Figure 8.5: Load Steps, Substeps, and Time
0 0. 5 1. 0 1.5 1. 75 2. 0TimeLoadstep 2Loadstep 1LoadstepSubstepSubstepsLoad
The program gives you a number of choices when you designate convergence criteria: you can base
convergence checking on forces, moments, displacements, or rotations, or on any combination of these
items. Additionally, each item can have a different convergence tolerance value. For multiple-degree-
of-freedom problems, you also have a choice of convergence norms.
You should almost always employ a force-based (and, when applicable, moment-based) convergence
tolerance. Displacement-based (and, when applicable, rotation-based) convergence checking can be
added, if desired, but should usually not be used alone.
8.2.1. Conservative vs. Nonconservative Behavior; Path Dependency
If all energy put into a system by external loads is recovered when the loads are removed, the system
is said to be conservative. If energy is dissipated by the system (such as by plastic deformation or sliding
friction), the system is said to be nonconservative. An example of a nonconservative system is shown
in Figure 8.6: Nonconservative (Path-Dependent) Behavior (p. 198).
An analysis of a conservative system is path independent: loads can usually be applied in any order
and in any number of increments without affecting the end results. Conversely, an analysis of a noncon-
servative system is path dependent: the actual load-response history of the system must be followed
closely to obtain accurat e results. An analysis can also be path dependent if more than one solution
could be valid for a given load level (as in a snap-through analysis). Path dependent problems usually
require that loads be applied slowly (that is, using many substeps) to the final load value.
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