Page 196 - The Combined Finite-Discrete Element Method

5

Temporal Discretisation

5.1 THE CENTRAL DIFFERENCE TIME INTEGRATION SCHEME

Contact between discrete elements together with the deformability of discrete elements is
described in terms of nodal forces and nodal displacements. Since each discrete element
is discretised into finite elements, the shape of each discrete element and its position in
space at any time instance is given by the current coordinates of the finite element nodes,
i.e. nodal coordinates.
 
x 1
 x 2 
 
 x 3 
(5.1)
 
x =  ... 
 
 x i 
...
 
x n
where n is the total number of degrees of freedom for a particular discrete element.
In a similar way, the velocity field over the discrete element is defined by nodal veloc-
ities v:
 
˙ x 1
 ˙x 2 
 
 ˙x 3 
(5.2)
 
v =˙x =  ... 
 
 ˙x i 
...
 
˙ x n
The acceleration field over the discrete element is given by
 
¨ x 1
 ¨x 2 
 
 ¨x 3 
(5.3)
 
a = ˙ v =¨x =  ... 
 
 ¨x i 
...
 
¨ x n
The Combined Finite-Discrete Element Method A. Munjiza
 2004 John Wiley & Sons, Ltd ISBN: 0-470-84199-0