Transversely Cracked Beam's Finite Elements with a Hinged End

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.