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: 37 Povezava na celotno besedilo

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 Povezava na celotno besedilo