Buckling of cracked functionally graded plates supported by Pasternak foundation

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

“…It is concluded that critical buckling load has an inverse relation with number of cracks, the length of a crack, and the gradient index of a plate. Buckling analysis of cracked FG plates was done by Panahandeh-Shahraki and Amiri [99]. Results show that increase in crack to width ratio decreases critical buckling load.…”

A Kerr‐type elastic foundation model for the buckling analysis of a beam bonded on an elastic layer

“…The buckling of a beam on an elastic foundation is of significant concern in various engineering applications, [1][2][3][4] therefore attracts considerable interests for decades. To mention a few, the buckling of a beam on soils is visited in [5][6][7], the buckling of a stiff thin beam on a compliant substrate is investigated in [3,8,9], the buckling of a functionally graded material beam on an elastic foundation is studied in [1,4,10], the wrinkling of skin on an elastic foundation is analyzed in [2]. In addition, the buckling of a fiber in matrix can be also analyzed as a beam on an elastic foundation.…”

“…To overcome this weakness, the two-parameter models such as Pasternak's model [10,17,18] and Wieghardt model, [19] and the threeparameter models such as Reissner's model [20] and Kerr's model [21] (which is different from the present Kerr-type model [22] ), were employed to define the constitutive relation of the elastic layer beneath the beam. [4,6,7,11,17,[23][24][25][26][27][28][29][30][31][32][33][34] Dillard proposed an incompressible elastomeric foundation model, [35] which was recently employed in the analysis of the buckling of a laterally supported beam. [36] To obtain a precise critical buckling force theoretically, it is essential to find a suitable elastic foundation model which is able to accurately describe the mechanical response of the elastic layer.…”

An exact solution for stability analysis of orthotropic rectangular thin plate under biaxial nonlinear in-plane loading resting on Pasternak foundation

“…Using Levy solution, the buckling equation was transformed to an ordinary differential equation with variable coefficients and then was solved exactly using power series of Frobenius method [30]. Panahandeh Shahraki et al, studied the buckling of FGM cracked plates supported by Pasternak foundation [31]. Foroughi and Azhari presented the buckling and free vibration of thick FGM plates resting on Pasternak elastic foundation, using finite strip method.…”