| The discovery of QCs has brought a historical breakthrough in solid state physics, which broke the inherent traditional attitudes in the solid structure of crystals and glassy solids, possesses significant in both theorical and practical field. Unlike glassy solids, QCs have complete and orderly structure. However, QCs have not the translational symmetry which crystal materials should have. In virtue of the particular structure symmetry, compare to tranditional materials, the mechanical property of QCs is very complex and unique. QCs have many desirable properties, such as low friction coefficients, high wear resistance and low porosity, which are expected to be applied in coating surface of engines, thermoelectric converters and containers of nuclear fuel and other industrial fields. In particular, the field of linear elastic theory of QCs has been studied by many researchers, and underwent great development. However, due to the particular characteristics and complexity of QCs with piezoelectric effect, such as coupling effects and non-continuity, the analysis of QCs becomes more complicated and rare. In virtue of the linear elastic theory of QCs, this dissertation studies the elastic problem of1D QCs with piezoelectric effect by using both theorical and numerical methods. The fundamental folutions, Green’s functions, and exact solutions of single crack problem are obtained, which are the theorical basis for the further study of1D QCs with piezoelectric effect.1. Based on the linear elastic theory of QCs with piezoelectric effect, by decoupling the equilibrium equation, the general solutions of1D QCs with piezoelectric effect are obtained. For one of the solutions, accurate and analytical expressions are exhibited in case of four diffierent eigenvalues. In utilized of the general solutions, fundamental solutions of infinite plane, wedge/half-infinite plane and bi-materials plane problems under different loadings are investigated in closed-form and numerical results. The effect on mechanical behivaer of1D piezoelectric QCs material is studied.2. In virtue of the Stroh formalism, Green’s functions for infinite plane, half-infinite plane and bi-materials plane problems under different loadings, such as line force, line dislocations, and point charge are investigated in closed-form, and then the numerical solutions are plotted in polar coordinates. Unlike general solution methods, Stroh formalism is more common and can be conveniently used to solve plane problems of other kinds of QCs. For the plane problem of bi-material, Green’s function and Surface Green’s function are derived in closed-form and the effect on mechanical behivaer of1D piezoelectric QCs material constant and coupling effect is studied.3. Using the Muskhelishvili-Lekhnitskii complex variable function theory, the problem of elliptical hole or crack under uniformly distributed load at infinity is analyzed. Analytical solutions for the field intensity factor, crack opening displacement and energy release rate are exhibited, which show the electric displacement intensity factor is only determined by the stress intensity factor, and the energy release rate is greater than zero identically.4. In virtue of Betti’s theorem of reciprocity, the crack weight functions for1D QCs with piezoelectric effect are obtained. The crack weight functions play an important and effective role in calculating the field intensity factors for the crack under point force, point dislocations and point charge at arbitrary locations, respectively. Finally, for three kinds of loading cases, numerical results for different field intensiy factors are plotted, and the effect of material constants is studied... |
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