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Delamination fracture analyses of linear-elastic functionally graded beams

Rizov V. I.

Engineering Transactions

2017

Vol. 65, iss. 3

483--498

An analytical approach for investigation of delamination cracks in three-dimensional functionally graded linear-elastic beams was developed. Beams which are functionally graded along their width, height and length were analyzed. The fracture was studied in terms of the strain energy release rate. Beams loaded by a combination of bending moments and an axial force were considered. The approach was applied to determine the strain energy release rate for a delamination crack in a functionally graded beam of rectangular cross-section loaded in eccentric tension. An additional analysis was performed by using the beam strain energy for verification. The effects of material gradient and crack length on the delamination were evaluated.

Application of the differential transform method to the free vibration analysis of functionally graded timoshenko beams

Özdemir Ö.

Journal of Theoretical and Applied Mechanics

2016

Vol. 54 nr 4

1205--1217

In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton’s principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies are calculated and effects of several parameters are investigated.