1

Introduction

Modern and advanced engineering is constantly challenged to

incorporate advancing technologies, such as Computer Aided Engineering software

and applications, Finite Element Analysis (FEA) is one of

them. FEA is the computer modelling of products and systems, in order to solve

potential (or existing) structural or performance problems. FEA is the

practical application of the finite element method (FEM) which is the

mathematically method to solve partial differential by discretizing the domain into a finite

mesh, as showed in Figure 1. FEA is an

approximate solution of a mathematical representation of a physical problem

Figure 1

An object subjected to

three-dimensional loading can present six components of stress, in reference to

Cartesian coordinate system components are Normal Stresses (,,) and Shear Stresses (, , ), as showed in Figure 2.

Figure 2 Representation of Stresses in 3D

It is generally assumed that normal

stress distribution in an axially loaded member is uniform, with exception of

the nearest point of the applied load where the value of stress is considerable

higher representing stress concentration.

Increase

in the amount of stress created is caused by a change in geometry; the increase

in stress is known as the stress concentration factor. The factor is a ratio

that lies between the maximum stresses which is produced at the discontinuity

and divided by the normal stress placed far away from the hole; this has been

studied and documented 1.

Programs

such as ANSYS can often be used to bring the stress concentration factors

together, as they are calculated using a closed type equation for a given

geometry 2. There are two way in which the model accuracy can be increased

2. The first way is to increase the mesh density around the discontinuity,

this will help capture the increase in stress 2. The second way is to

increase the order of elements; an example is to use an 8-noded quad element

vs. a 4-noded quad element 2.

1.1 Aims and objectives

The main objective of this assignment

(simulation) is to study and analyse the stress concentration in a plate with

hole by finding the stress concentration factor at Point A, obtain the

longitudinal stress profile between points A and B and also obtain the stress

value at Point C, as shows in Figure 3. x.

To produce this analyse ANSYS software

will be used, where two element types will be used, the 2D plane stress 4 Noded

Quadrilateral (ANSYS Plane42) and the 2D plane stress the 4 Noded Quadrilateral

(ANSYS Plane82). The results abstained from ANSYS will be compared to the hand

calculation carried out, by studying the convergence and error estimation.