An Introduction to the Elastic Stability of Structures

Simitses, George J.

doi:10.1115/1.3423874

Cited by 159 publications

(108 citation statements)

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“…In Fig. 5b, the force direction remains radial (this problem is often referred to as t he "flagpole" problem), and the elastic buckling load is equal to p 2 EI / L 2 (Simitses [7]). Both of these are examples of conservative forces.…”

Section: Conservative Forcesmentioning

confidence: 99%

Second order moments in torsion members

Trahair¹,

Teh²

2001

Engineering Structures

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Section: Conservative Forcesmentioning

confidence: 99%

Second order moments in torsion members

Trahair¹,

Teh²

2001

Engineering Structures

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“…The point of bifurcation instability for elastic columns is defined in many textbooks as the sudden transition between the column displacing axially in the direction of the applied load, also defined as the primary path, to an alternative transverse displacement path, defined as the post-buckling path (Simitses, 1986). Because of the presence of the BRB's restrainer, the post-buckling path may not be fully realized.…”

Section: Equation 41 Is Then Substituted Into Equation 34 and After Cmentioning

confidence: 99%

Development of an Ultra-Lightweight Buckling-Restrained Brace Using Analytical and Numerical Methods

Tinker¹

2000

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An ultra-lightweight buckling-restrained brace (ULWBRB) is developed using a highly ductile aluminum core and FRP restrainer. Utilization of lightweight materials results in a BRB that is 25% the weight of traditional mortar-filled tube varieties allowing easy installation in small to medium sized buildings requiring seismic retrofit without the need for heavy equipment. Construction utilizes commonly stocked materials able to be customized for required strength, drift, and geometry limitations.Analytical single degree of freedom (SDOF) and Euler buckling models are compared with published equations to determine the required restrainer stiffness (RRS).SDOF models yield RRS values 200% higher than the Euler model. Applied end moments due to frame deformation are incorporated into a modified design method that gives RRS values 50% higher than Euler model without eccentricity. RRS is provided using a bundled and wrapped FRP tube configuration using a developed shear flow method considering composite action.Uniaxial low-cycle fatigue (LCF) testing of a 6061-T6 candidate alloy provides data for a constitutive model using combined kinematic-isotropic hardening. LCF testing of round short gage coupons indicates the candidate alloy is capable of stable cycling to 2%, 3%, and 4% total strain with excellent ductility. Early fracture of specimens at 24, 18, and 11 cycles, respectively, also indicates that other candidate alloys should be examined for improved fatigue life. However, inconsistency is noted between similar tests of 6061-T6 that were able to achieve up to 76 cycles at 2.5% total strain.ii ULWBRB FEA models loaded monotonically consistently give higher RRS values as compared to the analytical methods. This is due to assignment of initial imperfections, longer more realistic unbraced length, higher axial loads achieved through the post-yield region, and plastic hinging potential. Cyclic simulations of braces with the same RRS values are also able to achieve reliable and stable hysteretic behavior through 21 cycles. If a less stiff restrainer is used, cumulative energy dissipation potential is reduced considerably due to pinched hysteresis loops and strain ratcheting. Applied end moments are found to have a linear effect on the RRS that can be modeled by superposition of the buckling effect plus end moment.iii

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“…Now, more than two centuries after Euler, there is a vast literature dedicated to structural stability. Several methods exist for obtaining the stability criteria; see, for instance, [3], [4], and [5]. Soon after Euler, Lagrange was probably the first to formalize the framework for stability analysis in his study of the stability of planetary orbits (1776).…”

Section: Introductionmentioning

confidence: 99%

Can complex systems really be simulated?

Kalmár‐Nagy¹,

Stanciulescu²

2014

Applied Mathematics and Computation

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The simulation of complex systems is important in many fields of science and in real-world applications. Such systems are composed of many interacting subsystems. There might exist different software packages for simulating the individual subsystems and co-simulation refers to the simultaneous execution of multiple interacting subsystem simulators. Simulation or co-simulation, if not designed properly, can return misleading numerical solutions (unstable numerical solutions for what is in fact a stable system or vice versa). To understand the cause of these numerical artifacts, we first propose a simple mathematical model for co-simulation, and then construct stability charts. These charts shed light on transitions between stable and unstable behaviour in co-simulation. Our goal is to understand the stability properties of the simulated and co-simulated representation of the continuous system. We will achieve this goal by expressing the trace and determinant of the discretized system in terms of the trace and determinant of the continuous system to establish stability criteria.

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An Introduction to the Elastic Stability of Structures

Cited by 159 publications

References 0 publications

Second order moments in torsion members

Second order moments in torsion members

Development of an Ultra-Lightweight Buckling-Restrained Brace Using Analytical and Numerical Methods

Can complex systems really be simulated?

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