FEM

Question 1

Gap elements to model contact are rarely use today in fe simulations. What are the advantages and disadvantages of using gap elements in the contact analysis of a sealing system. (8marks)

Answer 1

Advantages are minimising the contact area therefore minimising contact non-linearities in the model.

Disadvantages are the high CPU requirement even when both bodies are assumed to be elastic.

Question 2

Use sketches to present the three main causes of non-linearity present in analysis (8marks)

Answer 2

Material, geometry, contact

Question 3

Why is the CPU requirement for a non-linear problem high? (8marks)

Answer 3

The umber of equations that needs to be solved is much greater. As the solution is not linear it is not easily solved

Newtons method is used as an iterative method.

(Not complete what else can input here?)

Question 4

What are the 4 requirements that need to be satisfied by the displacement function to make an element complete and compatible and hence accurate she used to model engineering problems?

Answer 4

1. The function and it’s first derivatives should be continuous within the element
2. The function should allow nodal displacements caused by rigid bid translations and rotations to occur without straining the element. (So without changing the strain energy in the element)
3. The function should allow for all states of uniform strain within the element
4. The function should satisfy internal compatibility within the element and a compatibility of displacements between adjacent elements at the nodes along the boundaries. (This is referred to as a conforming function)

Question 5

Is the theory of elasticity an exact function for a bar with axial load or for a beam with pure bending? What sense is the term exact being used? (6marks)

Answer 5

It is exact for a bar with an axial load however not for a beam in pure bending as it does not model the secondary deformation in the plane perpendicular to the beams length.

The term exact is used in the the deformation modelled is the only significant deformation present

Question 6

What is the difference between displacement and force approach. In FEM and why is the former the most popular? (6marks)

Answer 6

The difference between the two is the unknown in the model. The displacement approach uses the displacement of each node as the unknown and the force approach uses the force.

The displacement approach is most popular because there’s an associated simple displacement at each node. The approach has been developed further and there has been major advance in discretising the continuum fully using a continuum of subregions. (Elements)

Question 7

In the FEM the chosen displacement field takes the form of polynomial expressions and the expressions are known as displacement functions. Using the example of a 3 nodes triangular plane stress element discuss the restrictions on defining its polynomial expressions in terms of generalised coefficients.

Answer 7

Using a generalised coefficient odds not give the actual displacement but a linear combinations of the element nodal point displacements. (Finish off)

Question 8

Why do linear stress strain relationships simplify the analysis of a structural engineering problem?

Answer 8

It dramatically reduces the number of equations to be solved as it linear analysis assumes the stiffness of the model does not change with loading.

Question 9

Summarise the modelling requirements and technical data required to develop a contact model under real operational conditions.
Assumed rigid bodies and discuss this assumption. (8marks)

Answer 9

Geometry of the structure
Material properties
Applied loading conditions
Restraints (boundary conditions)

(Using a rigid body doesn’t allow for material non-linearity. It doesn’t show how the structure deforms therefore how it interacts or all of the contact areas. The CPU requirement also increases)