The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio.
The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated.
In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution.
In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.
The author appreciates all the support given by the Materials Engineering Department (Lorena School of Engineering) and the Structural Engineering Department (São Carlos School of Engineering), both from the University of São Paulo.
Pascon, J. (2016), "Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio", Engineering Computations, Vol. 33 No. 8, pp. 2421-2447. https://doi.org/10.1108/EC-08-2015-0225Download as .RIS
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