Stress systems in an infinite strip

Abstract

The problem of determining the stresses and displacements in a rectangular strip of elastic material whose long edges are acted upon by any system of tractions was attacked by Filon, who gave a solution which is almost complete if the breadth of the strip is small compared with its length. The problem was treated as one of "generalised plane stress," i. e ., the stresses and displacements considered were means taken with respect to the thickness. It was found possible to express these mean stresses and displacements by series so that the boundary conditions over the long edges were completely satisfied while the total forces and couples over the short edges could be adjusted. In the limiting case of an infinitely long strip the series were replaced by integrals which proved in many cases more convenient for calculation. The cognate problem of finding the stresses and displacement produced by forces acting within the strip instead of on its edges appears to have received but little attention. An attempt to find the solution for an isolated force acting at a central point and in the direction of the length of the strip was recently made by E. Melan, but he was unable to satisfy the boundary conditions without introducing shears on the edges.