Exact solution of the multi-cracked Euler–Bernoulli column
By Salvatore Caddemi, Ivo Caliò. 2008
105 citations recorded by the source corpus.
Abstract The use of distributions (generalized functions) is a powerful tool to treat singularities in structural mechanics and, besides providing a mathematical modelling, their capability of leading to closed form exact solutions is shown in this paper. In particular, the problem of stability of the uniform Euler–Bernoulli column in presence of multiple concentrated cracks, subjected to an axial compression load, under general boundary conditions is tackled. Concentrated cracks are modelled by means of Dirac’s delta distributions. An integration procedure of the fourth order differential governing equation, which is not allowed by the classical distribution theory, is proposed. The exact buckling mode solution of the column, as functions of four integration constants, and the corresponding exact buckling load equation for any number, position and intensity of the cracks are presented. As an example a parametric study of the multi-cracked simply supported and clamped–clamped Euler–Bernoulli columns is presented.
Subfields: Civil and Structural Engineering, Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/675997041446fb9f7876989a01f6a0b5be6ce6b0
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In Civil and Structural Engineering
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Citations in the corpus
- Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams (2011, methodology): “…form, and has been also used for a range of further structural problems, including theoretical buckling and modal analyses of multi-cracked Euler-Bernoulli members (Caddemi and Calió, 2008, 2009), and experimental static (Buda and Caddemi, 2007) and dynamic (Caddemi et al., 2010) investigations.”
- Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks (2009, methodology): “Within the framework of the distribution theory, a model for columns in the presence of multiple concentrated cracks was presented in [45].”
- Closed-form solutions for stepped Timoshenko beams with internal singularities and along-axis external supports (2013, background): “To this aim, the authors have proposed an approach to beam with discontinuities, based on suitable reductions in the flexural stiffness, modelled bymeans of generalised functions such as the Dirac’s delta and the Heaviside unit-step function [10,11] that allowed also the study of multiple cracked be”