| Summary: | 博士 === 國立交通大學 === 土木工程系所 === 97 === In functionally graded materials (FGMs), the volume fractions of two or more materials vary continuously with a function of position in a particular dimension(s) to achieve a required functionality. The continuous change in the microstructure of functionally graded materials gives the materials better mechanical properties than traditional laminated composite materials, which are prone to debonding along the interfaces of layers because of the abrupt changes in material properties across an interface. The gradual changes of material properties in FGMs can be designed for various applications and working environments. Consequently, over the last two decades, FGMs have been extensively explored in various fields including electron, chemistry, optics, biomedicine, aeronautical engineering, mechanical engineering and others.
Plates in various geometric forms are commonly employed in practical engineering. Numerous places of various shapes have a re-entrant corner. Stress singularities are well know to be typically present at the re-entrant corner, and stress singularity behaviors have to be taken into account in order to perform accurate numerical analyses. The main purpose of the dissertation is to develop asymptotic solutions for FGM plates and to investigate the stress singularities induced by geometry of plate. Then, the asymptotic solutions are further employed to analyze the vibrations of cantilevered skewed plates and simply supported plates with side cracks ,and to determine stress intensity factors of plates with side cracks.
Asymptotic solutions for FGM plates are first developed to elucidate the stress singularities at a corner of the plate, using third-order shear deformation plate theory. The eigenfunction expansion technique is used to establish the asymptotic solutions by solving the equilibrium equations in terms of displacement functions. The characteristic equations are given explicitly for determining the order of the stress singularity at the vertex of a corner with two radial edges having various boundary conditions.
The asymptotic solutions supplement regular polynomials as the admissible functions in the Ritz method for accurately determining the natural frequencies of cantilevered skewed thick plates and simply supported rectangular plates with side cracks. The asymptotic solutions properly account for the singularities of moments and shear forces at the re-entrant corner and accelerate the convergence of the solution. Detailed convergence studies are carried out for plates of various shapes to elucidate the positive effects of asymptotic solutions on the accuracy of the solution. Frequency parameters are presented for different aspect ratios, chord ratios, skewed angles, and material nonhomogeneity parameters.
Finally, the asymptotic solutions are used in a mesh free method to determine the stress intensity factors of FGM thick plates with side cracks. A moving least-squares technique with polynomial basis functions and the asymptotic solutions is employed to construct shape functions in a mesh free method. Careful convergence studies are performed to demonstrate the effect of the asymptotic solutions on accurately determining the stress intensity factors. The stress intensity factors are directly evaluated using their original definitions, instead of using J-integrals.
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