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1.
On critical buckling load estimation for slender transversely cracked beam-columns by the application of a simple computational model
Matjaž Skrinar, 2008, izvirni znanstveni članek

Opis: This paper brings new insights into the implementation of a simplified computational model in the prediction of buckling load Pcr for slender beam-type structures with a transverse crack. From among several approaches discussed, two of them produced applicable results exhibiting considerably good agreement with those values from more precise and complex computational models. In the first approach, the critical load value is obtained from numerical solutions of analytically expressed characteristic equations (obtained from governing differential equations). Although producing excellent results, this approach limits the application since an analytical solution of the governing differential equation can only be obtained for moderate structures. The second approach implements a new cracked beam-columnfinite element, derived at on the basis of a fairly accurate approximation of the governing differential equation's solution. It allows for flexible utilization and also yields the smallest compact computational model, thus exhibiting itself as very suitable for inverse identification problems. Numerical examples covering several structures with different boundary conditions are briefly presented in order to support the discussed approaches. The results obtained using the presented approaches are further compared with those values from either references or more complex models, thus clearly proving the quality of the presented compact FE model.
Ključne besede: beam columns, transverse cracks, stability problems, buckling load, computational model, finite element method
Objavljeno: 31.05.2012; Ogledov: 1503; Prenosov: 38
URL Povezava na celotno besedilo

2.
Analysis of cracked slender-beams on Winkler's foundation using a simplified computational model
Matjaž Skrinar, Boris Lutar, 2011, izvirni znanstveni članek

Opis: This paper discusses the coupling of Winkler's soil model with a simplified computational model that is widely used for the calculation of transverse displacements in transversely cracked slender beams. The bending problem of a cracked beam embedded in Winkler's soil is addressed by means of an analytical approach. The solving of the corresponding differential equation solutions is studied in order to obtain exact analytical expressions for the transverse displacements of the simplified computational model. After the solutions for the displacements of the beam are obtained, the inner bending moment and the shear force distributions within the beam can be calculated, either by using known, established relationships from the Euler-Bernoulli beam theory or by implementing two mechanical equilibrium conditions. Numerical examples covering several load situations are briefly presented in order to support the discussed approach. The results obtained with the presented approach are then further compared with the values from huge 2D finite-element models, where a detailed description of the crack was achieved using the discrete approach. It is evident that any drastic difference in the computational effort is not reflected in the significant differences in the results between the models.
Ključne besede: beams with transverse cracks, simplified computational model, elastic foundation, Winkler's soil, transverse displacements, bending moment, shear forces
Objavljeno: 01.06.2012; Ogledov: 1008; Prenosov: 15
.pdf Celotno besedilo (356,02 KB)
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3.
On the application of a simple computational model for slender transversely cracked beams in buckling problems
Matjaž Skrinar, 2007, izvirni znanstveni članek

Opis: This paper discusses the implementation of a simplified computational model that is widely used for the computation of transverse displacements in transversely cracked slender beams into the Euler's elastic flexural buckling theory. Two alternatives are studied instead of solving the corresponding differential equations to obtain exact analytical expressions for the buckling load ▫$P_{cr}$▫ due to the complexity of this approach. The first approach implements wisely selected polynomials to describe the behavior of the structure, which allows the derivation of approximate expressions for the critical buckling load. Although the relevance of the results strongly depends on the proper prime selection of the polynomial, it is shown that the later upgrading of the polynomials can lead to even more reliable results. The second approach is a purely numerical approach and presents the geometrical stiffness matrix for a beam finite element with a transverse crack. To support the discussed approaches, numerical examples covering several structures with different boundary conditions are briefly presented. The results obtained with the presented approaches are further compared with the values from enormous 2D finite elements models, where a detailed description of the crack was achieved with the discrete approach. It is evident that the drastic difference in the computational effort is not reflected in the significant differences in the results between the models.
Ključne besede: columns, transverse cracks, stability problems, buckling load, computational model, polynomial solutions, finite element method, geometrical stiffness matrix
Objavljeno: 01.06.2012; Ogledov: 1238; Prenosov: 30
URL Povezava na celotno besedilo

4.
New finite element for transversely cracked slender beams subjected to transverse loads
Matjaž Skrinar, Tomaž Pliberšek, 2007, izvirni znanstveni članek

Opis: The paper covers the derivation of a new finite element for beams with transverse cracks. The derivation is based on a simplified computational model that has already proved itself suitable for the inverse identification of cracks. The model embodies all the necessary major information about the structure's response from the inverse identification point of view, where the presence and location and, if possible, the depth of the crack should be detected from the measured response, usually dynamic. In such situations the stress distributions obtained from 2D finite elements analysis are not as important as the computational model being capable of reliably describing the displacement of the structure. However, from numerical studies it also became evident that the relevance of the model decreases with element thickness. This indicated that shear forces should be included in the analysis process. Therefore, derivation of a new finite element with the inclusion of shear forces effect has been executed. The stiffness matrix for transversely cracked slender beams, as well as the derivation of interpolation functions is presented and all expressions are given in symbolic forms. The example shows that, although with significantly less computational effort than with 2D FE meshes, significant improvement in transverse displacements can be obtained with the presented beam finite element.
Ključne besede: beams, transverse cracks, computational model, finite element method, transverse displacements
Objavljeno: 01.06.2012; Ogledov: 1105; Prenosov: 33
URL Povezava na celotno besedilo

5.
New linear spring stiffness definition for displacement analysis of cracked beam elements
Matjaž Skrinar, Tomaž Pliberšek, 2004, kratki znanstveni prispevek

Opis: The paper describes the reasons for the derivation of a new definition of a rotational spring that can be utilised in the simplified computational model for the computation of transverse displacements of cracked beam structures dueto transverse load. This definition plays an extremely important role in the inverse identification of cracks.
Ključne besede: linear springs, rotational spring, displacement analysis, transverse displacements, cracked beam structures, transverse load, inverse problems, transverse displacements, inverse identification of cracks
Objavljeno: 01.06.2012; Ogledov: 1147; Prenosov: 36
URL Povezava na celotno besedilo

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