Algorithms
A basic menu of the algorithms and problem types available in Zebulon
are as follows:
- Newton/Quasi-Newton The best convergence for non-linear
problems is achieved with the Newton method when a high quality
consistent tangent matrix is supplied for each element integration.
Because of the cost of inverting the global stiffness, the initial
iteration can be used repeatedly for subsequent iterations giving slower
convergence but perhaps faster CPU time.
- BFGS is a quasi-Newton algorithm initially developed
for optimization problems, which updates an already inverted matrix
(e.g. the initial problem matrix, or the 1st iteration inverse).
The updates are made using the residual vector and the displacement
increment is quite efficient.
- Riks is an algorithm used to bypass instability
points, or situations where "snap-through" can occur without
going to a dynamic solution.
- 2D/3D Contact Contact is available using an associated
stiffness method which employs iterations to solve a sub-problem
(much like a super element). The iterations generally are quickly
achieved relative to the global inversion, so contact problems are
not very expensive. The contact can be enforced exactly, or use
"soft" contact allowing contact to interact with boundary conditions
at the cost of very small penetrations.
- Implicit dynamic with contact is implemented using a trapezoid
rule time integration.
- Explicit dynamic with contact (under development). The next
version of Zebulon will include a full featured explicit solver.
- Eigen solutions is available with post processing of the deformed
mode shapes. A stiffness matrix can be loaded from a deformed configuration.
- Thermal stationary/transient solutions are available. The
model kinematics can be imposed also from previously calculated
mechanical solutions (i.e. during coupled solution).
- Multi-problem "stepped" coupling Currently only stepped
coupling is available. This can include any number and order of solutions
and the import/export of model data is quite general.
Some other algorithmic features which are available include:
- Automatic time stepping, init-ddof are features allowing
a fine tuned control over the increments in a solution. These options
can ensure the quality of quality and maximize efficiency
of a solution. An example would be to ensure that the change in
Mises stress over the increment is below 10MPa.
- Arbitrary external parameters (fields)
are essentially loading for the problem, affecting
parametric strains (thermal dilatation) and coefficient
values. Any number of field variables are possible, with
different "locations," and any material coefficient can depend on
any number of parameter.
- Debonding with contact activation
Debonding interfaces are available with automatically activated
contact surfaces. A number of different "debond material" models
are available to predict different types of damage which occur
such as the degradation of interfaces between fiber and matrix in
composites. The interface models are user-definable of course.
- Post step computations coupled to BCs
Algorithms have the ability for post-step computations such as
strain energy, J, delta J, etc, which can be used to control
subsequent boundary conditions.
- Cycle skipping
extrapolates the internal state variables on a cyclic basis.
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