Finite Element Method (Part 1) EG55M1 Assignment 1 - University of Aberdeen

Finite Element Method (Part 1)
EG55M1
Assignment One
Completed by Group 1
Group Members
ADELEKE OLUGBENGA
GANGADHARAN NAMITA
MINHAJ MD HABIBULLAH

INTRODUCTION
Finite Element Method is a numerical method used to analyse complex engineering
structures and systems. This is achieved by partitioning the structure into smaller simpler
parts or elements. This method gives approximation solutions to physical problems.
Using finite element analysis method, we can determine the stress, strain and deformation
in the structure. In this problem the type of finite element analysis systems used is linear
static structural capabilities which is a beam in the x-y plane with degrees of freedom 𝑢𝑥,
𝑢𝑦 and 𝜃𝑧 at each end.
The element properties are given, which are then used to construct global properties, and
after the boundary conditions are imposed, then the displacement in the x-direction and the
rotation about the z-direction are calculated.
These are the steps required to solve the problem using finite element method.
 Discretisation
 Determination of the local element characteristics
 Transformation of the element characteristics
 Assembly of the global element characteristics
 Application of the boundary conditions
 Determination of the unknowns from the finite element equation
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AIM
The aim of this report is to calculate the displacement in the x-direction and the rotation
about the z-direction for global node A of the beam shown below, using all the information
provided.
Question.
The stiffness matrix of a 2D beam element (i.e., a beam in the x-y plane with degrees of
freedom 𝑢𝑥, 𝑢𝑦 and 𝜃𝑧 at each end) is shown below (note the symmetry about the
leading diagonal).
Use the element stiffness matrix to construct the global stiffness matrix. Note that the
member 1 and member 2 are fully fixed at one end.
In the figure member 1 is ∅800𝑚𝑚 × 20𝑤𝑡 × 10𝑚 long and member 2 is∅600𝑚𝑚 × 15𝑤𝑡
× 8𝑚 long. Neglect the shear deformation (i.e., Φ = 0). Young’s modulus is 200 GPa.
Calculate the displacement in the x-direction and the rotation about the z-direction for
global node A when 𝐹𝑥 = 1𝑀𝑁 and 𝑀𝑧 = −2.4 𝑀𝑁𝑚. The transformation matrix for
this problem is a matrix with the rotational degree of freedom at each node.
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