| Summary: | 碩士 === 國立臺灣科技大學 === 營建工程系 === 100 === The main purpose of this thesis is to analyze the mechanical analysis of FGM continuous plates with one opposite edges simply supported and other edges fixed under uniform loads and linear thermal loads. The Young’s modulus of the continuous plates is assumed to vary along thickness direction based on three kinds of functions, which are power-law function, sigmoid function, and exponential function. The coefficient of thermal expansion of the continuous plates is assumed to be constant or functionally distributed along thickness direction.
In solving the problem, first, the continuous plate is divided into three individual spans which are further split into some fundamental problems. The solutions of these fundamental problems are obtained by using Fourier Serious expansion. Then the rotation angles at the continuous portions of the FGM continuous plates are solved by using superposition method and the aid of the compatibility conditions in these three individual spans. Consequently, the closed-form solutions of the continuous plate are found by substituting the obtained rotation angles into the fundamental solutions. Finally, the analytical solutions are compared with the numerical solutions obtained by MARC software of finite element method.
The mechanical behavior of three types of continuous plates which are FGM plates, FGM coated plates, and FGM undercoated plates are investigated. The influences of the external loads, thermal loads, material properties, and the aspect ratios of the plate are all discussed. The deflections along the y-axis and the stresses, strains along the z-axis are presented and compared with the numerical solutions. Results show that different distributions of Young’s modulus are not present great influences on the displacements of the continuous plates under the same uniformly distributed load and thermal load. However, under the same thermal load, the stresses of FGM continuous plate are strongly affected by the distributions of the Young’s modulus, and the mechanical behaviors are strong influenced by the coefficients of thermal expansion. These phenomena imply that stress behaviors of the continuous FGM plates can be predicted and designed. Moreover, the influence of the uniformly distributed load on the mechanical behaviors of the continuous FGM plates increases as the aspect ratio increases when the linear thermal loads are fixed.
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