1 element method (FEM) which is the mathematically method


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

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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.

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.

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.


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