A LOWER BOUND FOR THE BUCKLING LOAD OF A DIVERGENT NON-CONSERVATIVE SYSTEM

1988 ◽  
Vol 12 (3) ◽  
pp. 129-132
Author(s):  
B.L. LY
Keyword(s):  
Lower Bound ◽  
Eigenvalue Problem ◽  
Adjoint System ◽  
Conservative System ◽  
Buckling Load ◽  
Smallest Eigenvalue

The divergent non-conservative problems considered in this paper are pseudo self-adjoint. It is shown that a self-adjoint eigenvalue problem is related to the original non-conservative problem. The smallest eigenvalue of this self-adjoint system provides a lower bound for the buckling load of the non-conservative system.

On the Sufficiency of the Energy Criterion for the Stability of Certain Nonconservative Systems of the Follower-Load Type

1972 ◽  
Vol 39 (3) ◽  
pp. 717-722 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Lower Bound ◽  
Critical Load ◽  
Energy Criterion ◽  
Conservative System ◽  
Buckling Load ◽  
Follower Load ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
Divergence Type ◽  
The Stability

Using Galerkin’s method it is shown that in the domain of divergence, the nonconservative system of the follower-load type is always more stable than the corresponding conservative system. Hence, for nonconservative systems of the divergence type, the critical load of the corresponding conservative system becomes a lower bound for the buckling load, and the energy criterion remains sufficient for predicting stability. Moreover, it is proven that even for more general nonconservative systems, the energy criterion is sufficient under certain restrictions.

Lower Bounds for the Buckling Loads and the Fundamental Frequencies of Elastic Bodies

1974 ◽  
Vol 41 (1) ◽  
pp. 151-154 ◽  
Author(s):  
C. H. Popelar
Keyword(s):  
Lower Bound ◽  
Elastic Body ◽  
Fundamental Frequency ◽  
Lower Bounds ◽  
Upper Bound ◽  
Elastic Stability ◽  
Buckling Load ◽  
Buckling Loads ◽  
Fundamental Frequencies ◽  
Elastic Bodies

Within the classical theory of elastic stability a lower bound to the buckling load of an elastic body is presented. The Timoshenko load is shown to be a better upper bound to the buckling load than the Rayleigh load. By appropriate modifications of the potential and complementary energies, these bounds are applicable to the fundamental frequency of an elastic body. The application of the bounds is illustrated.

Variation in the Geometric Interpretation of the Eigenvalue Problem of a Structure Due to Damage

1999 ◽  
Author(s):  
Frederick A. Just Agosto ◽  
Scott L. Hendricks
Keyword(s):  
Eigenvalue Problem ◽  
Convex Hull ◽  
Convex Set ◽  
Conservative System ◽  
Geometric Interpretation ◽  
Degree Of Freedom ◽  
Damage Scenarios ◽  
Spring System ◽  
Two Degree Of Freedom

Abstract This paper studies the behavior of the geometric interpretation of the eigenvalue problem. An arbitrary two degree of freedom structure is modeled as a two mass, two spring system. The damage in the system is represented as a reduction in stiffness and the structure is assumed to be a natural conservative system. The geometric interpretation of the system is an ellipse which is examined under various damage conditions occurring on the structure. It is shown that this representation is a convex set and that damage produces a new set which is the convex hull of the existing condition. These results are graphed for several damage scenarios of the system.

scholarly journals Hartman-Type and Lyapunov-Type Inequalities for a Fractional Differential Equation with Fractional Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Imed Bachar ◽  
Hassan Eltayeb
Keyword(s):  
Differential Equation ◽  
Lower Bound ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

We prove Hartman-type and Lyapunov-type inequalities for a class of Riemann–Liouville fractional boundary value problems with fractional boundary conditions. Some applications including a lower bound for the corresponding eigenvalue problem are obtained.

Lower Bound Buckling Load of a Floating Roof Pontoon

2010 ◽  
Author(s):  
Shoichi Yoshida
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Large Diameter ◽  
Buckling Load ◽  
Bottom Plate ◽  
Element Analysis ◽  
Oil Storage ◽  
Bending Load ◽  
Stiffness Method ◽  
Shell Finite Element

The 2003 Tokachi-Oki earthquake caused severe damage to oil storage tanks due to liquid sloshing. Seven single-deck floating roofs had experienced sinking failures in large diameter tanks at a refinery in Tomakomai, Japan. The pontoons of the floating roofs might be buckled due to bending load during the sloshing. The content in the tank was spilled on the floating roof from small failures which were caused in the welding joints of pontoon bottom plate by the buckling. Then the floating roof began to lose buoyancy and sank into the content slowly. The elastic buckling of the pontoon is important from the viewpoint of the single-deck floating roof sinking. The authors had reported the buckling strength of the pontoons subjected to bending and compressive loads in the published literatures. The axisymmetric shell finite element method for linear elastic bifurcation buckling was used in the analysis. The buckling characteristics of the pontoon both with and without ring stiffeners were investigated. The initial geometrical imperfection may diminish the buckling load. This paper presents the lower bound buckling load according to the reduced stiffness method proposed by Croll and Yamada. The lower bound buckling loads of the pontoon subjected to circumferential bending load are evaluated from the axisymmetric finite element analysis which includes the reduced stiffness method.

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