Page 26 - Finite Element Analysis with ANSYS Workbench

2.3 Academic Example 17

3 2x x 2 4 4x x 2
()
()  1
Nx  ; Nx   ;
1
L L 2 2 L L 2
x 2x 2
()  
Nx L  L 2
3
The assumed displacement distribution of the three-
node element is more complicated than that of the two-node
element. Thus, the three-node element can provide higher solution
accuracy. However, the element requires more computational time
because it contains more nodal unknowns.
The finite element equations for the two-node element
are,
1 AE  1  u 1   F  1  
u
L   11         F 2  
2 
If we have a finite element model consisting of 10 elements, we
need to establish 10 sets of finite element equations. These element
equations are then assembled to form up a system of equations.
The problem boundary conditions are applied before solving for the
displacement unknowns at nodes.
If a finite element model containing many truss
elements is in two or three dimensions, the finite element equations
above are needed to transform into to two or three dimensions
accordingly. The transformation causes the finite element matrices
to become larger leading to a larger set of algebraic equations.
Such the larger set of algebraic equations requires more computer
memory and computational time. However, these requirements do
not pose any difficulty to current computers. Commercial software
packages today have been developed to analyze complex truss
structures containing a large number of elements effectively.

2.3 Academic Example

2.3.1 Two Truss Members in One Dimension

A model with two truss members connected together in
one dimension is shown in the figure. The two truss members have