The Ansys trace display in "Reprint" Nonlinear Analysis

Original address: http://muchong.com/html/201209/4936556.html

When Ansys output Windows has the force Convergenge valu value and the criterion value, when the current person is less than the latter, the convergence is complete.
Nonlinear computation is a process of iterative computation in which the curve represents the error between two iterations, in which the error between each iteration of the force and displacement in the iterative process is shown.
The meanings of the two lines are:
F L2:2 norm of unbalance force
F Crit: The convergence tolerance of the unbalance force,
If the former is greater than the latter, the description does not converge and continues to be calculated.
U is displacement.
Of course, if the bending moment M is the convergence criterion, then it corresponds to M L2 and M crit.
The two lines in the figure, the purple is the residual force, namely ({F}-{FNR}), the blue is the convergence criterion, when the residuals are below the criterion, the solution converges.
It is not recommended to use the displacement convergence criterion because the displacement convergence criterion is a relative quantity.

Nonlinear convergence criterion of Ansys
Cnvtol, Lab, VALUE, Toler, NORM, Minref
In Ansys, the nonlinear convergence criterion is mainly strong convergence, the convergence of the displacements, the convergence of the moment and the convergence of the corner. In general, when loading with force, the 2-norm of residual force can be used to control the convergence, while displacement control is best controlled by the norm of displacement.
When Solcontrol,on, Toler Defaults to 0.005 (0.5%) for force and moment, and 0.05 (5) for displacement when rotational do Fs is not present.
When Solcontrol,off, defaults-0.001 (0.1%) for force and moment.
The convergence accuracy can be relaxed to 5% to improve the convergence speed.
Accelerate ConvergenceThere are several ways to do this:
1 can increase the number of load steps, Nsubst,nsbstp,nsbmn,carry
2 Modifying the convergence criteria, cnvtol,lab,value,toler,norm,minref
3 Open the Optimized nonlinear default solution setting and some hardening of the internal solution algorithm, Solcontrol,key1,key2,key3,vtol (typically, by default, is turned on)
4 re-dividing the grid, the grid cells should not be too large or too small, generally in the 5~10 cm or so
5 checking the correctness of the model
understanding of convergence criteria (cnvtol) in Ansys
Based on the default convergence criteria in Ansys, the program compares the values of the unbalanced force SRSs with the Value*toler value, while the default value of value is to take a larger value in SRSs and Minref.
The following command flow:
　　 cnvtol,f,5000,0.0005,0
cnvtol,u,10,0.001,2
If the Unbalance force (independent checking of each degree of freedom) is less than or equal to 5000*0.0005 (that is, 2.5), and if the displacement change is less than or equal to 10*0.001, the sub-step is considered convergent.

The convergence criterion in Ansys, the program's default force and displacement control, and the convergence control coefficient seems to be 0.001. Such convergence accuracy is generally difficult to make the plasticity analysis convergence, for the general plasticity analysis convergence problem, the first several load steps (elastic phase) force and displacement joint control, into the plastic after the force control or displacement control, can also be forced after the use of displacement control (displacement control is easier to converge), as to the control coefficient to take, Zoom in and out as necessary until you converge! It is also suggested that the final use of energy to control convergence,
Convergence value is convergent, convergence norm is the convergence criterion. Ansys can be used cnvtol commands, such as: cnvtol,f,10000,0.00001,2, where F refers to the use of force results, 10000 is the absolute value of convergence, 0.00001 is the convergence coefficient, 2 is the convergence 2 norm.
Convergence criteria should refer to the selection of the results of convergence judgment, there are usually three options, namely Force (f), Displacement (U), and energy. Of course, these three forms can be used alone or in conjunction with each other. Another layer of convergence criteria should be what norm form (1, 2, 3 norm) is chosen. Typically, a 2-norm format is selected for general structures.
The convergence value is only part of the convergence criterion, such as the product of the convergence absolute value and the convergence coefficient in the cnvtol command should be the convergent values (convergence value) you mean.
Ansys uses convergence criterion to have l1,l2,l~~ (infinity) three convergence criteria.
In the project, the general use of the Convergence tolerance (0.05) can be pulled.
It is suggested to use the displacement convergence criterion (cnvtol,u,0.05,,,) and the Force Convergence criterion (cnvtol,f,0.05,,,). Because only one convergence criterion is used, there is a large error.
If you can only use a convergence criterion, it is recommended that you increase the convergence tolerance (below 0.01).

