II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy
II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy
II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy
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3.2 Explicit Time Integration<br />
SANTOS uses a modified central difference scheme to integrate the equations <strong>of</strong> motion through time. By this<br />
we mean that the velocities are integrated with a forward difference, while the displacements are integrated with a<br />
backward difference. The integration scheme for a node is expressed as<br />
tit=<br />
t<br />
( )<br />
f ‘XT – ftNT / M<br />
(3.2.1)<br />
‘t+At<br />
=ut+Atut<br />
(3.2.2)<br />
and<br />
‘t+At = Ut =tAt tit+& (3.2.3)<br />
where f t~andft ~ are the external and internal nodal forces, respectively, M is the nodal point lumpedmass,<br />
and At is the time increment.<br />
The central difference operator is conditionally stable. It can be shown that the Courant stability limit for the<br />
operator is given in terms <strong>of</strong> the highest eigenvalue in the system (Max):<br />
At
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