EQUILIBRIUM

An EQUILIBRIUM command redefines and/or lists the data for an EQUILIBRIUM statement. If an EQUILIBRIUM statement is not included in the Adams Solver model and an EQUILIBRIUM command is not issued before a static or quasi-static simulation, Adams Solver (C++) uses the default values for ALIMIT, ERROR, IMBALANCE, MAXIT, PATTERN, STABILITY, and TLIMIT for the analysis.

Format

 

Arguments

 
ALIMIT=r
Specifies the maximum angular increment allowed per iteration during a static or quasi-static equilibrium analysis. The default units for ALIMIT are radians. To specify ALIMIT in degrees, add a D after the value.
Range: ALIMIT > 0
DEFAULT
Resets all options to the default values specified in the EQUILIBRIUM statement, namely:
ALIMIT = 10D
ERROR = 1.0E-4
IMBALANCE = 1.0E-4
MAXIT = 25
PATTERN = T:T:T:T:T:T:T:T:T:T
STABILITY = 1.0E-5
TLIMIT = 20
ERROR=r
Specifies the relative correction convergence-threshold. The iterative process carried out during the equilibrium analysis can not converge prior to all relevant relative corrections being smaller than this value.
Range: ERROR > 0
IMBALANCE=r
Specifies the equation imbalance convergence threshold. The iterative process carried out during the equilibrium analysis can not converge prior to each equation imbalance being smaller than this value.

Range: IMBALANCE > 0
LIST
Lists the current values of the data in the EQUILIBRIUM statment.
MAXIT=i
Specifies the maximum number of iterations allowed for finding static equilibrium.
Range: MAXIT > 0
PATTERN=c1[:...:c10]
Specifies as many as ten character strings that together establish the pattern for evaluating the Jacobian matrix during the modified Newton-Raphson iteration. For each iteration, T or TRUE indicates that Adams Solver (C++) evaluates the Jacobian and F or FALSE indicates that Adams Solver (C++) does not evaluate the Jacobian. Thus, cj determines whether or not Adams Solver (C++) evaluates the Jacobian at the jth iteration. If necessary, Adams Solver (C++) repeats the pattern of evaluations until it reaches the maximum number of iterations (MAXIT). The number of Ts or TRUEs and Fs or FALSEs together must be at least one and no more than ten.
STABILITY=r
Specifies the fraction of the mass and damping matrices (subsets of the
equilibrium Jacobian matrix) Adams Solver (C++) adds to the stiffness matrix (a subset of the equilibrium Jacobian matrix) during static simulations performed using static analyses. Adding a fraction of the mass and damping matrices to the stiffness matrix can stabilize the iteration process and prevent the iteration from diverging. Often the stiffness matrix is singular for a system because the system is neutrally stable (for example, the system moves in certain directions without affecting the potential energy). Adding a fraction of the mass and damping matrices to the stiffness matrix removes this singularity and makes it possible to solve for equilibrium positions. The value of STABILITY does not affect the accuracy of the solution, but it does affect the rate of convergence of the iteration process.>

Range: STABILITY >0
TLIMIT=r
Specifies the maximum translational increment allowed per iteration.
Range: TLIMIT > 0
METHOD=i
Specifies the option which determines the static solver method to be used for equilibrium solution.
1. ORIGINAL, for running only the ORIGINAL Solver
2. ADVANCED, runs, in order, the following methods until one shows progress:
a. ORIGINAL
b. ORIGINAL+Krylov
c. ORIGINAL+UMF
d. Newton+Krylov
e. Tensor-Krylov block-3
f. Tensor-Krylov block-2+
3. AGGRESSIVE, runs, in order, the following methods until one shows progress:
a. ORIGINAL
b. ORIGINAL+Krylov
c. ORIGINAL+UMF
d. Newton+Krylov
e. Tensor-Krylov block-3
f. Tensor-Krylov block-2+
g. Broyden-Armijo
h. Trust-Region
4. ALL, runs, in order, all the available methods, until one shows progress:
a. ORIGINAL
b. ORIGINAL+Krylov
c. ORIGINAL+UMF
d. Newton+Krylov
e. Tensor-Krylov block-3
f. Tensor-Krylov block-2+
g. Broyden-Armijo
h. Trust-Region
i. Hooke-Jeeves
Default: ORIGINAL
ATOL
Specifies the absolute tolerance value
Default: 1.0e-6
Range: 0.0 < ATOL < 1.0
RTOL
Specifies the relative tolerance value
For all solvers, except ORIGINAL and ORIGINAL+Krylov, the tolerance is defined as : TOL=ATOL+||xIC||*RTOL.
For ORIGINAL and ORIGINAL+Krylov solvers the tolerance is equal to ERROR.
Default: 0.0
Range: 0.0 < RTOL < 1.0
MAXITL
Specifies the maximum number of allowed inner loops in all the solvers. ORIGINAL, ORIGINAL+Krylov and ORIGINAL+UMF solver methods ignore this parameter. For Hooke-Jeeves method, allowed budget of function evaluations is set to MAXITL*N, where N is the size of the problem (number of unknowns).
Default: 40
Range: > 0
ETAMAX
Specifies the maximum threshold for the error tolerance of the linear Krylov solver (for Newton+Krylov and Tensor-Krylov methods) that solves the linear systems required by Krylov algorithm. Maximum error tolerance for residual in inner iteration. The inner iteration terminates when the relative linear residual is smaller than eta*| F(x_c) |. eta is determined by the modified Eisenstat-Walker formula if etamax > 0. If etamax < 0, then eta = |etamax| for the entire iteration.
Default: 0.9
Range: 0.0 < ETAMAX < 1.0
ETA
Specifies the initial residual tolerance for the linear Krylov Solver for Tensor-Krylov method. The Tensor-Krylov ETA parameter is maintained adaptively by the Krylov algorithm but ETA is the indicated starting value, while ETAMAX is the maximum threshold for ETA.
Default: 1.0e-4
Range: 0.0 < ETA < 1.0
Specifies the dimensionless radius of the trust-region for Trust-region method. The smaller the value, the more the refinement of Trust-region solution (hence more work).
Range: 0.0 < ETA < 0.25

Extended Definition

For an extended definition on the EQUILIBRIUM command and corresponding tips, cautions, and examples, refer to the EQUILIBRIUM statement.
See other Analysis parameters available.