| Summary: | 碩士 === 國立交通大學 === 土木工程系所 === 107 === This research studies the anti-plane problem of functionally graded fibrous composites in power law of elasticity theory, in which the functionally graded material’s gradient properties express without a clear interface between the materials. We investigate the changes in material property with the fiber radius r as a power function ( is a gradient parameter).
This experiment consists of square array and hexagonal array, the equivalent elastic modulus of the composite material that is obtained by the Rayleigh method; finite element analysis (COMSOL Multiphysics 5.0) and composite cylinder assemblages model are used to compare the results predicated by the Rayleigh’s method. In addition, the convergence analysis is used to understand the convergence of the displacement coefficient and the displacement and choose the mesh applied in the finite element analysis. Furthermore, we confirm the continuity of the displacement equation at the interface.
Numerical calculations are divided into two cases. First, in the fiber-matrix case, when the gradient parameter is -2, there is a significant improvement on the equivalent elastic modulus , but the error will increase as the gradient parameter becomes larger. In the section that changes the material property ratio, it is found that has a greater influence on the equivalent elastic modulus . Next, in the fiber-shell-matrix case, when the gradient parameter is +25 and c is 0.1 (where c is the shell thickness to core thickness ratio), the effect on the equivalent elastic modulus is more significant, and the error has good consistency in different volume fractions. Additionally, we discuss the impact on equivalent elastic modulus by changing the material property ratios and shell thickness. Numerical results demonstrated that the material property ratio has a greater influence on the equivalent elastic modulus . In the case of different gradual parameters, the equivalent elastic modulus will reach an extreme value at a particular thickness rather than being proportional to the thickness.
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