位移函数及十二次对称二维准晶平面弹性问题的简化

摘要

The paper considers the plane elastic problems of dodecagonal system in two-dimensional quasicrystals.By introducing displacement functions,the complicated partial difference equations of the plane elastic problems of dodecagonal system in two-dimensional quasicrystals are turned into two biharmonic equations,which are familiar in the classical elastic theory and can be solved by means of some methods such as Fourier transformation method,complex variable function method,and Riemann-Hilbert method and so on.Meanwhile,the analytic represents of displacements and stresses of elastic fields about the problem are given.Using this method and conformal transformation in complex variable function theory,some crack problems of the dodecagonal quasicrystals can be solved.The present work generalized Fan Tianyouwork about point group 12mm.%研究了十二次对称二维准晶的平面弹性问题.通过引入位移函数,把该问题数量巨大的复杂的偏微分方程转化为两个双调和方程,从而可用Fourier变换法、复变函数法和Riemann-Hilbert法等经典的方法去求解,使问题得到了大大地简化.同时,给出了这一问题的应力场和位移场的解析表示,推广了关于点群12mm准晶的相应结论.