Potentials in plane elasticity by distribution of dislocation doublet or force doublet along a curve

Abstract

Four types (DD1, DD2, FD1 and FD2) of complex potential are introduced in this paper. All types are obtained by distributing the dislocation doublet or force doublet along a plane curve. If the axis of dislocation doublet is placed in the tangential (normal) direction of curve, the DD1 (DD2) type of complex potential is obtainable. Similarly, if the axis of force doublet is placed in the tangential (normal) direction of curve, the FD1 (FD2) type of complex potential is obtainable. The continuous and discontinuous behaviors of the displacement and the resultant force function for four types of complex potential are discussed. It is found that: (a) the complex potential of the type DD1 can model the curve crack problem, (b) the complex potential of the type FD1 can model the curve rigid line problem, (c) the complex potential of the type DD1 can be obtained by a superposition of the types FD1 and FD2, (d) the complex potential of the type FD1 can be obtained by a superposition of the types DD1 and DD2. In this paper, the dislocation doublet (the force doublet) is abbreviated as DD (FD), respectively.