Margin Check Analysis in StressCheck

The Margin Check is a nonlinear analysis capability (material or general nonlinear) with failure criteria control. To solve a Margin Check analysis a linear problem must be solved first. A nonlinear material stress-strain law must be specified if a material nonlinear analysis is involved.

After the linear problem is solved, the nonlinear analysis is performed for the original load until convergence is achieved. The load is then incremented according to the specified step and the nonlinear solution is obtained for the new load. At the end of each load step the program checks if any of the predefined failure/margin criteria, each based on a formulaic margin of safety, was exceeded. A report is issued summarizing the load at which each criterion was exceeded, and a solution is kept for further post-processing.

In the following, we refer to PlateHole.scw (found in the Tutorial Handbook folder) to demonstrate the Margin Check solver.

Defining Margin of Safety (MS) Formulae

In order to define failure/margin criteria, one or more formulaic margin of safety (MS) expressions comprised of standard engineering functions must be specified in the Formulae dialog. These MS expressions are typically in the form of 1 – Ratio such that a negative value represents failure.

The following are typical MS expressions used to compute failure/margin criteria, and are included in PlateHole.scw (Figure 2):

Defining Failure/Margin Criteria

The failure/margin criteria are predefined extraction procedures based on extraction functions (typically MS expressions). These extraction procedures can be defined in the Points or Min/Max tabs of the Results dialog.

For example, to define the margin criteria specified by MS2 in PlateHole.scw, go to the Results dialog and select the Points tab. Then, supply the following information:

• Points tab > Select > Any Boundary > Selection > Solution: NSOL (for Margin Check any name in this field will be ignored) > Run: 8 to 8 (same for this field) > Func: Fmla > # of pts: 30 > Average switch on > Formula: MS2 > Settings Name: Displ (this is the name that will appears in the scroll window of the Margin Check tab in the Solve dialog).
• With the mouse cursor select the line where the load is applied and then click on the Save button of the Settings pane.

Note that “Displ” already exists in PlateHole.scw within the Points tab’s Settings pane drop-down list (Figure 3), as well as another margin criteria “Ligament”.

Margin Check Solver Options

For PlateHole.scw, select the “1_Linear” solution setting from the Settings pane drop-down in the Solve dialog and click Solve. After the linear analysis is complete, check the quality of the linear solution. The estimated relative error in energy norm should be small, typically below 5%, before proceeding with the rest of the analysis.

Next, select the Margin Check tab from the Solve dialog. Proceed as follows to execute the Margin Check solution for PlateHole.scw:

• Click on the linear solution (Linear Sol) which is to be the starting solution for the Margin Check analysis. The linear solution name, run number, type of analysis, and associated degrees of freedom (DOF) appear in the scroll window of the dialog box.
• Select the Type of nonlinear analysis, the choices are General and Material Nonlinear. For this problem, select Material. For a small-strain, small-displacement, elastic-plastic analysis, the option Material should be used.
• Select Convergence. The choices are Stress or Energy. Refer to the Nonlinear Analysis Overview for additional details about convergence options. Select Stress for this problem, as the stresses are expected to be smooth and continuous in the model domain.
• Define the Tolerance. Since Stress was selected as the Convergence option, we will set the tolerance to one percent.
• Enter the Iteration Limit, that is the number of iteration cycles you wish StressCheck to perform automatically for each load step. StressCheck will continue until the Iteration Limit is reached, unless the specified error tolerance is reached first. For this problem set the Iteration Limit to 50.
• Set the Load parameter. From the Param. pull down menu select the parameter S that defines the load; its Initial value will be provided automatically. Specify the maximum load (Limit) and the load Step. For this problem we chose Sult (24000 psi) to be the maximum and we want the load to be increased in equal increments of DelS (100 psi) from the minimum to the maximum. Note that the name of a parameter was entered in the input field for the Step and Limit.
• Select the Margin Criteria. The small scroll window in the Solve dialog shows the different margin criteria extraction options available. The selection is made by left clicking on the records while holding down the Shift key. When several margin criteria are selected, the “Stop at 1st M.S. failure” toggle switch can be used. Figure 4 shows the settings for this problem. In this case, three margin criteria are selected. This implies that after each load step, the values of MS1, MS2 and MS3 should remain positive in order to proceed with the next load increment. Once the first margin criterion is exceeded, the program will continue because the toggle “Stop at 1st M.S. failure” is off.
• Change Execute to Initialize and then click the Solve button (“Yes” to the dialog).

Once the Margin Check analysis is complete, the Solve dialog Status Window will display the MarginCheck Status and a Margin Check summary will be displayed once complete (Figure 5):

Figure 5 shows the values of the applied traction for which the margin criteria is exceeded. The Margin Check summary is displayed in a report window once the analysis is completed. A record is also kept in the Project Log, that can be retrieved at any time by selecting View > Project Log. It follows that the traction should not exceed 22300 psi if no margin criterion should be exceeded.

After the Margin Check analysis is completed, several solution records are available for post-processing depending on the results of the analysis. A solution record with the name _LAST_NL (last nonlinear run) is always available, even if no margin criteria were exceeded after the load increments. In addition, for each exceeded margin there will be a solution record composed of the name of the margin criterion followed by a number representing the load step at which the margin was exceeded.

For example, for the margin criterion Disp, the solution record is DISP_25, since it took 25 load steps to exceed this margin. The Figure 6 shows the von Mises stress distribution corresponding to LIGAMENT_24:

The ‘Ligament’ criterion was exceeded for load step #24 while the ‘Disp’ criterion was exceeded at load step #25. For that reason the difference in the stresses distribution between the two cases is almost negligible. The ‘Max_Eeq’ criterion was exceeded for load step #31 and the stress distribution corresponding to this load (23000 psi) can be differentiated from the other two cases.

For an example of setting up and executing a Margin Check analysis, refer to StressCheck Demo: 2D Margin Check Analysis.