Mathematical modelling of a plate weakened by a circular hole in pure bending condition

Abstract

The task of this paper is mathematical modelling of a plate weakened by a circular hole in pure bending condition. The mathematical model is formed using the complex variable method, and allows complete analytical solution of stresses at every point of the plate, and especially around the hole where the well-known problem of stress concentration is present. The presented methodology can be applied for the solution of any plate weakened by a circular hole in pure bending condition. In the paper, methodology is applied for the solution of the one concrete example. The comparative analysis has shown a high accuracy of analytically obtained results with FEM results obtained by the calculation in ANSYS 12 software package. The application of the results of this paper is of great importance for quality of design and optimization of thin-walled structures of type plate weakened by a circular hole, which are very common in engineering practice.