Ansys calculates the nonlinearity by drawing a convergence graph, where the horizontal axis is the cumulative iteration number ordinate is absolute convergence norm. They are cumulative iterations and absolute convergence norms, which are used to determine whether nonlinear analysis is convergent.
Ansys calculates the nonlinear convergence criterion and calculates the residual error in the iteration of each load step. The residual error is the norm of the internal force of all units, and only when the residuals are less than the criterion, the nonlinear iteration is convergent. The displacement convergence of Ansys is based on the convergence of force, which provides the absolute value of convergence for the force-based convergence, while the displacement-based convergence provides only a relative measure of the convergence of the performance. Generally do not use the displacement convergence criterion alone, otherwise there will be a certain deviation, some cases will causefalse Convergence. (Ansys non-linear analysis guide-basic process page.6). Therefore, ANSYS officials recommend that users try to force-based (or torque) convergence errors, and if necessary, can also increase the displacement-based convergence check. The ANSYS default is to control convergence with the L2 norm. Other L1 and L0 norms can be set using the Cnvtol command. In the calculation, the L2 value is constantly changing, if the L2<crit is determined to be convergent. Also known as the L2 norm of the unbalanced force is less than the set criterion when the convergence is judged. Because the ANSYS default criterion calculation is the square and open Square (SRSS) *valuse of all your variables (the value you set), Crition also has a small change. If necessary, you can also specify Crition as a constant, cnvtol,f,10000,0.0001,0 the convergence control value of the specified force is 10000*0.0001=1. In addition, a switch used in nonlinear calculations isSolcontrol
If the Solcontrol option is turned off, then the software default convergence criterion: The convergence tolerance of the force or moment is 0.001, regardless of the convergence tolerance of the displacements; if the Solcontrol option is turned on, the same default convergence criterion: The convergence tolerance of the force or moment is 0.005, and the displacement convergence tolerance is 0.05.
The nonlinear convergence is very troublesome, which is related to a series of factors, such as mesh precision, boundary condition, load step and so on, the characteristics of the unit have great influence on the convergence, and the property of the unit is difficult to converge; reasonable step length can make the solution not oscillation around the true solution, the step is too small, the calculation is too large, will cause non-convergence due to excessive load steps. Grid density is appropriate to facilitate convergence, too dense grid calculation is too large, of course, too sparse calculation results will have a greater error. How many times do you often have to try to solve the problem.
If you do not converge, consider ways to improve
1. Loosen the nonlinear convergence criterion.
(Cnvtol #Sets convergence values for nonlinear analyses).
2. Increase the number of load steps.
(Nsubst #Specifies The number of substeps to being taken this load step)
3. Increase the number of iterations per calculation (the default 25 times)
(neqit #Maximum number of equilibrium iterations allowed each substep)
4 re-dividing the unit try to get different answers later.

Ansys Newton-Raphson method uses the following equation to iterate over aConvergent Solution:
[KT] {deta U} = {F}-{FNR}
Gradually Schhoga the load in incremental form.
Balance iterations are completed in each load increment to achieve a balanced incremental solution.
Solving the equilibrium equation [kt]{deta u} = {F}-{FNR}
[Kt]= Tangent stiffness matrix
{deta U} = bit wasted increment
{F} = external load vector
{FNR} = internal Force vector
Iteration until {F}-{FNR} is within the allowable error range. The program repeatedly solves this equation (two-part load increment) until the residuals (unbalance force), {F}-{FNR}, are small to acceptable degrees.
For this residual, the maximum acceptable value is called the Force convergence criterion.
Mathematically expressed as:
if: | | {r}| | < (ER*RREF)
Then: Solve the convergence.
In the formula
|| {r}| | is the vector norm of the residuals (the norm is the operator that converts a vector to a single scalar value).
L1 residuals norm: | | {r}| | 1 = sigma| ri| Accumulator
L2 (SRSS) residuals norm: | | {r}| | 2 = sqrt (Sigma (Ri*ri))
Residual norm limit: | | {r}| | = Max (| ri|)
(ER Rref) is the Force convergence criterion
ER is the tolerance coefficient, Rref is the reference force value
Rref can be the norm of all forces and forces exerted, | | {f}| |
For most engineering applications, the default convergence criterion works well:
|| {r}| | 2 < (0.5% * | | {f}| | 2)
For special cases, you can change this criterion.
You can tighten or loosen the convergence criteria.
The tighter the guideline, the better the accuracy, but the more difficult it is to converge.
You can also select other items to check for convergence.
Can force, torque, displacement and rotation criteria.
In addition, you can change the norm used to measure convergence.
L1, L2, or limit norm.

2.jpg

"Reprint" The Ansys trace display in nonlinear analysis