Finite Plate with Circular and Square Hole under Partial Loading


Mechanical Engineering, Yazd University, Yazd, Iran


In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the partial loading is transformed to new boundaries as form of triangular functions. The Airy stress functions are selected according to these triangular functions and the unknown factors of Airy stress functions are derived by applying boundary conditions. The stresses in this plate with circular hole are mapped to plate with square hole using Muskhelishvili’s complex variable method. The results of this method are compared with theoretical solution of infinite plate and finite elemnt method solution of finite plate. The results showed the dimensions of plate and square hole and length of biaxial partial loading affected on Von Mises stress around the square hole. Von Mises stress increases around the square hole by decreasing length of the plate or increasing hole’s area.