On the Application of the Simplified Crack Model in the Bending, Free Vibration and Buckling Analysis of Beams with Linear Variation of Widths

Abstract

Adequate computational models are crucial for a reliable representation of the mechanical behaviour of structural elements and, therefore, numerous investigations are oriented towards the modelling of cracked structures. This paper studies the behaviour of transversely cracked beams of rectangular cross-sections with linearly-varying widths. The governing differential equations of bending are analytically solved for various beams with different boundary conditions. These simplified model’s solutions are further validated by the results from corresponding 3D finite models of the considered structures. Furthermore, strain and kinetic energy, as well as the work done by an external axial compressive force P are evaluated from the computed transverse displacement functions. These values allowed for estimations of the first eigenfrequency as well as the buckling load. These structural’s parameters were additionally evaluated by implementing dedicated polynomial functions for some cases considered.The results from the simplified model have exhibited very good agreement with the results from more detailed 3D FE models for all performed analyses. The simplified model thus yields an adequate, as well as accurate, approach for the modelling of cracked beams with a linear variation of width in engineering situations, where cracks have to be considered during analysis.
 The results from the simplified model have exhibited very good agreement with the results from more detailed 3D FE models for all performed analyses. The simplified model thus yields an adequate, as well as accurate, approach for the modelling of cracked beams with a linear variation of width in engineering situations, where cracks have to be considered during analysis.