Abstract:

Based on the two-parameter foundation model, the buckling of orthotropic thin plates on graded elastic foundations is studied. Firstly, the buckling governing differential equation of orthotropic thin plates on graded elastic foundations and the expressions of two elastic parameters of the elastic foundation are obtained by using the energy method and the variational principle. Then, by expanding the displacement into trigonometric functions, the calculation formula of the uniaxial compression buckling load for orthotropic thin plates on graded elastic foundations with simply supported edges is obtained. In the example, the proposed solution is validated by comparing the degenerated results for an orthotropic thin plate with the classical elasticity solution. Finally, this paper studies the buckling load of the orthotropic thin plate on a graded elastic foundation, whose Young's modulus obeys a power law against the thickness. The effects of the top-bottom surfaces' Young's modulus ratio and the volume fraction exponent are also discussed.

Key words:

orthotropic plate|two-parameter foundation model|buckling|functionally graded materials|variation principle