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

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Abstract

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).

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Abbreviations

\(\emptyset\) :

Real stress function

\(\nu\) :

Poisson ratio

a :

Inner radius of the circle/ellipse hole

a 1 :

Major axes of the elliptical hole with bead reinforcement

b :

Outer radius of the reinforcement hole

b 1 :

Minor axes of the elliptical hole with bead reinforcement

x :

Thickness of the bead reinforcement

n :

m Ratio of thickness reinforcement to the thickness of the plate

h :

Thickness of the panel

ht :

Thickness of the bead reinforcement

Q :

Equivalent stress

K :

Stress concentration factor

Kt :

Theoretical stress concentration factor for normal stress

q :

Notch sensitivity factor

σ x, σ y, τ xy :

Stress components

σ θ, σ r, τ rθ :

Stress components

σ y :

Yield strength stress components

\({\text{Net }}O\) :

ANN result

\(w_{i,j}\) :

Weights of each layer

\(x_{k}\) :

Input variable of the layers

\(b_{m}\) :

Bias variable of each layer

\(v_{m,n}\) :

Weight of the bias variable of each layer

P :

Number of experiments

t j :

Numerical result of jth element

o j :

ANN result of jth element

RMSE:

Root mean square error

R 2 :

Coefficient of determination

MEP%:

Mean error percentage

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Authors and Affiliations

  1. Department of Industrial Design Engineering, Faculty of Technology, Gazi University, 06500, Ankara, Turkey

    Murat Tolga Ozkan

  2. Graduate School of Natural and Applied Sciences, Gazi University, 06500, Ankara, Turkey

    Fulya Erdemir

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  1. Murat Tolga Ozkan
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  2. Fulya Erdemir
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Correspondence to Murat Tolga Ozkan.

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Ozkan, M.T., Erdemir, F. Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques. Neural Comput & Applic 33, 12641–12659 (2021). https://doi.org/10.1007/s00521-021-05914-x

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