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This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Coordinates, Nodes, Three-dimensional, Simplex, Element, Shape, Functon, Interpolation, Model
Typology: Exercises
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Problem 3.13:
The coordinates of the nodes of a three-dimensional simplex element are given below:
Determine the shape functions of the element. Solution: for a 3D simplex element, if DOF is one then interpolation model can be written as
i e j k l
^ T^ 1 x y z
Then
( ) 1 0 0 0 ( ) 1 10 0 0 ( ) 1 0 15 0 ( ) 1 0 0 20
T T T T
at nodei at node j at node k at nodel
By solving it in Mat-Lab we get,
1
As,
T^1
So,
N^ N 1^ N^ 2 N 3^ N 4
On simplifying
N^ ^ (1^ ^ 0.1 x^^ ^ 0.067^ y^ 0.05 )0.1 z^ x^^ 0.067^ y^ 0.05 z So,
1 2 3 4
N x y z N x N y N z
