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1. FEA/CFD for
Biomedical
Engineering
Week 2: FEA Theory

2. Session Aims
By the end of this week you will be able to:
• Detail the basic principals of Finite Element
Analysis and detail the basic underlying maths
• Perform a basic hand-calculation to calculate the
deformation in a static problem

3. Methods for
mechanically
analysing a solid
structure

4. 1. Experimental
• Probably the most reliable
method
• Usually time consuming and
expensive
• Engineers may choose to
conduct experiments on
small scale models, then
extrapolate to full scale
models

5. 2. Analytical methods
• Also called theoretical method
• Use mathematical equations to analyse the behaviour of
a system
• Some assumptions are needed
• Able to solve simple problems only

6. 3. Finite element analysis
• Reduce large and complex structures into small non-
overlapping elements;
• Equations (using classic mechanics) are used to
describe the physical behaviour of each node;
• Entire structural
behaviour calculated
assembling the
equations.

7. Elements
Meshing: Divide the problem domain into a very
large number of very small regions elements
Element
Node
Model is sub-divided into a
number of Elements
The elements share common
points called nodes.
The behaviour of these elements
is well-known under all possible
support and load scenarios
The motion of each node is fully
described by translations in the
X, Y, and Z directions. These are
called degrees of freedom (DOF)

8. 2D Elements
Truss Element (2 nodes)
• Long and slender, can assign cross sectional
area
• Allow translation of each node only; 3 DOF
element
• Take axial load and motion only
• Uniform cross section
Beam Element (3 nodes)
• Long and slender,
• Allow both translation and rotation at each node;
6 DOF element
• Carry moment and rotation
• Can have shear motion out of or not along
length of element

9. 2D Elements
Membrane Element (3 or 4 node)
• Allow translation of each node only
• Not able to take a moment or stress
normal to the surface.
• A uniform thickness can be defined
• E.g. fabric, skin
Plate Element (3 or 4 node)
• Usually thicker than membrane element
• Allow both translation and rotation at
each node
• Able to take a moment and stress
normal to the surface e.g. pressure
vessels, automobile bodies

10. 3D Elements
Depending on the geometry of our
model, required accuracy and
computational resource, we can choose
one of these different 3D elements
Most FE package allows meshing to be
automatically done
Tetrahedra Element (4
Nodes)
Tetrahedra Element, 6 Nodes Brick Element, 8 Nodes

11. 3D Elements
Additional mid-side nodes can be
added improving computational
accuracy
Most FE package allows meshing to
be automatically done

12. Nodes
• Nodes of the elements
represent the possible
movement under loading
• Mathematical relation
between nodes transfers
forces and moments
• Element stiffness
between nodes acts like a
spring
• Stresses and strains are
given at the nodes

13. Meshing Types
• Structured 
• Orthogonal 
• Uniform 
• Boundary fitted 
• Fine 
• Unstructured
• Non-orthogonal
• Non-uniform
• Non-boundary fitted
• Coarse