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A new approach for buckling analysis of axially functionally graded beams

Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 2

95--102

EN

The object of considerations are axially functionally graded (FG) beams, which are loaded by an axial force varying along the length of the beam. The main idea presented here is to approximate FG beams by an equivalent beam with piecewise exponentially varying material properties, geometrical properties and axial load. Numerical solutions of the buckling analysis are obtained for four various types of boundary conditions associated with pinned and clamped ends. The usefulness of the proposed method is confirmed by comparing numerical results with those available for graded beams of special polynomial non-homogeneity.

2

Nonlinear analysis of functionally graded beams

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

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 18, nr 1-2

315--318

EN

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.

3

A new approach for the analysis of functionally graded beams

Mirzababaee M., Tahani M., Zebarjad S. M.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 17, nr 1-2

265--268

EN

Purpose: It is the intention of the present study to develope a new beam theory for the analysis of functionally graded compopsite beams to overcome the shortcomings present in the existing beam theories. Design/methodology/approach: Within the displacement field of a first-order shear deformation theory and by using the Hamilton principle the governing equations of motion are obtained for both the new and the existing beam theories. The beams are assumed to have isotropic, two-constituent material distribution through the thickness. Findings: It is found that the procedure used is simple and straightforward and similar to the one used in the development of shear deformation plate and shell theories. It is analytically showed that the new approach yields identical results as those obtained by using the existing first-order shear deformation theory. Research limitations/implications: The new approach can be adopted in developing higher-order shear deformation and layerwise theories. It is believed that the new approach has advantage with respect to the existing beam theories especially for developing beam layerwise theories. Practical implications: The new shear deformation beam theory can be used to develop a new beam element for analysis of practical composite beam structures. Originality/value: The paper introduces an approach to develop a new theory for modeling composite beams. The resulting equations of motion may be solved analytically or by using finite element method.