The general solution of the elastic equations for an arbitrary homogeneous anisotropic solid is found for the case where the elastic state is independent of one (say x3) of the three Cartesian coordinates x1, x2, x3. Three complex variables zl = x1 + plx2 (l = 1, 2, 3) are introduced, the pl being complex parameters determined by the elastic constants. The components of the displacement (u1, u2, u3) can be expressed as linear combinations of three analytic functions, one of z(l), one of z(2), and one of z(3). The particular form of solution which gives a dislocation along the x3-axis with arbitrary Burgers vector (a1, a2, a3) is found. (The solution for a uniform distribution of body force along the x3-axis appears as a by-product.) As is well known, for isotropy we have u3= 0 for an edge dislocation and u1 = 0, u2 = 0 for a screw dislocation. This is not true in the anisotropic case unless the x1x2 plane is a plane of symmetry. Two cases are discussed in detail, a screw dislocation running perpendicular to a symmetry plane of an otherwise arbitrary crystal, and an edge dislocation running parallel to a fourfold axis of a cubic crystal.

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fourfold axis symmetry homogeneous anisotropic solid of body force x3axis burgers vector x1x2 plane displacement u1 u2 u3 screw dislocation elastic equations cartesian coordinates x1 x2 cubic crystal

J.D. Eshelby and W.T. Read and W. Shockley,.Anisotropic elasticity with applications to dislocation theory. 1 (3),251-259.

J.D. Eshelby and W.T. Read and W. Shockley,"Anisotropic elasticity with applications to dislocation theory" 1

J.D. Eshelby and W.T. Read and W. Shockley,"Anisotropic elasticity with applications to dislocation theory"