New Warping Function for Thin-Walled Beams. I: Theory

Prokić, Aleksandar

doi:10.1061/(asce)0733-9445(1996)122:12(1437)

Cited by 37 publications

(7 citation statements)

References 3 publications

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“…This work utilized the concept of generalized higher-order warping functions originally introduced by Capurso [21] to provide more accurate results both for static and dynamic responses [22]. Prokic [17,23,24] published a new warping function to be used in three-dimensional thin-walled beams. The approach is able to handle a beam of any arbitrary closed and open cross-sections as well as the issue of discontinuity.…”

Section: Thin-walled Beam Of Discontinuous Cross Sectionsmentioning

confidence: 99%

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Kunaporn¹,

Singh²,

Patil³

et al. 2010

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Probabilistic Analysis of a Thin-walled Beam with a CrackChalitphan Kunaporn (ABSTRACT) It is reasonable to assume that an aircraft might experience some in-flight discrete source damage caused by various incidents. It is, thus, necessary to evaluate the impact of such damage on the performance of the aircraft. This study is focused on evaluating the effect of a simple discrete damage in an aircraft wing on its static and dynamic response.The damaged wing is modeled by a thin-walled beam with a longitudinal crack the response of which can be obtained analytically. As uncertainties are present in the location and size of the crack as well as in the applied loads, their effects are incorporated into the framework consisting of structural response, crack propagation and aeroelasticity.The first objective of this study is to examine the effect of damage represented by a crack on the wing flexibility that influences its deformation and aero-elastic divergence characteristics. To study this, the thin-walled beam is modeled by Benscoter thin-walled beam theory combined with Gunnlaugsson and Pedersen compatibility conditions to accurately account for the discontinuity at the interface of the cracked and uncracked beam segments. Instead of conducting a detailed finite element analysis, the solution is obtained in an exact sense for general distributed loads representing the wind pressure effects. This analytical approach is shown to provide very accurate values for the global beam response compared with the detailed finite element shell analysis. This analytical solution is, then, used to study the beam response probabilistically. The crack location and size are assumed to be uncertain and are, thus, characterized by random variable. For a specified limit state, the probability of failure can be conveniently calculated by the first order second moment analysis using the safety index approach. The same analytical solution is also used to study the aero-elastic divergence characteristics of a wing, the inner structure of which is represented by a thin-walled beam with a crack of uncertain size and position along the beam.iii The second objective of this study is to examine the time growth of a crack under dynamic gust type of loading to which a wing is likely to be exposed during flight.Damage propagating during operation further deteriorates the safety of the aircraft and it is necessary to study its time growth so that its impact on the performance can be evaluated before it reaches its unstable state. The proposed framework for the crack growth analysis is based on classical fracture mechanics where the remaining flight time is obtained by Monte Carlo simulation in which various uncertainties are taken into account. To obtain equivalent cyclic loading required for crack growth analysis, random vibration analysis of the thin-walled beam is conducted for stochastic wind load defined by a gust load spectral density function. The probability of failure represented by the crack size approaching the critical crack size wit...

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Section: Thin-walled Beam Of Discontinuous Cross Sectionsmentioning
confidence: 99%

Probabilistic Analysis of a Thin-Walled Beam with a Crack
Kunaporn¹,
Singh²,
Patil³
et al. 2010
51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
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“…Both Gjelsvik [4] in 1981 and Prokić [8,11,12] in 1990 introduced the thickness warping u t by assuming that this additional warping varies linearly through the thickness and vanishes along the midline. Prokić [8] kept the assumption that the contour warping u c is linear for each branch for cross sections composed of linear segments.…”

Section: General Overviewmentioning
confidence: 99%

“…The warping function of Prokić [11] is modified hereafter and the kinematics of the present work allow the study of coupled effects for asymmetric thin-walled cross sections. h n is modified to be the distance of any point of the cross section to the normal issued from the shear center C (xðy; zÞ ¼ h n ðsÞe, Fig.…”

Section: Kinematics Of Present Workmentioning
confidence: 99%

Non-uniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections
Saadé
¹
,
Espion
²
,
Warzée
³

2004
Thin-Walled Structures
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16
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“…Beam models based on a cross-section discretization that considers warping functions of thin-walled cross-sections were presented in Laudiero [29], Razaqpur and Li [41], Prokić [37], Razaqpur and Li [42], Prokić [38,39], Kim and Kim [25], Prokić [40], Kim and Kim [26], Saadé et al [44]. A new finite beam model for the analysis of non-uniform torsion of beams that considers the cross-section warping through an additional degree of freedom and includes secondary torsional phenomena and shear effects has been proposed in Murin [34].…”

Section: Introductionmentioning
confidence: 99%

A higher order beam model for thin-walled structures with in-plane rigid cross-sections
Vieira
¹
,
Virtuoso
²
,
Pereira
³

2015
Engineering Structures
20
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3
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New Warping Function for Thin-Walled Beams. I: Theory

Cited by 37 publications

References 3 publications

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Non-uniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections

A higher order beam model for thin-walled structures with in-plane rigid cross-sections

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