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**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**Finite Element Study of Structural Discontinuities, 2003**Computation Time**Finite Element Study of Structural Discontinuities, 2003**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**Peterson’s Stress Concentration Factors, 1997 • Model 1 Finite Element Study of Structural Discontinuities, 2003**Previous Work**• Model 1 (continued) Finite Element Study of Structural Discontinuities, 2003**Previous Work**Peterson’s Stress Concentration Factors, 1997 • Model 2 Finite Element Study of Structural Discontinuities, 2003**Previous Work**• Model 2 (continued) Finite Element Study of Structural Discontinuities, 2003**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**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 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