scholarly journals Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Static Analysis ◽  
Geometrically Nonlinear ◽  
Timoshenko Beams ◽  
Graded Material ◽  
Nonlinear Static ◽  
Fgm Beam

Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM) subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.

Analytical Solutions Using a Higher-Order Refined Theory for the Static Analysis of Functionally Graded Material Plates

2013 ◽  
Vol 705 ◽  
pp. 30-35
Author(s):  
K. Swaminathan ◽  
D.T. Naveenkumar
Keyword(s):  
Shear Deformation ◽  
Static Analysis ◽  
Functionally Graded Material ◽  
Analytical Solutions ◽  
Degrees Of Freedom ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Simply Supported ◽  
Graded Material

Analytical formulations and solutions to the static analysis of simply supported Functionally Graded Material (FGM) plates hitherto not reported in the literature based on a higher-order refined shear deformation theory with nine degrees-of-freedom already reported in the literature are presented. This computational model incorporates the plate deformations which account for the effect of transverse shear deformation. The transverse displacement is assumed to be constant throughout the thickness. In addition, another higher order theory with five degrees-of-freedom and the first order theory already reported in the literature are also considered for comparison. The governing equations of equilibrium using all the computational models are derived using the Principle of Minimum Potential Energy (PMPE) and the analytical solutions are obtained in closed-form using Naviers solution technique. A simply supported plate with SS-1 boundary conditions subjected to transverse loading is considered for all the problems under investigation. The varying parameters considered are the side-to-thickness ratio, power law function, edge ratio and the degree of anisotropy. Correctness of the formulation and the solution method is first established and then extensive numerical results using all the models are presented which will serve as a bench mark for future investigations.

Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material

2011 ◽  
Vol 18 (1-2) ◽  
pp. 21-34 ◽  
Author(s):  
Turgut Kocatürk ◽  
Mesut Şimşek ◽  
Şeref Doğuşcan Akbaş
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Functionally Graded ◽  
Element Approximation ◽  
Large Rotations ◽  
Non Linear ◽  
Graded Material ◽  
Newton Raphson

AbstractIn this study, non-linear static analysis of a cantilever Timoshenko beam composed of functionally graded material (FGM) under a non-follower transversal uniformly distributed load is studied with large displacements and large rotations. Material properties of the beam change in the thickness direction according to a power-law function. In this study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The non-linear problem is solved by using the incremental displacement-based finite element method in conjunction with the Newton-Raphson iteration method. To use the solution procedures of the Newton-Raphson method, there is a need to linearize equilibrium equations, which can be achieved through the linearization of the principle of virtual work. In this study, the effects of large deflections, large rotations and various material distributions on displacements and normal stress and shear stress distributions through the thickness of the beam are investigated in detail. The convergence study is performed for various numbers of finite elements. In addition, some of the particular results of the present study which are obtained for the homogeneous material case are compared with the results of the SAP2000 packet program. Numerical results show that geometrical non-linearity and material distribution play very important roles in the static responses of FGM beams.

scholarly journals Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Nguyen Thi Hong
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Third Order ◽  
Aspect Ratios ◽  
Graded Material ◽  
Nonlinear Static

Bidirectional functionally graded material (2D-FGM) plates have mechanical properties that vary continuously in both the thickness and one-edge directions; these plates are more and more widely used in design and engineering applications. When these structures are subjected to strong loads, they can be largely deformed; therefore, nonlinear calculations, in this case, are necessary. In this paper, nonlinear static bending and nonlinear free vibration behaviors of 2D-FGM plates are studied by using the finite element method based on the third-order shear deformation theory; the Newton-Raphson method is used to solve this problem. The accuracy of this approach is confirmed by comparing the results with respect to other papers. The effects of some numerical aspect ratios such as volume fraction index and thickness-to-length ratio on nonlinear static bending and free vibration of the plates are explored. This study shows that there is a big difference between the numerical results obtained from the nonlinear problem and those from the linear one.

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