Elastic beam finite element with an arbitrary number of transverse cracks

Skrinar, Matjaž

doi:10.1016/j.finel.2008.09.003

Cited by 31 publications

(13 citation statements)

References 14 publications

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“…Ref. [15]), therefore neglecting the effects of the damaged cross sections on the inertial forces. Indeed, when the approximation with lumped masses is resorted to, the mass of the whole FE is concentrated at the two end nodes, like in the undamaged beam, despite the fact that the damage on the member can significantly alter the distribution of the inertial forces (see Refs.…”

Section: Mass Matrixmentioning

confidence: 99%

“…In the FE proposed by Skrinar [15,16], cubic splines are used to represent the field of transverse displacements in each uncracked region of the beam, while the additional kinematic and static unknowns arising at each crack have been eliminated with the help of compatibility and equilibrium equations combined with the Hooke's law for the rotational springs simulating the cracks. However, this study has only considered slender Euler-Bernoulli beams in bending and masses lumped at the two nodes of the resulting FE, which may limit its applicability.…”

Section: Introductionmentioning

confidence: 99%

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An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia

Donà

Palmeri

Lombardo

et al. 2015

Computers & Structures

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Section: Mass Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia

Donà

Palmeri

Lombardo

et al. 2015

Computers & Structures

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“…The Dirac delta function was implemented twice: by Biondi and Caddemi [3] in regard to the rigidity, and by Palmeri and Cicirello [4] in regard to the flexibility. Sequential solutions of coupled differential equations were implemented by Skrinar [5], while Skrinar and Pliberšek [6] implemented the principle of virtual work.…”

Section: Introductionmentioning

confidence: 99%

On the Bending Analysis of Multi-Cracked Slender Beams with Continuous Height Variations

Skrinar

Imamović

2018

Period. Polytech. Civil Eng.

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IntroductionAs the cracks are degenerative effects that might severely impact the behaviour of engineering structures, their immediate detection is vitally important for safety reasons. However, the efficiency of structural health monitoring is a combination of accurate data measurements and the versatility of mathematical representation of mechanical behaviour. Although suitable 2D or 3D meshes of finite elements yield the best description of the crack and its surroundings, this approach is advantageous only when all the crack's details are known in advance. Consequently, simplified models are more efficient for inverse problems where none of the potential crack's details (presence, location, intensity) is known.The appropriate simplified model that has been the subject of numerous researches in the past, is the model provided by Okamura et al. [1]. This model simulates cracks by massless rotational linear springs. Each spring connects those neighbouring non-cracked parts of the beam that are modelled as elastic elements and the linear moment-rotation constitutive law is adopted. Such a mathematical model allows for all the essential data (transverse displacements and inner forces) to be evaluated with adequate accuracy.Okamura's computational model was effectively implemented in finite element solutions for the computation of transverse displacements. Initially, Gounaris and Dimarogonas [2] presented a numerical procedure for the computation of a beam element with a single transverse crack. Afterwards, closed-form solutions for the static transverse displacements and stiffness matrix of a beam's finite element having an arbitrary number of transverse cracks have been derived at by several authors by implementing different mathematical methods. The Dirac delta function was implemented twice: by Biondi and Caddemi [3] in regard to the rigidity, and by Palmeri and Cicirello [4] in regard to the flexibility. Sequential solutions of coupled differential equations were implemented by Skrinar [5], while Skrinar and Pliberšek [6] implemented the principle of virtual work.Due to its simplicity (the depth and the location are the only crack's parameters required) the "discrete spring" model has been intensively implemented in vibration analysis of cracked

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“…Zhang and Charalambides [18] further improved the above methods to include interface cracks bounded by heterogeneous orthotropic media. Skrinar [19] [20] initially introduced a 2-D damaged finite element for fracture mechanics application. Hall and Potirniche [21] extended the 2-D damaged finite element to 3-D.…”

Section: Introductionmentioning

confidence: 99%

The fracture mechanics of cantilever beams with an embedded sharp crack under end force loading

Fang

Charalambides

2015

Engineering Fracture Mechanics

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Elastic beam finite element with an arbitrary number of transverse cracks

Cited by 31 publications

References 14 publications

An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia

An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia

On the Bending Analysis of Multi-Cracked Slender Beams with Continuous Height Variations

The fracture mechanics of cantilever beams with an embedded sharp crack under end force loading

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