A torsion bending element for thin-walled beams with open and closed cross sections

Shakourzadeh, H.; Guo, Yousong; Batoz, Jean‐Louis

doi:10.1016/0045-7949(94)00509-2

Cited by 55 publications

(29 citation statements)

References 4 publications

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“…Benscoter [8], thus, introduced a more generalized approach of employing an additional warping degree of freedom to describe displacement fields independently. This theory is illustrated in [13,[17][18][19].…”

Section: Timoshenko's Theorymentioning

confidence: 99%

“…Shakourzadeh et al [13] published a work discussing on differences between Vlasov's and approaches can be divided into two categories. The first discretizes the continuous system by lumping the masses at discrete points while the second discretizes by assuming the final form of solution as the product of time and space-dependent functions [29].…”

Section: Thin-walled Beam Of Discontinuous Cross Sectionsmentioning

confidence: 99%

“…Early works based on this theory did not include the effect of restraining warping such as in [10] while later works that include warping stiffness can be found in [12,13,[18][19][20][21][22][23]]. …”

Section: Timoshenko's Theorymentioning

confidence: 99%

“…The beam is subjected to a stochastically defined load which causes the crack to grow. For calculating random characteristics of the stress in the beam, an analytical approach based on Benscoter beam theory [8,13] is used. The equations of motion are derived using the principle of virtual work.…”

Section: Probabilistic Safety Analysismentioning

confidence: 99%

“…Such a beam when subjected to lateral loads or a twisting moment is expected to warp. The thin-walled beam theories that allow us to include warping can be mainly divided into two categories: Vlasov beam theory [4,5,22,43,129] and Benscoter beam theory [8,13,18,20,26,130,131]. In this study, the derivation is based on Benscoter beam theory where the warping degree of freedom is considered independent of the rate of twist.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Timoshenko's Theorymentioning
confidence: 99%

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

Section: Timoshenko's Theorymentioning
confidence: 99%

Section: Probabilistic Safety Analysismentioning
confidence: 99%

Section: Introductionmentioning
confidence: 99%

See 3 more Smart Citations
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
0
0
0
0
View full text Add to dashboard Cite
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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Study of warping torsion of thin-walled beams with open cross-section using macro-elements
Musat
¹
,
Epureanu
²

1999
Int. J. Numer. Meth. Engng.
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SUMMARYThin-walled beams with open cross-section under torsion or complex load are studied based on the hypotheses of the classical theory (Vlasov). Di erent from previous techniques presented in the literature, the concept of a strip-plate is introduced. This concept is used to accurately model the e ect of bending induced by torsion and to deÿne an alternate ÿnite element called macro-element. The macro-elements are shown to model more accurately the thin-walled beams under warping torsion or complex load therefore giving better results than the classical theory.

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The analysis of thin walled composite laminated helicopter rotor with hierarchical warping functions and finite element method
Dechao
¹
,
Deng
²
,
Wang
³

2001
Acta Mech Sinica
5
0
1
0
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In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free bending as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method is introduced to form a numerical algorithm. Both static and natural vibration problems of sample box beams are analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor.

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A torsion bending element for thin-walled beams with open and closed cross sections

Cited by 55 publications

References 4 publications

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Study of warping torsion of thin-walled beams with open cross-section using macro-elements

The analysis of thin walled composite laminated helicopter rotor with hierarchical warping functions and finite element method

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