Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 7M

Year: Dec 2015

Coarse and Fine Mesh

As we have learnt, dicretization is the first step in FEA. Discretization is nothing but dividing the domain into a number of elements. This is also called as mesh generation. In general, elements chosen are triangular, rectangular or quadrilateral type. Each edge of the element may have two or more nodes depending upon variation of the primary variables along the domain. Different elements may have different number of nodes but care should be taken to see that the common edge joining the two elements have the sasme number of nodes. This is normally done by using a transition element.

Initially, the domain is divided into a certain number of elements based on experience and judgement of the analyst. This mesh is called as coarse mesh. A second trial is taken by taking still more number of elements and again the results are checked. This is called as refining of the mesh. If the results obtained in thye two trials show significant variations, further trials are taken by contineously refining the mesh till we get satisfactory convergence. The mesh containing more and more number of elements is called as fine mesh. Care is to be taken to see that the aspect ratio, which is defines as the ratio of the biggest side of the element to its smallest side, does not exceed 10 as far as possible. Refining of the mesh can be done in two ways -

• By subdividing the existing elements into two or more number of elements which is called as h-method and
• By increasing the order of the existing elements in which it is called as p-method. Both h and p methods are shown in fig.

It is to be noted that computational costs increase significantly with increase in the number of the elements. Hence judicious use of type and order of the elements is to be made while discretizing the domain.

General rules of mesh generation are given below:

1. Elements chosen should characterize the governing differential equation of the problem.
2. Number, shape and type of elements should be such that geometry of the domain is represented as accurately as possible.
3. Higher order elements should be used to represent region of large gradient.
4. As far as possible, avoid elements with large aspect ratio which is defined as ratio of the largest dimension to the element. This should not normally exceed 10.