1. Truss Structure Workshop Five Convergence Criteria REFERENCE: Training Manual Obtaining the Solution (3-51)

2. Workshop Supplement October 15, 2001 Inventory #001566 W5-2 5.Convergence Criteria Truss Structure Purpose Demonstrate the importance of nonlinear convergence criteria settings Goal Compare results of a nonlinear analysis solved with both default and user-specified convergence criteria Model Description 2D truss configuration Multi-linear stress-strain curve cross-sectional area = 1.0 in. 2 truss length = 100 inches E = 50,000 PSI 1020 lbs. 60 degrees

3. Workshop Supplement October 15, 2001 Inventory #001566 W5-3 5.Convergence Criteria …Truss Structure STEPS TO FOLLOW: 1.Start an ANSYS Interactive session in the working directory specified by the instructor using “truss” as the jobname 2.Resume the TRUSS database –Utility Menu > File > Resume from Select “truss.db1” [OK] –OR enter the following command: RESUME, truss, db1 NOTE: The truss.db1 database contains the completed geometry, material, boundary condition, and loading definitions for this finite element model.

4. Workshop Supplement October 15, 2001 Inventory #001566 W5-4 5.Convergence Criteria …Truss Structure 3.Solve the nonlinear plasticity analysis (with default convergence controls) –Main Menu > Solution > Current LS [OK] –OR enter the following commands: /SOLUTION /STATUS, SOLUTION SOLVE NOTE: The current convergence controls are set to use defaults.

5. Workshop Supplement October 15, 2001 Inventory #001566 W5-5 5.Convergence Criteria …Truss Structure 4.Plot the vertical displacement –Main Menu > General Postproc > Plot Results > Nodal Solu DOF solution UY [OK] –OR enter the following commands: /POST1 PLNSOL, U, Y Note the maximum displacement for this analysis: DMX = 4.1 inches 5.Review the contents of the monitor file (truss.mntr)

6. Workshop Supplement October 15, 2001 Inventory #001566 W5-6 5.Convergence Criteria …Truss Structure 6.Tighten the force convergence criteria –Main Menu > Solution > Sol’n Control Select tab: “Nonlinear” Set convergence criteria … Replace … Structural Force F TOLER Tolerance about VALUE = 0.0001 NORM Convergence norm = L2 norm MINREF Minimum reference value = 1.0 [OK] [Close] [OK] –OR enter the following commands: /SOLUTION CNVTOL, F,, 0.0001,, 1.0 NOTE: See additional GUI menu windows on the next page.

7. Workshop Supplement October 15, 2001 Inventory #001566 W5-7 5.Convergence Criteria …Truss Structure

8. Workshop Supplement October 15, 2001 Inventory #001566 W5-8 5.Convergence Criteria …Truss Structure 7.Solve the nonlinear plasticity analysis (with user-specified convergence controls) –Main Menu > Solution > Current LS [OK] –OR enter the following commands: /STATUS, SOLUTION SOLVE NOTE: The current convergence controls are set to the user-specified values.

9. Workshop Supplement October 15, 2001 Inventory #001566 W5-9 5.Convergence Criteria …Truss Structure 8.Plot the vertical displacement –Main Menu > General Postproc > Plot Results > Nodal Solu DOF solution UY [OK] –OR enter the following commands: /POST1 PLNSOL, U, Y Note the maximum displacement for this analysis: DMX = 6.09 inches 9.Review the contents of the monitor file (truss.mntr)

10. Workshop Supplement October 15, 2001 Inventory #001566 W5-10 10.Why didn’t the default convergence criteria provide acceptable accuracy? The input stress-strain curve includes three data points and hence three slope segments. The first segment slope is equal to the input elastic modulus. The second slope decreases slightly and is equal to 80% of the elastic modulus. The third slope decreases significantly and is equal to only 0.4% of the elastic modulus. For this model, the stress in each truss is equal to 1020 psi. Equilibrium iteration #2 spans the second data point on the stress-strain curve (see graph on next page). After equilibrium iteration #2, the default convergence criteria is satisfied at a stress level of 1018.01 psi. Because the slope is very small on this part of the curve (segment #3), the converged solution did not capture the additional plastic strain between 1018 psi and 1020 psi. This small 2 psi difference in stress translates to a large increase in plastic strain of about 1%. For the truss length of 100 inches, this 1% increase in strain equals about 1 inch increase in length. Because there are two truss members, the total increase in length is about 2 inches. (6.09 - 4.1) 5.Convergence Criteria …Truss Structure

11. Workshop Supplement October 15, 2001 Inventory #001566 W5-11 5.Convergence Criteria …Truss Structure DATA POINT # 1 DATA POINT # 2 DATA POINT # 3 DATA POINT # 1 DATA POINT # 2 DEFAULT CRITERION ITER #2 ITER #1 INPUT STRESS-STRAIN CURVE NEWTON-RAPHSON ITERATIONS APPLIED STRESS CONVERGED SOLUTION