13-06-2012, 02:41 PM
EXTERNAL NODES IN FINITE ELEMENT ANALYSIS
EXTERNAL NODES IN FINITE ELEMENT ANALYSIS[.doc (Size: 226.5 KB / Downloads: 50)
Abstract:
The nodes outside the physical domain of the element called ‘external nodes’ are used here to enhance the capability of the element. The paper shows that the constants associated with the shape function need not only associated with the nodes inside the element boundary but in general it can be associated with the nodes outside the element boundary also.
. Introduction
The finite element analysis starts with the idea to divide the domain into number of
parts, called finite elements. These elements are defined between the nodes and may
also have internal nodes. While deriving the element stiffness matrix, the constants
associated with shape function need to be identified from these nodes, contained within element. Selecting nodes within the element boundary is self- imposed barrier, seen to be followed in the finite element analysis since the birth of the first element.
Ideally all the nodes in the structure affect individual element stiffness. The question
remain is of the economy of analysis which restrict the number of nodes per element
and the number of element to be consider in the analysis.
. Development of 4node- external node element
The element is shown in Figure 1(a), between node 3 and node 4. The element has node ‘1’ and node ‘2’ outside the element boundary called ‘external nodes’. Ordinate of the nodes in Cartesian co-ordinate system are x1, x2 , x3, x4. Relation between natural co-ordinate, ξ and Cartesian co-ordinate x, based on assumption that internal node are placed at equidistance .
Comparative study with conventional element
The study is made based on the observation of global stiffness matrices and the numerical example shown in figure 2. The detailed discussion on global stiffness matrices is made here to highlight the coupling between more degrees of freedom in case of external node element. The global stiffness matrices are shown in Figure 3 for conventional and external node element for the bar problem shown in Figure 2.
. Conclusions
To conclude the discussion on the ‘external node element’ requires further investigations on different elements to identify its effectiveness. To choose such an element, it requires the observations and those observations are summarized here based on the work carried herein.