How to select the Finite Elements for Physical Domain

Volumetric & Topological Change

We can consider 1D, 2D and 3D types of elements in a body depending on the physical volume and the “Topology”. By the basic methods like implementation of elements on any physical domain we have to consider the curvature changes per unit area that implies if curvature changes per unit area is too frequent than we will have to consider 3D element types. Numbers of elements we can change by two possible processes, either by changing the element shape function or by decreasing the element size. Main aim must be to cover the whole physical domain with maximum topology area. The pre-requisites considerations are as follows for Physical Domain –

1. Volume & Topology type

2. Curvature Changes per unit area

Representing a physical domain with finite element integration is referred to as meshing, and the resulting set of elements is known as the finite element mesh .As mentioned previously if the physical domain have straight edges , it is generally possible to cover whole or maximum physical domain because all the elements do have almost straight curvature shape ,but if physical domain we have is asymmetric or with the NURBUS topology than it is impossible to cover whole physical domain with straight elements. Such situations are given in (a) and (b).

As you can analyse from figure (a), curved boundary domain is meshed in coarse manner using square elements. Where as in figure (b) has refined meshing for the same domain. By the comparison we can conclude that fine mesh will cover more area and topology of physical domain in compare to coarse manner but will have more numbers of elements hence more numbers of nodes. If the interpolation functions satisfies certain mathematical requirements, the finite element solution for a particular problem converges to the exact solution of problem. As the number of elements increased and the physical dimensions of the elements are decreased the finite element solution changes incrementally.