Recalc > Dynamics/Iterations

Dynamics

Definition of the relevant parameters for dynamic calculations. Reasonable default values are defined for all parameters, except damping parameters which must essentially be defined by the user (otherwise damping is zero).

Setting	Description
g	Gravity constant (acceleration of gravity) in internal database units (independent from the selected unit system always in m/s2). The constant is used for computing the actual mass values from defined equivalent forces. Default: g = 9.81m/s2
dt	Time step length for the dynamic time history calculation (schedule action Tint). Default: dt = 0.01 sec Tip: For required time step length, the Newmark method is a numerically unconditionally stable integrations method. However, in order to avoid numerical damping of vibrations with higher frequency, the highest considered vibration period shall be divided into at least 10 time steps. I.e. the default value of 0.01 sec allows for sufficiently accurate consideration of vibration frequencies of up to 10 Hz (period 0.1 sec).
c1	Integration constant 'Delta' for NEWMARK time integration (see relevant textbooks) Default: C1 = 0.5 = standard value (best approximation)
c2	Constant 'Alpha' for NEWMARK time integration (see relevant textbooks) Default: c2 = 0.25 = standard value (best approximation) Note: c1 and c2 shall in general not be modified by the user
Alfa	Mass coefficient for calculating the damping matrix [C] = Alfa[M] + Beta[K] Default: Alfa = 0 = no mass dependent damping
Beta	Stiffness coefficient for calculating the damping matrix [C] = Alfa[M] + Beta[K] Default: Beta = 0 = no stiffness dependent damping Note: The effective damping percentage of Rayleigh damping is dependent on the frequency. Design codes and guidelines usually define damping as damping ratio in %of the critical damping and Rayleigh coefficients are usually not known. Therefore, they commonly recalculated from damping ratios given for 2 relevant frequencies. RmBridge offers a respective subfunction when pressing the arrow button on the right. (see Subfunction > Rayleigh coefficients )
Xsi	Global damping ratio (actual to critical) for the modal superposition. The value is for instance used for calculating the correlation coefficients of the CQC superposition, if no other value is defined for the respective earthquake event (absolute value, not in percent!). Default:Xsi = 0.0
Tol(mi/ki)	Mass tolerance for calculation of natural modes (schedule action Eigen). Small, irrelevant masses are eliminated in order to make the subspace iteration stable and reliable. For each DOF the ratio of the diagonal terms of the mass and stiffness matrices is checked against the defined tolerance value (mii/kii .lt. Tol). The respective DOF will be eliminated from the subspace if the condition is true. Default: Tol = 1.E-8

Iteration control

Definition of the convergence parameters for non-linear iterative structural deformation analysis. The default values ensure in general a fast and sure convergence to an extremely accurate solution. Variation of the values is recommended only in special cases where convergence problems arise.

Setting

Description

RELAX

The relaxation factor in the Newton Raphson iteration.

Default: 0.7

Note: By increasing the factor up to 1.0 it is sometimes possible to decrease the number of required iteration steps, however, this can also lead to oscillation behavior and possibly illegal intermediate states during iteration.

NITER

Maximum number of iterations in the Newton Raphson process to achieve convergence. The iteration is stopped irrespective of the achieved error (disequilibrium) values.

Default: 40

TOL-1

Tolerance for disequilibrium of internal and external forces (root of sum of squares) (DF2)

Default: 0.005

Note: High accuracy is achieved by using this extremely small value. In case of convergence problems this value should be increased to a reasonable value.

TOL-2

Tolerance for disequilibrium of forces (maximum of absolute values) (DFMAX)

Default: 0.005

TOL-3

Tolerance for correction values of displacements (square root of sum of square values) (DU2, not printed in the iteration protocol)

Default: 0.000005 (5E-6)

Note: High accuracy is achieved by using this extremely small value. In case of convergence problems this value should be increased to a reasonable value.

TOL-4

Tolerance for correction value of displacements (maximum of absolute values) (DUMAX)

Default: 0.000015 (15E-6)

Convergence protocol

The convergence progress during the iteration process of the non-linear calculation of a load case is shown in the Log-file. The presented values are:

Setting	Description
Step	Iteration step - step 1 is the initial linear solution
DF2 %:	Integral disequilibrium (square root of sum of squares) related to the respective integral of the load vector in percent (at begin of the iteration step).
DF2:	Integral disequilibrium compared with the value TOL-1.
DFMAX:	Maximum disequilibrium compared with the value TOL-2.
U:	Maximum value of total deformations at begin of the respective iteration step
DUMAX:	Maximum value of differential deformations of the previous iteration step compared with tolerance value TOL-4.

Cross Section Integration

Definition of governing parameters for calculation functions on cross-section level. The default values are set such that a stable and quick solution is provided in general. In critical situations the values can be adapted to achieve an improvement of the calculation procedure to get the required solution.

Setting	Description
Iteration	Max. number of iterations determination of position and angles of the neutral axes. Used for calculating cross-section values in in the ultimate capacity check (UltChk).
Recurs.level	Maximum number of recursions. Only used in reinforcement design (UltChk/Rein). The increasing factor is further reduced if no equilibrium is found.
Increasing factor	Used in the ultmate capacity check (UltChk). The program first calculates the strain plane for a partial load and increases the load in steps. The position of the neutral axis of the previous step is the iteration start for the next step. Default: 0.25
Relax.factor	Only used in reinforcement design (UltChk/Rein). Theoretically required increments of reinforcement area are in the iteration process reduced by this factor. Default: 0.2
Tolerance	Calculation toleranz related to the norm N(F) of force vector F [abs(N(Fi)-N(F))/N(F)] Default: 1e-6
Check-button: Try with best reinforcement	Optimization function - Additional variation of distribution of the total reinforcement to different reinforcement groups to get minimum total amount Default: No
Check-button: Try to reduce small values	The program checks, whether omitting reinforcement groups with small area is possible by a reasonable increase of the amount of other groups. Default: Yes
Eigen Solver	There are two options available: Skyline and Parallel Sparse (INTEL). The new Parallel Sparse solver improves the calculation speed for dynamic analysis in bigger models.
Modal Analysis	There are two options available: Eigen and Ritz. The load dependent Ritz vector analysis provides faster extraction of more relevant modes for response spectra modal superposition analysis.