Page 330 - The Combined Finite-Discrete Element Method

DEFORMABILITY WITH FINITE ROTATIONS IN 3D 313

.........continued from previous listing.............
/* free memory */
FREE(i1cnx);
FREE(i1cny);
FREE(i1cnz);
FREE(i2cfx[1]);
FREE(i2cfx[0]);
FREE(i2cfy[1]);
FREE(i2cfy[0]);
FREE(i1cfz);
}} }
Listing 10.36 Dynamically allocated memory is returned in reverse order to avoid any memory
fragmentation.

10.7 DEFORMABILITY WITH FINITE ROTATIONS IN 3D

The basic concepts of finite displacement, finite rotation and finite strain deformability
can be found in Chapter 4. Finite rotation elasticity using a constant strain, four-noded
tetrahedron finite element is described in detail in Chapter 4. Implementation of the algo-
rithmic procedures described in Chapter 4 is given in the form of code listings in this
section. The notation employed is shown in Figure 10.4, while the local variables used
to process this element are shown in Listing 10.37.
In Listing 10.38, the global components of the base vectors for the frames of reference
are calculated. First the global components of the base vectors of the initial frame (see
Figure 10.4) are calculated. These components are as follows:

 

i x j x k x

i y
j y
 (10.1)
k y

i z j z k z
and are represented by the two-dimensional array FO[3][3].

Initial (undeformed)
configuration 2
3
j 2 k
y j 1
i
k
3
0
j 0
1
k i
i x Deformed (current)
configuration
z

Figure 10.4 Global, initial and deformed initial frames of reference used in processing
finite-rotation elasticity.