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1 Journal of Achievements in Materials and Manufacturing Engineering

1 2006

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Nonlinear analysis of functionally graded beams

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Tahani M. , Torabizadeh M. A. , Fereidoon A.

tom Vol. 18, nr 1-2

315--318

Purpose: It is the intention of the present study to examine the effect of geometric nonlinearity on displacements and stresses in beams made of functionally graded materials (FGMs) subjected to thermo-mechanical loadings. Design/methodology/approach: The nonlinear strain-displacement relations are used to study the effect of geometric nonlinearity. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Then the equilibrium equations are obtained within the framework of the first-order shear deformatyion beam theory (FSDBT) and then solved exactly and also by using a perturbation technique. The results obtained from these two methods are compared for various loadings and boundary conditions. Findings: The numerical results showed that the nonlinearity effect on the displacements and stresses of the beams is significant. Also the effects of material constant n and the boundary conditions on the nonlinear bending behavior of the beams are determined. Research limitations/implications: The exact solution method of nonlinear equilibrium equations can only be developed for composite beams with the same boundary conditions at the ends. Practical implications: It is showed that for the maximum deflections greater than 0.3h a nonlinear solution is required. Originality/value: The paper introduces a new method to obtain analytical solution for nonlinear equilibrium equations. This method can be used in developing higher-order shear deformation and layerwise theories.