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DOI: 10.14738/aivp.92.10131

Publication Date: 25

th April, 2021

URL: http://dx.doi.org/10.14738/aivp.92.10131

Machine Learning Solutions of Stress Concentration

Factors in Perforated Plate With Single Circular Hole

1Yafeng Chang, 2Hui Wang

1College of Civil Engineering, Henan University of Technology, Zhengzhou, China

2School of Civil Engineering and Architecture, Hainan University, Haikou, China

ABSTRACT

The discontinuities such as holes, grooves, notches and fillets in the structural

geometry in structures would lead to significant increase of stress level, which can

be represented by stress concentration factor (SCF), and further influence the

strength of structures. Therefore, SCF plays a vital role in quantitatively

understanding the influence of discontinuities on the peak stress. However,

analytical or empirical solutions for predicting localized high-stress around the

discontinuities are usually difficult to be derived, owing to the complex interaction

of the specific boundary conditions and the discontinuities. In this work, machine

learning (ML) solutions of SCF of circular holes in a finite perforated plate under

tension are modeled using finite element analysis and back propagation neutral

network (BPNN) technique. The locations and sizes of circular holes are input as

input variables, and the SCFs are target variable. The feasibility and accuracy of the

model are demonstrated through numerical examples. It’s found that the developed

ML approach base on BPNN technique can provide accurate prediction of SCF value

for each set of structural parameters, and vice versa.

Keywords: Machine learning, neutral network, stress concentration factor, circular

hole.

INTRODUCTION

Considering the fact that almost all engineering structures involve interruptions in

section and/or shape, i.e. cracks on aircraft wings, grooves or shoulders on shafts,

oil holes, screw threads, shape reentrant corners of auxetics, etc. Typically, these

interruptions arise from discontinuities of geometry and may cause a local increase

in stress in the engineering structure, where a high stress gradient exists [1-3]. Such

stress rise is known as stress concentration normally. Obviously, the stress

concentration may result in the part failure in practice, and further affects the

material or structure designing. Therefore, stress concentration analysis plays an

important role, especially in designing the structures under alternating loads.

For engineers, a simple and reliable solution can bring great convenience to

engineering applications. However, so far, most of the existing estimators for stress

concentration factor (SCF) near a circular hole in a finite plate are some empirical

formulas, which are provided by curve fitting technology based on the experimental

measurement (usually using photoelasticity) involving many contributors through

several years [4]. Moreover, these empirical solutions are usually not reliable for the

extreme cases that the circular hole diameter is large compared to the dimensions

of finite plate. As an alternative to the empirical solutions, the finite element

solutions are popularly resorted, due to the advantages of easy implementation of

programing and strong applicability to complex problems [5, 6]. However, the

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344

Chang, Y., & Wang, H. (2021). Machine Learning Solutions of Stress Concentration Factors in Perforated Plate With

Single Circular Hole. European Journal of Applied Sciences, 9(2). 343-350.

URL: http://dx.doi.org/10.14738/aivp.92.10131

efficiency of numerical solutions is doubtable and you have to conduct simulation

for each structural configuration and each loading condition. Even today, it is

difficult to determine the exact value of SCF for most extreme cases. Therefore, a

practical requirement seeking reliable solutions is naturally raised.

Machine learning (ML) solutions are a promising way to achieve this purpose [7-

11]. It has been reported that the ML solutions behave not only ease of

implementation but also low computational cost for some complex engineering

problems, i.e. fracture mechanics problems of the pentagonal cross-section

microcantilever at nanoscale [9], stress hotspots in polycrystalline materials under

uniaxial tensile deformation [12], stress concentration depiction at the low points

of rough surfaces by interpretable convolutional neural network [13]. More

recently, Ozkan and Erdemir developed nonlinear ML models based on neural

network (also known as artificial neural network, ANN) for predicting SCF for

circular/elliptical holes in an infinite plate [11]. Interestingly, in these successful

applications, the ML process thoroughly avoids the complex mathematical formulas

related to the controlling parameters and the desired mechanical response.

Taking inspiration from these successful applications of ML, in this context, the

stress concentration in a finite plate perforated with a circular hole is investigated

by using BPNN based ML technology. The size and position of the circular hole can

be arbitrary. Thus, from the view of data analysis, the input in the BPNN framework

is the geometrical information (e.g., radius of hole, location coordinates) and the

output is the results of stress concentration factor. To drive the BPNN algorithm, a

dataset including the geometric parameters of the problem and the corresponding

stress response is synthetically generated from finite element simulation. After that,

we used genetic algorithm to continuously optimize and find the maximum stress

from all the predicted data.

PROBLEM DESCRIPTION

The peak stress in a finite plate perforated by a circular hole located at an arbitrary

position is investigated in this study, as shown in Fig. 1. The plate is subject to a

uniform tension with a specific tension force σ0 along the x direction. The solid

material is isotropic and elastic.

Fig 1. Schematic diagram of finite plate with circular perforation subject to

unidirectional tension

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European Journal of Applied Sciences, Volume 9 No. 2, April 2021

Services for Science and Education, United Kingdom

To characterize the peak stress better, the SCF concept is normally introduced to

perform both design and analysis of the loaded members with geometric

discontinuities. Here the SCF for the problem under consideration is defined as the

ratio of the peak stress to the normal stress at the circular hole,

Ks =

σmax

σnom

σmax

σ0

(1)

where Ks denotes the SCF, σmax is the unknown peak stress, and σnom is the

reference nominal stress, which usually corresponds to the case without hole.

Obviously, the value of SCF for isotropic material is independent of material

properties and is strongly relevant to the geometries of the structure, including the

size of circular hole, the location of circular hole in the plate. Thus, Ks

is a function

of L1

, L2

, W1

, W2 and R

Ks = Ks

(L1

, L2

,W1

,W2

,R) (2)

Traditional theoretical methods to compute the SCF of the structure involving

multiple parameters are usually very complex. In order to solve this problem and

further improve the predictive efficiency, the nonlinear machine learning model

with BPNN algorithm is established to predict the SCF.

BACK-PROPAGATION NEURAL NETWORK

Generally, a typical BPNN model composes of three layers [14, 15]. The first layer is

input layer containing inputs (also known as predictors), and the last layer is output

layer containing target outputs. Between them are one or more hidden layers which

are interconnected between neuron nodes which simulate the biological nervous

system of human brain to process information, as shown in Fig. 2. The input layer

takes in input information and then transfer them throughout the middle neuron

network layer in which nonlinear activation functions are employed to capture the

nonlinear relationship in the data set. Theoretically, the more the hidden layers and

hidden neurons, the more capabilities a network can model a complex and nonlinear

system.