Transversely Cracked Beamâ€™s Finite Elements with a Hinged End

M Skrinar,T Plibersek

doi:10.3844/ajassp.2008.55.60

Abstract

Two new beam finite-elements to be used for the transverse displacement analysis of slender beams with transverse cracks are presented where the derivations are based on a simplified computational model. The beam stiffness matrixes are presented in symbolic forms for beams with a single transverse crack and a hinge at one of the nodes. Since in the derivations the corresponding interpolation functions were implemented, the transverse displacements within the finite element can be afterwards obtained by introducing the discrete values of nodal displacements and rotations into presented analytical solutions. A numerical example concludes the material and shows that, although with considerably less computational effort than with 2D finite element meshes, the presented beam finite elements yield results that exhibit excellent agreement with the results from the huge 2D FE meshes. Due to the fact that the number of parameters describing the cracked beam structure is thus reduced to its minimum it can be expected that these elements could be efficiently implemented in inverse identification of cracks.

Highlights

Cracks are doubtlessly one of the most unfavourable and negative effects that might appear on a structure during its utilization
From Figures 4 and 5 it is clearly evident that only moderate discrepancies appeared when comparing the results from the appropriate simplified model with the Besides transverse displacements, bending moments and shear forces were evaluated for both load cases and compared with the values obtained with elementary static analysis
This paper overcomes the limitation on hinge modeling within the structural element as two new beam finite elements for the analysis of beams with transverse cracks are presented in the paper

Summary

Introduction

Cracks are doubtlessly one of the most unfavourable and negative effects that might appear on a structure during its utilization. By using controlled forced vibrations and measured displacements at two selected points the location of the crack has been identified on a cantilever[2]. Implementing measured eigenfrequencies only, the location of the crack has been experimentally identified on a single beam with free ends[3]. In both approaches the differential equation of motion was solved, and the location of the artificially introduced crack was identified over the rotational spring stiffness value Kr instead of the crack depth d itself

Methods

Results

Conclusion