Finite Element Study of Structural Discontinuities Project Advisor: Ioannis Korkolis
Finite Element Study of Structural Discontinuities Presented By: Ike Lee and Nick Lin Project Advisor: Ioannis Korkolis Presentation Objectives Discuss background of structural discontinuities Introduce the finite element method Explain how to generate a finite element model Review previous work Present new work Discuss possibilities for future work Answer questions What is a Structural Discontinuity? A break or gap within a structural component that alters its behavior under load Examples of Structural Discontinuities Holes: Often used to lighten an aerospace structure or to rivet components together Cracks: Usually a result of material imperfections or areas of high stress Concerns Uniform loading of a square plate results in a uniform stress distribution Concerns Holes alter the stress distribution and induce stress concentrations. Study of Mesh Refinement EM 360 Fall 2002 Concerns Stress concentrations at crack tips Crack propagation Possible Consequences Stress fields around discontinuities can interact with each other and cause failure. Cessna 402C Mishap Investigation, 1999 Solution Method Structural discontinuity problems are often very difficult to solve analytically, sometimes impossible. Our method is to use ABAQUS, a finite element program. The Finite Element Method (FEM) General technique for constructing approximate solutions to boundary value problems Study of Mesh Refinement EM 360 Fall 2002 How to Generate a Finite Element Model An input file must be written containing the following two parts: Model Data: This portion defines the geometry of the model and material properties. History Data: This portion defines how the model will be loaded and what values should be outputted. Some Important Factors to Consider Boundary Conditions Load Type and Directions Mesh Refinement Study of Mesh Refinement EM 360, Fall 2002 Some Important Factors to Consider : Mesh Refinement Peterson’s Stress Concentration Factors, 1997 11 Elements 1 Second K=4.342 s max K= ____ s Finite Element Study of Structural Discontinuities, 2003 Some Important Factors to Consider : Mesh Refinement 67 Elements 1 second K=4.41 Finite Element Study of Structural Discontinuities, 2003 Some Important Factors to Consider : Mesh Refinement 211 Elements 1 second K=4.47 Finite Element Study of Structural Discontinuities, 2003 Some Important Factors to Consider : Mesh Refinement 823 Elements 2 seconds K=4.512 Finite Element Study of Structural Discontinuities, 2003 Some Important Factors to Consider : Mesh Refinement Approx. 3000 Elements 4 seconds K=4.517 Finite Element Study of Structural Discontinuities, 2003 Some Important Factors to Consider : Mesh Refinement Approx. 19000 Elements 21 seconds K=4.520 Finite Element Study of Structural Discontinuities, 2003 Mesh Convergence Curve 4.54 4.52 4.5 4.48 4.46 Ktg 4.44 4.42 4.4 4.38 4.36 4.34 4.32 0 2000 4000 6000 8000 10000 12000 14000 16000 Number of Elements Mesh Convergence Finite Element Study of Structural Discontinuities, 2003 18000 20000 Computation Time 25 Computation Time (sec) 20 15 10 5 0 0 2000 4000 6000 8000 10000 12000 14000 16000 Number of Elements Effect of Number of Elements on Compuation Time Finite Element Study of Structural Discontinuities, 2003 18000 20000 Mesh Convergence Refining a coarse finite element mesh will result in a more accurate solution at the cost of computation time. Caveat and Approach Just because a solution is obtained does not necessarily mean it is correct. Therefore, it is important to study the results and compare your solution with a known, correct solution. Previous Work Model 1 Peterson’s Stress Concentration Factors, 1997 Finite Element Study of Structural Discontinuities, 2003 Previous Work Model 1 (continued) 5 4.5 4 Ktg = smax /s 3.5 3 Ktg 2.5 2 1.5 ABAQUS 1 Peterson 0.5 0 0 0.1 0.2 0.3 0.4 0.5 d/H Stress Concentration Factor (Model 1) Finite Element Study of Structural Discontinuities, 2003 0.6 Previous Work Model 2 Peterson’s Stress Concentration Factors, 1997 Finite Element Study of Structural Discontinuities, 2003 Previous Work Model 2 (continued) 3.5 3 Ktg = smax /s1 2.5 2 Ktg 1.5 1 ABAQUS 0.5 Peterson 0 0 0.1 0.2 0.3 0.4 0.5 d/l Stress Concentration Factor (Model 3) Finite Element Study of Structural Discontinuities, 2003 0.6 0.7 New Work Reduction of stress concentrations from edges of holes Finite element modeling of cracks Reduction of crack stress intensity factor Reducing Stress Concentrations from Holes Method: Add another hole to alleviate the stress concentration. Constant: Radius of original hole = 2 in Tensile Load = 1 psi in horizontal direction Variables: R = radius of added hole L = distance between centers of holes Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes Conclusion: Adding holes in a plane perpendicular to the loading direction does not reduce the stress concentration factor. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003 Reducing Stress Concentrations from Holes 3.1 2.9 2.7 SCF 2.5 2.3 2.1 1.9 1.7 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 R (in) Variation of Stress Concentration Factor with Second Hole Radius (L = 4 in) Finite Element Study of Structural Discontinuities, 2003 2 Reducing Stress Concentrations from Holes 3.2 3 SCF 2.8 2.6 2.4 2.2 2 0 0.5 1 1.5 2 R (in) Variation of Stress Concentration Factor with Second Hole Radius (L = 5 in) Finite Element Study of Structural Discontinuities, 2003 2.5 Reducing Stress Concentrations from Holes 2.9 2.7 SFC 2.5 2.3 2.1 1.9 1.7 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 R (in) Variation of Stress Concentration Factor with Second Hole Radius (L = 7.50 in) Finite Element Study of Structural Discontinuities, 2003 2 Reducing Stress Concentrations from Holes 2.6 Optimal SFC 2.55 2.5 2.45 2.4 2.35 0 1 2 3 4 5 6 L (in) Effect of Hole Spacing on Stress Concentration Factor Finite Element Study of Structural Discontinuities, 2003 7 8 Reducing Stress Concentrations from Holes Conclusion: Adding holes in a plane parallel to the loading direction does reduce the stress concentration factor. Finite Element Analysis of Cracks Crack configuration models: Tada The Stress Analysis of Cracks Handbook Model 1 Model 2 Model 3 Finite Element Analysis of Cracks Crack Model 1 (Center Cracked Plate) Finite Element Analysis of Cracks Crack Model 2 (Edge Cracked Plate) Finite Element Analysis of Cracks Crack Model 3 Finite Element Analysis of Cracks Tada, The Stress Analysis of Cracks Handbook Crack Model 3 Finite Element Analysis of Crack Repair Crack repair models: Finite Element Study of Structural Discontinuities, 2003 Finite Element Analysis of Cracks Center Cracked Plate with Stop Holes Finite Element Analysis of Cracks Center Cracked Plate with an Array of Holes Near the Crack Tip Finite Element Analysis of Cracks Patch Repair of Center Cracked Plate Finite Element Analysis of Cracks Arrester Repair of Center Cracked Plate Finite Element Analysis of Cracks 2.9 2.8 2.7 K (psi-in 0.5 ) 2.6 2.5 2.4 2.3 2.2 2.1 2 0 1 2 3 4 5 6 L (in) Variation in Stress Intensity Factor with Arrester Strip Distance 7 Summary of Work Completed This Semester Used the FEM to determine how holes and cracks affect stress distributions. Devised a method to alleviate stress concentrations around holes. Investigated crack repair methods. Possibilities for Future Work Finite element modeling of structural discontinuities under cyclic loading Finite element modeling of structural discontinuities in more complex structures Adaptation of scripting feature in ABAQUS Questions?
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