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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: 1638; Downloads: 67
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On edge connectivity of direct products of graphs
Xiang-Lan Cao, Špela Brglez, Simon Špacapan, Elkin Vumar, 2011, original scientific article

Abstract: Let ▫$lambda(G)$▫ be the edge connectivity of ▫$G$▫. The direct product of graphs ▫$G$▫ and ▫$H$▫ is the graph with vertex set ▫$V(G times H) = V(G) times V(H)$▫, where two vertices ▫$(u_1,v_1)$▫ and ▫$(u_2,v_2)$▫ are adjacent in ▫$G times H$▫ if ▫$u_1u_2 in E(G)$▫ and ▫$v_1v_2 in E(H)$▫. We prove that ▫$lambda(G times K_n) = min{n(n-1)lambda(G), (n-1)delta(G)}$▫ for every nontrivial graph ▫$G$▫ and ▫$n geqslant 3$▫. We also prove that for almost every pair of graphs ▫$G$▫ and ▫$H$▫ with ▫$n$▫ vertices and edge probability ▫$p$▫, ▫$G times H$▫ is ▫$k$▫-connected, where ▫$k=O((n/log n)^2)$▫.
Keywords: mathematics, graph theory, combinatorial problems, connectivity, direct product, graph product, separating set
Published: 01.06.2012; Views: 1536; Downloads: 182
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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: 1353; Downloads: 64
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The influence of different parameters on surface pitting of contacting mechanical elements
Gorazd Fajdiga, Jože Flašker, Srečko Glodež, 2004, original scientific article

Abstract: The paper describes a general computational model for simulation of surface pitting of mechanical elements subjected to contact loading conditions. In the model it is assumed that the initial crack of length 0.015 mm is initiated at the contacting surfaces due to previously thermal, mechanical treatment of the material or running in process. The discretised model with the initial crack is then subjected to normal contact pressure, which takes into account the EHD lubrication conditions and tangential loading due to friction between contacting surfaces. The model accounts also for the influence of fluid trapped in the crack on crack prppagation. The virtual crack extension VCE method within FEM analysis is then used for 2 dimensional simulation of fatigue crack propagation from the initial crack up to the formation of the surface pit. The pit shapes and relationships between the stress intensity factor and crack length are determined for various combinations of contacting surface curvatures and loadings. The comparison of computational and available experimental results shows that the proposed model reliably simulates the surface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.
Keywords: machine elements, gears, contact problems, pitting, fatigue crack growth, simulation, model
Published: 01.06.2012; Views: 1147; Downloads: 69
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Integral formulation of a diffusive-convective transport equation for reacting flows
Niko Samec, Leopold Škerget, 2004, original scientific article

Abstract: This peper deals with a numerical solution of a diffusive-convective transport equation for reacting flows based on boundary domain integral formulation for diffusive-convective fundamental solution. A great part of attention has been dedicated to the numerical treatment of the diffusive-convective transport equation for high Pe number and reaction term values as the convective or reaction term becomes dominant compared to the diffusion one. In this case, the hyperbolic character predominates the ellipticity or parabolicity of the governing transport equation, and stability problems arise in the numerical solution. Numerical efficiency of the developed numerical implementation is tested against analytical and numerical results for the typical test cases of diffusive-convective transport problems (i.e. multicomponent reacting flows).
Keywords: fluid mechanics, boundary element method, diffusion, convection, transport problems, reacting flow
Published: 01.06.2012; Views: 928; Downloads: 63
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Symmetry preserving algorithm for large displacement frictionless contact by the pre-discretization penalty method
Dušan Gabriel, Jiři Plešek, Miran Ulbin, 2004, original scientific article

Abstract: A three-dimensional contact algorithm based on the pre-discretization penalty method is presented. Using the pre-discretization formulation gives rise to contact searching performed at the surface Gaussian integration points. It is shown that the proposed method is consistent with the continuum formulation ofthe problem and allows an easy incorporation of higher-order elements with midside nodes to the analysis. Moreover, a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments. Theproposed algorithm utilizes the BFGS method modified for constrained non-linear systems. The effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements. The symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders.
Keywords: mechanics, numerical methods, contacting surfaces, contact problems, 3D contact algorithm, discretization, higher order elements, finite element method, Gauss point search, pre-discretization penalty method
Published: 01.06.2012; Views: 1537; Downloads: 49
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New linear spring stiffness definition for displacement analysis of cracked beam elements
Matjaž Skrinar, Tomaž Pliberšek, 2004, short scientific article

Abstract: 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.
Keywords: linear springs, rotational spring, displacement analysis, transverse displacements, cracked beam structures, transverse load, inverse problems, transverse displacements, inverse identification of cracks
Published: 01.06.2012; Views: 1269; Downloads: 64
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Weakly coupled analysis of a blade in multiphase mixing vessel
Matej Vesenjak, Zoran Ren, Matjaž Hriberšek, 2004, short scientific article

Abstract: Two or more physical systems frequently interact with each other, where the independent solution of one system is impossible without a simultaneous solution of the others. An obvious coupled system is that of a dynamic fluid-structure interaction. š8đ In this paper a computational analysis of thefluid-structure interaction in a mixing vessel is presented. In mixing vessels the fluid can have a significant influence on the deformation of blades during mixing, depending on speed of mixing blades and fluid viscosity.For this purpose a computational weakly coupled analysis has been performed to determine the multiphase fluid influences on the mixing vessel structure. The multiphase fluid field in the mixing vessel was first analyzed with the computational fluid dynamics (CFD) code CFX. The results in the form of pressure were then applied to the blade model, which was the analysed with the structural code MSC.visualNastran forWindows, which is based on the finiteelement method (FEM).
Keywords: fluid mechanics, solid mechanics, coupled problems, computational analysis, two-phase fluid, mixing blade, pressure distribution, finite volume method, finite element method
Published: 01.06.2012; Views: 921; Downloads: 60
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Numerical procedure for predicting the rolling contact fatigue crack initiation
Matjaž Šraml, Jože Flašker, Iztok Potrč, 2003, original scientific article

Abstract: A computational numerical model for contact fatigue damage analysis of mechanical elements is presented in this paper. The computational approach is based on continuum mechanics, where a homogenous and elastic material model isassumed in the framework of the finite element method analysis. Cyclic contact loading conditions are simulated with moving Hertzian contact pressure. The time-depending loading cycles are defined for each observed material point on and under the contact area. Furthermore, the influence of friction upon rolling-sliding contact loading cycles is analysed in detail, using Coulombćs friction law. The model for prediction of the number of loading cycles, required for initial fatigue damages to appear, is based on Coffin-Manson relations between deformations and loading cycles, and includes characteristic material fatigue parameters. As a general example, the model isused to analyse a fundamental contact problem of a cylinder and flat surface, which is usually a substitutional model for analysing real mechanicalproblems. However, the results concerning the identification of critical material points and the number of loading cycles, required for initial fatigue damages to appear at those points, are the main purpose of thepresented study.
Keywords: machine elements, gears, contact problems, contact fatigue, crack initiation, numerical modelling
Published: 01.06.2012; Views: 1121; Downloads: 46
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