warping shape

f(z)

may be chosen as a variety of functions including polynomials, trigonometric functions, exponential functions, and so forth, some of which are listed in Table 1.…”

Section: Theoretical Formulationmentioning

confidence: 99%

Higher‐order effect of axial force on free vibration and buckling of functionally graded sandwich beams

Sun,

2024

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…Their results matched very well with the exact solutions, but the paper did not customize the solutions for different shapes of cross-sections (for example, rectangular, circular, and annular cross-sections). Regarding computation methods, Ma et al [ 10 ] computed critical buckling force considering various higher-order shear deformation beam theories based on Engesser’s hypothesis and Haringx’s hypothesis in comparison with Euler’s theory in order to show the effects of warping shape. That research showed that buckling loads were not influenced by the theory used in the case of very slender columns or in the case of those having high shear rigidity.…”

Section: Introductionmentioning

confidence: 99%

Design Solutions for Slender Bars with Variable Cross-Sections to Increase the Critical Buckling Force

Botiș

Cerbu

2022

Materials

View full text Add to dashboard Cite

In large metal civil constructions (stadium roofs, bridges), slender bars can lose their stability under compression loading. There is a lack in the literature regarding design solutions and methods for increasing the critical buckling force of bars with variable cross-sections. The aim of this research is to present a numerical model with finite elements used for a comparative analysis of increasing the critical force of stability loss in cases of (i) bars with stepwise variation in the cross-sections and (ii) bars with continuous variation in the moment of inertia along the bar axis (parabolic, sinusoidal, triangular, and trapezoidal variation). Considering the large-scale applications in civil engineering, bars that were pin-connected at one end and simple-supported at the other end were analyzed. Firstly, the analytical model was described to compute the critical buckling force for bars with stepwise variation in the cross-sections. Then, a finite element model for a slender bar and the assumptions considered were presented. The results were computed using the MATLAB program based on the numerical model proposed and were validated with the analytical model for stepwise variable cross-sections of the bars. The numerical model was adapted for bars with continuous variation in the moment of inertia along the bar axis. It was shown that, by trapezoidal variation in the second moment of inertia along the axis of a bar, i.e., as buckling occurred in the elastic field, the critical buckling force could be increased by 3.556 times compared to a bar with a constant section. It was shown that there was certain bar with stepwise variation in the cross-section for which the critical buckling force was approximately equal to the one obtained for the bar with sinusoidal variation in the moment of inertia (increased by 3.427 times compared to a bar with a constant section).

show abstract

Free vibration of radially graded hollow cylinders subject to axial force via a higher-order shear deformation beam theory

Cheng²,

Chen³

et al. 2021

Composite Structures

View full text Add to dashboard Cite

Effect of warping shape on buckling of circular and rectangular columns under axial compression

Cited by 9 publications

References 43 publications

Higher‐order effect of axial force on free vibration and buckling of functionally graded sandwich beams

Higher‐order effect of axial force on free vibration and buckling of functionally graded sandwich beams

Design Solutions for Slender Bars with Variable Cross-Sections to Increase the Critical Buckling Force

Free vibration of radially graded hollow cylinders subject to axial force via a higher-order shear deformation beam theory

Contact Info

Product

Resources

About