In addition to the MDL command analysis nonlinear, the following commands may be specified in the case block.
correction_type newtonaccelerated_newton

Specifies the type of correction in a given Newton iteration. Default is
newton
.The
newton
correction type only makes use of the residuum and the tangent matrix (updated or not) to compute the correction.The
accelerated_newton
correction type is meaningful with a modified Newton method. It monitors whether the sequence of Newton iterations converges (whether the residuum decreases), and if not (divergence), invokes the line search algorithm to find a better solution. With line search, it is often possible to find a solution outside the convergence region. Thus, when using the MDL commandsnewton_method modified
ornewton_method delayed_modified
, the accelerated Newton correction can converge for larger time steps than the normal Newton correction type.See also the MDL command line_search.
correction_termination_test flux_normalisedregulariseddof_and_residuenormalised_dof_and_residue

Specifies the type of test which indicates whether the Newton iterations of the correction phase have sufficiently converged. The tests make use of some or all of the MDL commands
tol_residuum
,tol_solution
, andtol_work
. Default isflux_normalised
.The
flux_normalised
correction termination test computes the residuum normalised by the energy flux for each type of field (displacements, rotations, Lagrange multipliers, etc.) separately. Theflux_normalised
test has additional options, see Section 5.The
regularised
correction termination test regularizes the residuum, the solution changes, and the energy change, with the goal of making the test independent of the units. Thus, changing the units of an FE model (e.g. [kg,m,s]) to another (consistent) unit system (e.g. [t,mm,s]) should not require modification of the tolerances. The following tolerances are used:tol_residuum
(default 1e3),tol_solution
(default 1e3), andtol_work
(default 1e7).The
dof_and_residue
correction termination test tests the L2norm residuum againsttol_residuum
and the L2norm of the solution changes w.r.t. the previous Newton iteration againsttol_solution
. The following tolerances are used:tol_residuum
(default 1e3) andtol_solution
(default 1e3).The
normalised_dof_and_residue
correction termination test divides the L2norm residuum by that of the first Newton iteration. The same is done for the L2norm of the solution changes w.r.t. the previous Newton iteration. The following tolerances are used:tol_residuum
(default 1e3) andtol_solution
(default 1e3). gradients
istep

Controls the computation of the gradients (strains, stresses, heat transfer, etc.) for the current case. If
istep
is set to 0 (default) no gradients are computed and saved, i.e. only dof solutions will be found on the database. Ifistep
is set to 1, the gradients for the last converged step of at stage or the linear solution step are computed and saved. Ifistep
is set to a positive value, the gradients will be computed at eachistep
step of at stage as well as for the last step of a stage. gradients_only yesno

Specifies whether only gradients (and reaction forces) should be computed, while the solution vector is defined solely by the the initial conditions, and the boundary conditions and the current load increment. Default is
no
. increment_control_type loadstatehyperplanehyperellipticlocal_hyperelliptic

Specifies the increment constraint strategy to use. The increment constraint strategy serves two purposes: It defines the increment constraint for the predictor phase and the corrector phase, and it computes the predictor solution from the solution of the last converged step. This predictor solution is then used as initial solution to the correction phase.
The following strategies are available:
load
means loadcontrolled. To avoid singularities at limit points in postbuckling analysis,residue_function_type artificial_damping
can be used.A statecontrolled strategy is used with
state
.The other strategies are of the continuation type. For the
hyperelliptic
andlocal_hyperelliptic
strategies, the parametershyperelliptic_a
andhyperelliptic_b
define the size of the ellipse.The default strategy is
load
.For more details on the kinds of constraints, refer to Section 6.2.
init_step_number
v

The initial step cycle number. Default is 1.
line_search yesno

Specifies whether line search should be used for the
accelerated_newton
method (see the MDL commandcorrection_type
). The line search method satisfies the strong Wolfe condition. When the cost of calculating the first variation is significantly lower than the cost of calculating the second variation, it is recommended to have line search enabled, as it improves the probability that the Newton iterations converge. Default isyes
. max_divergences
v

Defines the maximum number of consecutive divergences during the correction phase of a load step. Default is 4. When this number is reached, the correction phase is terminated unsuccessfully, and the step increment is restarted with a reduced step size.
max_newton_iterations
v

Specifies the maximum number of Newton iterations per increment. Default is 50.
max_steps
v

Maximum number of steps (increments) per stage. Default is 99999.
newton_method conventionalmodifieddelayed_modified

Specifies what kind of Newton method should be used. Default is
conventional
.The
conventional
method performs factorization for the predictor and for each Newton iteration, and thus is a full Newton method.For the modified
method, factorization of the tangent matrix is performed when the correction phase has terminated unsuccessfully. Hence, several increments may be performed without any factorization.The
delayed_modified
method performs a factorization for the predictor and for the first Newton iteration.Note that the
artificial_damping
option for the MDL command residue_function_type enforces factorization each time the step size changes. For themodified
anddelayed_modified
Newton methods, is is recommended to use thecorrection_type accelerated_newton
option. newton_periodic_update
v

For the modified and delayed modified, nonaccelerated Newton methods, this option specifies the maximum number of consecutive iterations without refactorization. When this number is reached, a refactorization will be performed, and the counter is reset. Note that for high values of
newton_periodic_update
and depending on thenewton_method
setting, several increments may be performed until this number of Newton iterations is reached. Default is 100. residue_function_type defaultartificial_dampingscaled

Specifies the type of residuum (first variation or internal forces vector) and its derivative (second variation or tangent matrix).
The
default
type computes the first and second variation without any modifications.In a loadcontrolled postbuckling analysis involving collapse, the
artificial_damping
type is necessary for the Newton iterations to converge. It adds viscous forces to the residuum vector (first variation). The velocities are computed from the difference of the solution to the last converged solution, divided by the step size. To the tangent matrix (second variation), the viscosity matrix divided by the step size is added. With artificial damping, singularity of the tangent stiffness matrix at limit points can be avoided and energy can be dissipated during mode jumps. See also Section 4.The
scaled
type scales the DOFs by their respective diagonal element in the tangent matrix. This may be beneficial in continuation analysis (e.g.increment_control_type local_hyperelliptic
). Due to the scaling, it is recommended to use the default correction termination test. step_size_init
v

The step size at the beginning of the stage. Default is 0.1.
step_size_max
v

The maximum step size during the stage. Default is 1.0. In continuation analysis, this is the size along the load path.
step_size_min
v

The minimum step size during the stage. Default is 1e12. In continuation analysis, this is the size along the load path.
step_size_lambda_max
v

The maximum lambda step size during the stage in a continuation method analysis. Default is 1.0.
step_size_lambda_min
v

The minimum lambda step size during the stage in a continuation method analysis. Default is 1e12.
step_size_dof_max
v

The maximum degrees of freedoms step size during the stage in a continuation method analysis. Default is 1.0.
step_size_dof_min
v

The minimum degrees of freedoms step size during the stage in a continuation method analysis. Default is 1e12.
tol_residuum
v

The error tolerance value for the residuum ('equilibrium') error; used by the Newton correction termination test. The default depends on the
correction_termination_test
option. tol_solution
v

The error tolerance value for the dof ('solution') error; used by the Newton correction termination test. The default value on the
correction_termination_test
option. tol_work
v

The error tolerance value for the work error; used by some Newton correction termination test. The default depends on the
correction_termination_test
option.