Analytical Modeling of Cracked Thin-Walled Beams Under Torsion

Dang, Thi D.; Kapania, Rakesh K.; Patil, Mayuresh

doi:10.2514/1.45393

Cited by 12 publications

(10 citation statements)

References 27 publications

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“…(30) after the condensation procedure is (132 × 132). Table 2 shows the comparison between results obtained from the current Ritz model and those in Literature [21].…”

Section: Euler-bernoulli Beam With Multiple Stepsmentioning

confidence: 99%

“…(6)). We first convert the three dimensional problem of a thinwalled beam to the one-dimensional problem in terms of twist angles using the displacement field as described by Dang, Kapania and Patil [30] for both the open and closed section thin-walled beam as.…”

Section: Ritz Model For a Cracked Thin-walled Beammentioning

confidence: 99%

“…In their paper, analytical solutions for twist angles, stresses and strains have been derived for closed thin-walled beams and for open thin-walled beams, nonclassical effects like primary and second torsional warping are taken into account. The authors extend their previous work [30] using a Ritz approach, to enhance the efficiency of the analysis, for modeling thin-walled beams under torsion with cracks in the present paper.…”

Section: Introductionmentioning

confidence: 95%

“…The modal analysis of cracked beams has been performed by many others [24][25][26][27][28][29], but all of these authors worked on solid beams with transverse cracks, and most of the cases are related to cracked beams under bending loads alone. Dang et al [30] have recently found a closedform expression of the Mode II stress intensity factor for the rectangular thin-walled beams with a longitudinal crack. In their paper, analytical solutions for twist angles, stresses and strains have been derived for closed thin-walled beams and for open thin-walled beams, nonclassical effects like primary and second torsional warping are taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Ritz analysis of discontinuous beams using local trigonometric functions

2010

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The objective of the current paper is to present a Ritz-type analytical model for predicting the behavior of discontinuous beams such as thin-walled beams with cracks and multiply-stepped beams. The beam is discretized in the cracked as well as the un-cracked domains for a cracked thinwalled beam and in uniform beams for a multiple-stepped beam. A set of local trigonometric trial functions is used to define the twist angle for the cracked domain and the un-cracked domains, as well as to define the displacement field for uniform domains. A global equation system of unknown Ritz coefficients is derived by minimizing the Lagrangian functional or the total potential energy. In the present Ritz model, the interface continuity conditions between sub-domains are investigated and enforced into the global equation system using the condensation procedure or the Lagrange multipliers. Examples are presented to illustrate the effectiveness of the current model for free vibration and torsional analysis. Results obtained from the current model are found to agree well with those obtained using a detailed Present Address: finite element method or with existing results in literature. The proposed model offers an efficient approach to reduce the modeling efforts and computational time required to analyze complex beams with cracks or multiple steps.

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“…(30) after the condensation procedure is (132 × 132). Table 2 shows the comparison between results obtained from the current Ritz model and those in Literature [21].…”

Section: Euler-bernoulli Beam With Multiple Stepsmentioning

confidence: 99%

Section: Ritz Model For a Cracked Thin-walled Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Ritz analysis of discontinuous beams using local trigonometric functions

2010

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“…For the particular case of a thin walled beam with a crack this factor as developed by Dang et al [133] is expressed as follows:…”

Section: Crack Growth Modelingmentioning

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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Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack
Lal
¹
,
Palekar
²
,
Mulani
³

et al. 2017
Aerospace Science and Technology
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Analytical Modeling of Cracked Thin-Walled Beams Under Torsion

Cited by 12 publications

References 27 publications

Ritz analysis of discontinuous beams using local trigonometric functions

Ritz analysis of discontinuous beams using local trigonometric functions

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack

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