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An Explicit-Implicit Analysis Scheme in a General-Purpose FEA Environment Abed M. Khaskia

An Explicit-Implicit Analysis Scheme in a General-Purpose FEA Environment Abed M. Khaskia Mallett Technology, Inc. Laurel, Maryland (301) 725-0060. Outline. Introduction System of Equations [Equations of Motion] Explicit Solution Scheme Implicit Scheme Mixed Explicit – Implicit

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An Explicit-Implicit Analysis Scheme in a General-Purpose FEA Environment Abed M. Khaskia

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  1. An Explicit-Implicit Analysis Scheme in a General-Purpose FEA Environment Abed M. Khaskia Mallett Technology, Inc. Laurel, Maryland (301) 725-0060

  2. Outline • Introduction • System of Equations [Equations of Motion] • Explicit Solution Scheme • Implicit Scheme • Mixed Explicit – Implicit • Illustrative Case

  3. Introduction - Applications • Vibration analysis • Impact analysis. Crashworthiness, Drop test • Rotating elements and machinery • Earthquake analysis • Explosives • Metal Forming/stamping/rolling • Random Vibration

  4. Car Crash Projectile Impact Applications

  5. Metal Forming Jet Engine Fan Containment Applications

  6. Pipe Whip Problem Applications

  7. Introduction - Challenges • Large systems • Material and geometrical behavior • Unknown material properties • Loading and system boundary conditions • Multiphysics and multiple domains • Available testing and verifications issues • Changing technologies in numerical analysis

  8. System of Equations • General Equations of Motion • Solutions: • Implicit • Explicit • Mixed dictated by physics and numerical behavior

  9. Resulting Equations Integration Scheme, Example, Newmark Effectively Resulting in Implicit Scheme

  10. Nonlinear Case – Requires Newton-Raphson Iterations and Satisfying Equilibrium Implicit Scheme

  11. No matrix conversion • Computations of internal and external force vectors • Critical Time Step Explicit Scheme

  12. Comparisons/Issues • Stability • Time step size • Nonlinear effects • Computations • Convergence • Mass matrices

  13. Explicit Solution Deformation, Acceleration Velocity, Stress, Strain Deformed Shape, Stresses and Strains Implicit / Static Equilibrium Solution time, Loads, BCs and Final State Element Types, Material Models Equivalency Solution Accuracy Mixed Scheme / Explicit - Implicit • Solution Steps

  14. Explicit Implicit Mixed Scheme / Explicit - Implicit • Solution Process on Material Model

  15. Force is applied at blank holder • Sinusoidal velocity is applied at punch • Mass and stiffness damping • Friction between components • Mass Scaling Explicit to Implicit Case Study – Cup Stamping • System Description and FE Model

  16. Explicit to Implicit Case Study – Cup Stamping • Modeling Challenge • Mass scaling to speed solution • Solution accuracy and verifications • Damping • Friction effects • Element deformation and proper shape • Time point and process to go from explicit to implicit • Preventing Rigid body motion in implicit solution • Convergence of the nonlinear implicit solution

  17. Explicit to Implicit Case Study – Cup Stamping • Results • Animation of process • Quality of solution – Hourglass energy check • Force applied by punch and blank velocity • Fluctuation in stress and strain data • Deformed shape and plastic strains at end of explicit • Spring back shape after implicit switch

  18. Explicit to Implicit Case Study – Cup Stamping • Stamping Process

  19. Explicit to Implicit Case Study – Cup Stamping • Blank Velocity

  20. Explicit to Implicit Case Study – Cup Stamping • Stress and Strains

  21. Deformed shape and plastic strains at end of explicit Explicit to Implicit Case Study – Cup Stamping

  22. Explicit to Implicit Case Study – Cup Stamping • Implicit FE Model

  23. Explicit to Implicit Case Study – Cup Stamping • Spring back shape

  24. Explicit to Implicit Case Study – Cup Stamping Conclusions • Experience shows that explicit/implicit is less than 25% of implicit CPU for same application • Implicit only is easier to validate and hence provides more confidence • Rigid body constraints in implicit part and time location for switch • Mass scaling and speed of process introduce simplifications • Certain aspects of the explicit/implicit process could be automated • Elements selections and compatibilities among them • Data management is important as time scale has two different meanings • The process is very promising for nonlinear applications as solvers will switch automatically between the two schemes based on solution behavior

  25. Acknowledgments/References Certain figures and images are courtesy of ANSYS, Inc. and Livermore Software Technology Corporation.

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