63 research outputs found

    A Levy-type solution for buckling analysis of micro-plates considering the small length scale

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    In this paper, a Levy-type solution based on the modified couple stress theory is developed to study the buckling behaviors of micro-plates. Based on this theory, length scale parameter is considered to capture the size effect of rectangular micro-plates. Minimum potential energy and adjacent-equilibrium criteria are exploited to obtain the stability equations and corresponding boundary conditions. Different boundary conditions with two opposite edges simply supported and arbitrary boundary conditions along the other edges are considered. To illustrate the new model, both uniaxial and biaxial loads are applied and the critical buckling loads are defined for over a wide range of thickness, different length scale parameters and various boundary conditions. To show the accuracy of the formulations, present results are compared with available results in literature for specific cases and a very good agreement is observed. Results reveal that the critical buckling load increases as the length scale parameter increases especially when the thickness of the micro-plates becomes in order of length scale parameter and this effect is more significant for free boundary condition

    Reformulation of Navier equations for solving three-dimensional elasticity problems with applications to thick plate analysis

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    In this paper, a new reformulation of the Navier equations of motion is introduced for solving the known three-dimensional elastostatics and elastodynamics problems. At first, three decoupled equations in terms of displacement components and three decoupled equations in terms of rotation components are obtained. These equations are also invariant with respect to the choice of the coordinate system. In order to solve a three-dimensional elasticity problem based on the presented formulation, one of the three equations in terms of displacement components and the corresponding rotation equation should be solved independently. Using some relations, the other two displacement components can be obtained in terms of the mentioned displacement and rotation component. In order to verify the relations, the closed-form solutions are obtained for deflection and natural frequencies of the thick rectangular plate. The numerical results are compared with available results in the literature and it can be seen that the results of the present study are identical to those of the previous works

    An analytical approach for stress analysis of functionally graded annular sector plates

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    In this paper, an exact analytical approach is used for bending analysis of functionally graded (FG) annular sector plates. The governing equilibrium equations are obtained based on the first order shear deformation plate theory. Introducing an analytical method, the coupled governing equilibrium equations are replaced by independent equations in term of transverse deflection and a new function. Using an equivalent flexural rigidity, the solutions of FG annular sector plates can be easily extracted from equation of homogeneous annular plates. Also, it is shown that the present method can provide accurate results. Finally, the effects of power of functionally graded material (FGM), plate thickness, inner to outer radius ratio and boundary conditions on the deflection and stresses of a functionally graded annular sector plate are studied
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