Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques

Özkan M. T. , Erdemir F.

NEURAL COMPUTING & APPLICATIONS, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2021
  • Doi Number: 10.1007/s00521-021-05914-x
  • Keywords: Theoretical stress concentration factor (Kt), Reinforcement with circular, elliptical holes, Finite element analysis, Artificial neural networks, Design optimization, Statistical method


Machine parts always work under different types of stresses or loading conditions. The sudden dimensional changes lead to sudden increase in stress on the critical section of the machine parts. This state is defined as stress concentration factor (SCF). The strength of the machine part decreases on the located point at maximum stress. In this study, SCFs of circular/elliptical holes with bead reinforcement in an infinite panel under uniaxial and biaxial stresses were modeled, simulated, calculated and verified using analytical, finite element analysis (FEA) and artificial neural networks (ANN) techniques. This study presents a new model for predicting SCF for panels using artificial intelligence techniques under uniaxial and biaxial loading conditions. Theoretical SCF (Kt) values for different shapes and loading conditions have been compiled and graphical forms of these experimental results were published by Peterson (Peterson's stress concentration factors, 3rd edn. Wiley, Hoboken, 2007). There is a need to convert these curves into a numerical data set to be used in machine part design easily. Theoretical SCF (Kt) was obtained from the Peterson's charts in numerical form according to dimensional parameter ratios using high-accuracy graphical computer software. Using these dimensional parameter ratios, a parametric finite element model (FEM) was created. Uniaxial and biaxial boundary conditions were applied to the FEM model. Mesh optimization was accomplished to the parametric FEM model. Mesh formation is compatible with the model according to dimensional sizes and ratios. Mesh optimization was provided to element size and per unit volume. Numerical and FEA results were tested, approved and confirmed with Peterson's original data using statistical methods. A code was created for the improvement of the ANN model in the Matlab ANN Toolbox Editor. Different ANN model variations were tested and the best-performing ANN model was determined among the tried models. Numerical, FEA and ANN model results were compared and confirmed with one another. The developed model provides an easy method to predict and calculate the stress in defining the Kt according to dimensional ratios and applied loading states (uniaxial/biaxial).