Stress in a Plate Containing an Infinite Row of Holes

Abstract

In this present paper, in order to solve the general problems of the stress distributions in an infinite plate having an infinite row of equal and equally spaced holes the tractions applied to which are regarded as similar, using almost the same method used by Howland in his paper published in 1935, the three stress functions x₁, x₂ and x₃ are introduced anew. x₁ is even in x and odd in y axis, x₂ is odd in x and even in y axis, and x₃ is odd in x and y axis, and they are expressed by means of some sets of periodic functions all derivable from one fundamental function. The results obtained are applied to the problems of the cases of simple bending or shearing and these stress distriburions are obtained clearly.