Multiple rigid line problems in an infinite plate

Abstract

The elastic analysis of the multiple rigid line problem in an infinite plate under the action of remote stresses is presented in this paper. It is assumed that the rigid lines are in a floating state, in other words, there are no resultant forces and moment applied on the lines. To solve the proposed problem, an elementary solution is derived and presented. The elementary solution is a particular solution of the infinite plate containing a single rigid line. In the elementary solution, the remote stresses and rotation are equal to zero and on the line the displacements are taken as Heaviside unit function and the rotation of the line, or the derivatives of displacements along the line are taken as Dirac delta function plus some constant. Using the obtained elementary solution and the principle of superposition, we found that the multiple rigid line problem can be easily converted into a system of Fredholm integral equations. Finally, the system is solved numerically and the stress singularity coefficients at the line tips can be easily calculated. Several numerical examples are given. © 1989.