Paper deals with finite element buckling analysis of shear deformable beam-type structures. Displacements and rotations are allowed to be large but strains are assumed to be small. The corresponding equilibrium equations are formulated in the framework of co- rotational description, using the virtual work principle. Displacements and rotations are allowed to be large while strains are assumed to be small. Linear shape functions are used for the axial displacement, while cubic shape functions are employed for transverse displacements and angle of twist. The algorithm is validated on test examples.
THE NATURAL FREQUENCIES AND MODE SHAPES OF AN EULER-BERNOULLI BEAM WITH A RECTANGULAR CROSS- SECTION WHICH HAS A SURFACE CRACK
The natural frequencies and mode shapes of an Euler-Bernoulli beam with a rectangular cross- section, which has a surface crack, is investigated. The crack is modeled as a change (sudden or gradual) in the cross-section of the beam, and the perturbation approach is used assuming that the crack is much smaller than the beam cross section. Computations of natural frequencies and mode shapes were carried out for four different crack shapes with rectangular, triangular and parabolic profiles when viewed through the side of the beam. The results are listed in non-dimensional form for various values of the parameters characterizing the crack.