Parametric Instability of Functionally Graded Timoshenko Beams with an Open Edge Crack

2010 ◽  
Author(s):  
Jie Yang ◽  
Sritawat Kitipornchai ◽  
Yang Xiang ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
...  
Keyword(s):  
Edge Crack ◽  
Parametric Instability ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Open Edge

Nonlinear bending of elastically restrained functionally graded graphene nanoplatelet reinforced beams with an open edge crack

2020 ◽  
Vol 156 ◽  
pp. 106972 ◽  
Author(s):  
Meifung Tam ◽  
Zhicheng Yang ◽  
Shaoyu Zhao ◽  
Henin Zhang ◽  
Yingyan Zhang ◽  
...  
Keyword(s):  
Edge Crack ◽  
Functionally Graded ◽  
Nonlinear Bending ◽  
Graphene Nanoplatelet ◽  
Reinforced Beams ◽  
Elastically Restrained ◽  
Open Edge

scholarly journals Mode Shape Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

2017 ◽  
Vol 14 (7) ◽  
pp. 1327-1344 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Đuc ◽  
Nguyen Tien Khiem
Keyword(s):  
Shape Analysis ◽  
Mode Shape ◽  
Functionally Graded ◽  
Timoshenko Beams

Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
S. P. Pavlov ◽  
M. V. Zhigalov ◽  
V. A. Krysko
Keyword(s):  
Differential Equations ◽  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Stability Loss ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Timoshenko Beams ◽  
Size Dependent ◽  
Rigid Layer ◽  
Graded Material

The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state.

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