Abstract
By introducing a stress potential function, we transform the plane elasticity equations of two-dimensional quasicrystals of point group 10, [Formula: see text] to a partial differential equation. And then we use the complex variable function method for classical elasticity theory to that of the quasicrystals. As an example, a decagonal quasicrystal in which there is an arc is subjected to a uniform pressure p in the elliptic notch of the decagonal quasicrystal is considered. With the help of conformal mapping, we obtain the exact solution for the elliptic notch problem of quasicrystals. The work indicates that the stress potential and complex variable function methods are very useful for solving the complicated boundary value problems of higher order partial differential equations which originate from quasicrystal elasticity.
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