scholarly journals Closure to “Discussion of ‘Determination of the Buckling Load for Columns of Variable Stiffness’” (1950, ASME J. Appl. Mech., 17, pp. 222–224)

1950 ◽  
Vol 17 (2) ◽  
pp. 224
Author(s):  
C. C. Miesse
Keyword(s):  
Variable Stiffness ◽  
Buckling Load

Determination of the Buckling Load for Columns of Variable Stiffness

1949 ◽  
Vol 16 (4) ◽  
pp. 406-410
Author(s):  
C. C. Miesse
Keyword(s):  
Lower Bounds ◽  
Axial Loading ◽  
Variable Stiffness ◽  
Buckling Load ◽  
Upper And Lower Bounds ◽  
Variable Section ◽  
Rayleigh Principle

Abstract A method is given for determining both upper and lower bounds on the critical or buckling load for variable-section columns with axial loading. This method, which is an extension of the Rayleigh principle, is illustrated by three examples.

Design of Variable Stiffness Cylinder with Holes Under Bending for Maximum Buckling Load Using Lamination Parameters

2019 ◽  
Author(s):  
Mazen Albazzan ◽  
Brian Tatting ◽  
Ramy Harik ◽  
Zafer Gürdal ◽  
Adriana Blom-Schieber ◽  
...  
Keyword(s):  
Variable Stiffness ◽  
Buckling Load ◽  
Lamination Parameters

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

Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters

AIAA Journal ◽  
2010 ◽  
Vol 48 (1) ◽  
pp. 134-143 ◽  
Author(s):  
Samuel T. IJsselmuiden ◽  
Mostafa M. Abdalla ◽  
Zafer Gurdal
Keyword(s):  
Variable Stiffness ◽  
Buckling Load ◽  
Lamination Parameters

Structural Analysis of Variable Stiffness Laminated Plates Using First-Order Shear Deformation Theory

2014 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
M. Arian Nik ◽  
D. Pasini
Keyword(s):  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Buckling Load ◽  
Shear Stresses ◽  
Critical Buckling Load ◽  
First Order ◽  
Stiffness Design ◽  
Transverse Shear Stresses

Constant and variable stiffness strategies have been developed to design a composite laminate. With the former, each layer is designed with straight fibers that have the highest stiffness and strength in the fiber direction. With the latter, on the other hand, the stiffness can change within each layer by placing the fibers along a curvilinear fiber path. A variable stiffness design results in improved structural performance, as well as opens up opportunities to search for trade-off among structural properties. During the manufacture of a variable stiffness design with Automated Fiber Placement, certain defects in the form of gaps and overlaps could appear within the laminate and affect the laminate performance. In this study, we use the first-order shear deformation theory to assess the effect of transverse shear stresses on the critical buckling load, free and forced vibration of a variable stiffness laminate with embedded defects, an issue so far rarely examined in literature. The governing differential equations for the static analysis are first derived. A semi-analytic solution is then obtained using the hybrid Fourier-Galerkin method and the numeric time integration technique. The eigenvalue analysis is also conducted to determine the fundamental frequency and critical buckling load of the plate. It is found that the behavior of a variable stiffness plate is much more affected by the shear stresses than a constant stiffness plate. Ignoring the effect of transverse shear stresses results in 34% error in the predicted buckling load of a variable stiffness laminate with overlaps and a length-to-thickness ratio of 10.

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).

Size-dependent behavior of laminates with curvilinear fibers made by automated fiber placement

2015 ◽  
Vol 22 (2) ◽  
pp. 157-163 ◽  
Author(s):  
Mahdi Arian Nik ◽  
Larry Lessard ◽  
Damiano Pasini
Keyword(s):  
Variable Stiffness ◽  
Buckling Load ◽  
Fiber Placement ◽  
Plate Size ◽  
Load Increase ◽  
Automated Fiber Placement ◽  
Fiber Path ◽  
Turning Radius ◽  
Curvilinear Fibers ◽  
Minimum Turning Radius

AbstractVariable stiffness laminates can be manufactured using curvilinear fiber paths. A curvilinear fiber path is generally defined based on the plate size and has a curvature that is dependent on the plate size. In practice, however, the fiber path must satisfy manufacturing constraints, such as the minimum turning radius imposed by the automated fiber placement machine, thereby limiting the possible amount of fiber steering. In this work, we studied the effect of the plate size on the structural properties of a plate manufactured with curvilinear fibers. We considered four plate sizes, which were designed by a constant curvature fiber path. We optimized the plates for both maximum buckling load and in-plane stiffness. The results showed that the in-plane stiffness of the plate was not controlled by the plate size, whereas the buckling load was highly affected by the curvature of the fiber path. Hence, the potential of a buckling load increase reduced for plate sizes smaller than the minimum turning radius. In addition, for a given maximum curvature of the fiber path, the influence of a complex layup on the buckling load was marginal.

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