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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, original scientific article

Abstract: 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.
Keywords: beam columns, transverse cracks, stability problems, buckling load, computational model, finite element method
Published: 31.05.2012; Views: 1657; Downloads: 68
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2.
Analysis of cracked slender-beams on Winkler's foundation using a simplified computational model
Matjaž Skrinar, Boris Lutar, 2011, original scientific article

Abstract: 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.
Keywords: beams with transverse cracks, simplified computational model, elastic foundation, Winkler's soil, transverse displacements, bending moment, shear forces
Published: 01.06.2012; Views: 1174; Downloads: 26
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3.
On the application of a simple computational model for slender transversely cracked beams in buckling problems
Matjaž Skrinar, 2007, original scientific article

Abstract: 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.
Keywords: columns, transverse cracks, stability problems, buckling load, computational model, polynomial solutions, finite element method, geometrical stiffness matrix
Published: 01.06.2012; Views: 1372; Downloads: 64
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4.
New finite element for transversely cracked slender beams subjected to transverse loads
Matjaž Skrinar, Tomaž Pliberšek, 2007, original scientific article

Abstract: 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.
Keywords: beams, transverse cracks, computational model, finite element method, transverse displacements
Published: 01.06.2012; Views: 1267; Downloads: 71
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5.
Computational simulations of unidirectional cellular material unipore subjected to dynamic loading
Matej Vesenjak, Kazuyuki Hokamoto, Zoran Ren, 2012, published scientific conference contribution

Abstract: Cellular structures have an attractive combination of mechanical properties and are increasingly used in modern engineering applications. Consequently, the research of their behaviour under quasi-static and dynamic loading is valuable for engineering applications such as those related to strain energy absorption. The paper focuses on behaviour of a newly developed cellular structure UniPore with unidirectional pores under dynamic loading. The computational model of the cellular structure was based on realistic (reconstructed) irregular geometry of the manufactured specimens and analysed using the code LS-DYNA. The mechanical properties have been investigated by means of parametric computational simulations considering various material and geometrical parameters. Additionally, the influence of the gaseous pore filler influence has been considered using fully coupled computational models. Furthermore, with computational simulations also the influence of the anisotropy has been evaluated.
Keywords: cellular materials, computational model, UniPore
Published: 10.07.2015; Views: 362; Downloads: 11
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6.
Critical and supercritical spatiotemporal calcium dynamics in beta cells
Marko Gosak, Andraž Stožer, Rene Markovič, Jurij Dolenšek, Matjaž Perc, Marjan Rupnik, Marko Marhl, 2017, original scientific article

Abstract: A coordinated functioning of beta cells within pancreatic islets is mediated by oscillatory membrane depolarization and subsequent changes in cytoplasmic calcium concentration. While gap junctions allow for intraislet information exchange, beta cells within islets form complex syncytia that are intrinsically nonlinear and highly heterogeneous. To study spatiotemporal calcium dynamics within these syncytia, we make use of computational modeling and confocal high-speed functional multicellular imaging. We show that model predictions are in good agreement with experimental data, especially if a high degree of heterogeneity in the intercellular coupling term is assumed. In particular, during the first few minutes after stimulation, the probability distribution of calcium wave sizes is characterized by a power law, thus indicating critical behavior. After this period, the dynamics changes qualitatively such that the number of global intercellular calcium events increases to the point where the behavior becomes supercritical. To better mimic normal in vivo conditions, we compare the described behavior during supraphysiological non-oscillatory stimulation with the behavior during exposure to a slightly lower and oscillatory glucose challenge. In the case of this protocol, we observe only critical behavior in both experiment and model. Our results indicate that the loss of oscillatory changes, along with the rise in plasma glucose observed in diabetes, could be associated with a switch to supercritical calcium dynamics and loss of beta cell functionality.
Keywords: beta cells, islets of Langerhans, self-organized criticality, intercellular dynamics, calcium waves, glucose oscillations, computational model, confocal calcium imaging
Published: 23.01.2018; Views: 519; Downloads: 231
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