Search results

In this research, the free vibration sensitivity analysis of cracked fiber metal laminated (FML) beams is investigated numerically and experimentally. The effects of single and double cracks on the frequency of the cantilever beams are simulated using the finite element method (FEM) and compared to the experimental results.

In FEM analysis, the crack defect is simulated by the contour integral technique without considering the crack growth. The specimens are fabricated with an aluminum sheet, woven carbon fiber and epoxy resin. The FML specimens are constructed by bonding five layers as [carbon fiber-epoxy/Al/carbon fiber-epoxy/Al/carbon fiber-epoxy]. First, the location and length of cracks are considered input factors for the frequency sensitivity analysis. Then, the design of the experiment is produced in the cases of single and double cracks to compute the frequency of the beams in the first and second modes using the FEM. The mechanical shaker is used to determine the natural frequency of the specimens. In addition, the predicted response values of the frequency for the beam are used to compare with the experimental results.

Consequently, the results of the sensitivity analysis demonstrate that the location and length of the crack have significant effects on the modes.

Effective interaction diagrams are introduced to investigate crack detection for input factors, including the location and length of cracks in the cases of single and double cracks.

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.

The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.

An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.

The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.