On the application of a simple computational model for slender transversely cracked beams in buckling problems

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

stebri;prečne razpoke;problemi stabilnosti;porušna obtežba;računski model;polinomske rešitve;metoda končnih elementov;geometrijska togostna matrika;columns;transverse cracks;stability problems;buckling load;computational model;polynomial solutions;finite element method;geometrical stiffness matrix;

Data

Language:	English
Year of publishing:	2007
Typology:	1.01 - Original Scientific Article
Organization:	UM FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
UDC:	624.131:531/533
COBISS:	10648342
ISSN:	0927-0256
Views:	1659
Downloads:	85
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	stebri;prečne razpoke;problemi stabilnosti;porušna obtežba;računski model;polinomske rešitve;metoda končnih elementov;geometrijska togostna matrika;
URN:	URN:SI:UM:
Pages:	str. 242-249
Volume:	ǂVol. ǂ39
Issue:	ǂiss. ǂ1
Chronology:	Mar. 2007
ID:	8718620