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Structural Engineering and Mechanics Volume 66, Number 5, June10 2018 , pages 557-568 DOI: https://doi.org/10.12989/sem.2018.66.5.557 |
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Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening |
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S. Amir M. Ghannadpour and Payam Kiani
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| Abstract | ||
| An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman\'s equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method. | ||
| Key Words | ||
| spectral collocation method; functionally graded plates; geometric nonlinearity; least squares technique; imperfection; quadratic extrapolation technique | ||
| Address | ||
| S. Amir M. Ghannadpour and Payam Kiani: Aerospace Engineering Department, Faculty of New Technologies and Engineering, Shahid Beheshti University, G.C, Tehran, Iran | ||