1. Frame with Cutout Random Load Fatigue

2. Background and Motivation A thin frame with a cutout has been identified as the critical component in a structure that is subjected to a random load. Although the stress is not very high, a concern arises that the frame will fail due to fatigue. The influence of the external load is measured on the frame with help of three strain gauges. The analysis simulates how the random load history affects the structure and examines the risk of fatigue. COMSOL Multiphysics can in one analysis model the structural response to a random load cycle and evaluate the results using fatigue models. Based on superposition very long or random load histories can be evaluated.

3. Frame with Cutout Module – Fatigue Module – Structural Mechanics Module Physics Interface – Shell – Fatigue Structural analysis Stress Fatigue

4. Modeling Steps Create geometry Prescribe boundary conditions Define local coordinate system Define material Mesh Compute response to generalized unit loads Convert strains to generalized load histories Define fatigue parameters Calculate fatigue results on both sides of the shell Evaluate results

5. Model Setup Geometry – Shell Material – Linear-elastic Boundary – Prescribed Displacement – Load applied using Rigid Connector Fatigue Evaluation – Cumulative Damage Rainflow Counting Palmgren-Miner – Generalized Loads

6. External Load Three strain gauges register response to an external load The frame is expected to experience 10000 such cycles Two strain gauges are rotated 45° relatively the global coordinate system

7. Local Coordinate System Define local coordinate system Assign the same material to all domains Assign different coordinate systems to different parts of the frame Local system rotated 45°

8. Mesh Highest stresses are experienced on the cutout rounding Capture stress gradient with sufficiently fine mesh

9. Generalized Loads The purpose of generalized loads it to describe the influence of an external load with help of few basic load cases. This assumes that the dynamic and nonlinear effects can be ignored, so that the external load can be prescribed using superposition This technique is suitable for evaluation of random and long load events

10. Generalized Unit Loads Define the external load using two bending moments and one twisting moment Use load groups to discriminate between the generalized loads

11. Evaluation of Generalized Unit Loads Calculate the response to each generalized load Extract relation between generalized loads and strains using the derived values feature

12. Time History of Generalized Loads Based on the relation between strains and applied loads, convert the strain output into generalized load history

13. Load History Prescribe all time histories in one function node

14. Palmgren-Miner Fatigue limit is prescribed through S-N curve R-value dependence is taken into account Use fatigue data for iron alloy 4340 from the material library Convert the maximum fatigue stress, given in the model library, to stress amplitude, used in the fatigue evaluation

15. S-N Curve R-value Stress amplitude Number of cycles for each R-value Define S-N curve with an interpolation function with Grid data format

16. Superposition Connect the response of generalized unit loads with corresponding time histories Verify that the function order for the generalized load histories is the same as the load case order of the generalized unit loads

17. Shell Evaluation The structural response of shells varies through its thickness A fatigue study processes shell data evaluated at height z Evaluate fatigue on both sides of the shell Two fatigue evaluations

18. Results The default line plot displays results along arc length Define fatigue usage factor along the rounding as a function of the angle Use Boolean operators to discriminate between arcs in the evaluated expression The variable ”dom” is the edge number

19. Fatigue Usage Factor Shell top sideShell bottom side

20. Stress Distribution 37% of the damage caused by a half cycle Cumulative Damage is evaluated in the most critical point

21. Matrix Histogram Matrix histogram is a dedicated plot type for visualization of stress and fatigue damage distribution It displays data in the most critical point A 3D graph can be created with the height expression option

22. Conclusions The analysis predicts a low fatigue usage factor. All damage is caused by few load cycles with a high amplitude stress and 37% of damage is caused by one half cycle of a 1000 load event history. Since the entire damage is caused by only few cycles, it is reasonable to assume that at different time an other random load sampling will record a different stress distribution that can predict a damage significantly different from the calculated one. It is therefore recommended to use a high safety factor in this type of analysis.