Large Deflections of a Non-linear Cantilever Functionally Graded Beam

Abstract

The analysis of the large deformation of a non-linear cantilever functionally graded material (FGM) beam is made. When subjected to an end moment, explicit expressions for deflection and rotation are derived for a functionally graded beam with work hardening of power law. The effects of the gradient distribution of Young’s modulus and the material non-linearity parameter on the deflections of the FGM beam are analyzed. Our results show that depth-dependent Young’s modulus and material non-linearity have a significant influence on the deflections of the beam, and a FGM beam can bear larger applied load than a homogeneous beam. Moreover, to determine an optimal gradient distribution, an optimum design of a beam of a lighter weight and larger stiffness is given. The influence of the geometric non-linearity of the beam is also studied. Large and small deformation theories predict nearly the same deflections with 5% error when rotation is less than 45°, and the predictions based on the small deformation theory are overestimated to exceed 10% when rotation is greater than 60°.

Thermomechanical buckling oftemperature-dependent FGM beams

“…where 1 E , 2 E , and 3 E are stretching, coupling stretching-bending, and bending stiffnesses, respectively, and…”

“…In this case the exact solution of Eq. (2) The constants of integration 1 C to 6 C are obtained using the boundary conditions of the beam. Also, the parameter  must be minimized to find the minimum value of 0 x N associated with the thermal or mechanical buckling load.…”

Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

“…obtained by different numbers of elements, nELE, for an index n=5 show good convergence of the proposed element, where both the axial and transverse displacements steadily converge towards the analytical solution by increasing the number of elements. A slight difference in the computed displacements of the present work with that of the analytical solution (Kang & Li, 2010) might be the result of the different beam theory used herein.…”

Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects

“…In particular, FG beams have been investigated vigorously using analytical, experimental and computational approaches [11][12][13][14][15][16][17][18][19][20]. However, most research work has been limited to linear analysis of FG beams on a two-dimensional plane.…”