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2. New linear spring stiffness definition for displacement analysis of cracked beam elementsMatjaž Skrinar, Tomaž Pliberšek, 2004, other scientific articles 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 in DKUM: 01.06.2012; Views: 2244; Downloads: 97
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3. New finite element for transversely cracked slender beams subjected to transverse loadsMatjaž 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 in DKUM: 01.06.2012; Views: 2431; Downloads: 112
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4. Analysis of cracked slender-beams on Winkler's foundation using a simplified computational modelMatjaž 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 in DKUM: 01.06.2012; Views: 2262; Downloads: 58
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