• Geomechanics and Engineering
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• v.10 no.3
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• pp.357-386
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• 2016

In this research work, an exact analytical solution for thermal stability of solar functionally graded rectangular plates subjected to uniform, linear and non-linear temperature rises across the thickness direction is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the efficient hyperbolic plate theory based on exact neutral surface position is employed to derive the governing stability equations. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the quadratic distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Just four unknown displacement functions are used in the present theory against five unknown displacement functions used in the corresponding ones. The non-linear strain-displacement relations are also taken into consideration. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the present theory, demonstrating its importance and accuracy in comparison to other theories.

• Magazine of the Korean Society of Agricultural Engineers
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• v.22 no.2
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• pp.83-100
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• 1980

This study was intended to computerize the structural analysis of two-dimensional continuum by finite element method, and to provide a preparatory basis for more sophisticated and more generalized computer programs of this kind. A computer program, applicable to any shape of two-dimensional continuum, was formulated on the basis of 16-degree-of- freedom rectangular element. Various computational aspects pertaining to the implementation of finite element method were reviewed and settled in the course of programming. The validity of the program was checked through several case studies. To assess the accuracy and the convergence characteristics of the method, the results computed by the program were compared with solutions by other methods, namely the analytical Navier's method and the framework method. Through actual programming and analysis of the computed results, the following facts were recognized; 1) The stiffness matrix should necessarily be assembled in a condensed form in order to make it possible to discretize the continuum into practically adequate number of elements without using back-up storage. 2) For minimization of solution time, in-core solution of the equilibrium equation is essential. LDLT decomposition is recommended for stiffness matrices condensed by the compacted column storage scheme. 3) As for rectangular plates, the finite element method shows better performances both in the accuracy and in the rate of convergence than the framework method. As the number of elements increases, the error of the finite element method approaches around 1%. 4) Regardless of the structural shape, there is a uniform tendency in convergence characteristics dependent on the shape of element. Square elements show the best performance. 5) The accuracy of computation is independent of the interpolation function selected.