Advanced Finite Element Analysis

Advanced Finite Element Analysis

Fertig Research Group: Multiscale Failure of Materials via YouTube Direct link

2-4: Nonlinear Finite Elements in 1-D (Total Lagrangian vs. Updated Lagrangian)

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2-4: Nonlinear Finite Elements in 1-D (Total Lagrangian vs. Updated Lagrangian)

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Classroom Contents

Advanced Finite Element Analysis

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  1. 1 Linear Elastic Finite Element Analysis (Overview)
  2. 2 1-1: Linear Elastic Finite Element Analysis (Weak Form of Governing Differential Equation)
  3. 3 1-2: Linear Elastic Finite Element Analysis (Galerkin Method)
  4. 4 1-3: Linear Finite Element Analysis (Interpolation Functions)
  5. 5 1-4a: Linear Finite Element Analysis (Matrix Equations of Motion - Part I)
  6. 6 1-4b: Linear Finite Element Analysis (Matrix Equations of Motion - Part II)
  7. 7 1-5a: Linear Finite Element Analysis (Mapping Integrals - Part I)
  8. 8 1-5b: Linear Finite Element Analysis (Mapping Integrals - Part II)
  9. 9 1-6: Linear Finite Element Analysis (Assembly of Global Stiffness Equations)
  10. 10 1-7: Linear Finite Element Analysis (Applying Boundary Conditions)
  11. 11 1-8: Linear Finite Element Analysis (Computing Stresses and Strains)
  12. 12 2-0: Nonlinear Finite Elements in 1-D (Overview)
  13. 13 2-1: Nonlinear Finite Elements in 1-D (Newton's Method in 1-D)
  14. 14 2-2: Nonlinear Finite Elements in 1-D (Newton's Method for Systems of Equations)
  15. 15 2-3: Nonlinear Finite Elements in 1-D (Lagrangian vs. Eulerian Meshes)
  16. 16 2-4: Nonlinear Finite Elements in 1-D (Total Lagrangian vs. Updated Lagrangian)
  17. 17 2-5a: Nonlinear Finite Elements in 1-D (Total Lagrangian Formulation - Problem Setup)
  18. 18 2-5b: Nonlinear Finite Elements in 1-D (Total Lagrangian Formulation - Conservation Equations)
  19. 19 2-5c: Nonlinear Finite Elements in 1-D (Total Lagrangian Formulation - Constitutive Law)
  20. 20 2-5d: Nonlinear Finite Elements in 1-D (Total Lagrangian Formulation - Boundary & Initial Cond.)
  21. 21 2-5e: Nonlinear Finite Elements in 1-D (Total Lagrangian Formulation - Weak Form)
  22. 22 2-5f: Nonlinear Finite Elements in 1-D (Total Lagrangian Formulation - FE Discretization)
  23. 23 2-6: Nonlinear Finite Elements in 1-D (Element and Global Vectors and Matrices)
  24. 24 2-7: Nonlinear Finite Elements in 1-D (Solution Methods - Explicit Central Difference)
  25. 25 2-8a: Nonlinear Finite Elements in 1-D (Updated Lagrangian - Governing Equations)
  26. 26 2-8b: Nonlinear Finite Elements in 1-D (Updated Lagrangian - Weak Form and FE Discretization)
  27. 27 2-8c: Nonlinear Finite Elements in 1-D (Updated Lagrangian - Mesh Distortion)
  28. 28 1-2a: Continuum Kinematics (Reference Frames and Deformation)
  29. 29 1-2b: Continuum Kinematics (Lagrange Finite Strain Tensor)
  30. 30 1-2c: Continuum Kinematics (Meaning of the Lagrange Finite Strain Tensor)
  31. 31 1-2d: Continuum Kinematics (Displacement-Based Strain Formulation)
  32. 32 3-1e: Nonlinear Finite Elements in 3-D (Continuum Kinematics - Rate of Deformation/Velocity Strain)
  33. 33 Continuum Stresses (Cauchy Stress Formula)
  34. 34 3-1g: Nonlinear Finite Elements in 3-D (Continuum Stresses - Stress Measures)
  35. 35 3-1h: Nonlinear Finite Elements in 3-D (Continuum Stresses - Example)
  36. 36 3-2: Nonlinear Finite Elements in 3-D (Total Lagrangian Formulation)
  37. 37 3-3: Nonlinear Finite Elements in 3-D (Updated Lagrangian Formulation)
  38. 38 4-1: Dynamic Finite Element Analysis (Natural Frequencies and Mode Shapes)
  39. 39 4-2: Dynamic FEA (Newmark-beta Implicit Integration)
  40. 40 4-3: Dynamic FEA (Damping)
  41. 41 4-4: Dynamic FEA (Mode Superposition - Modal Analysis)
  42. 42 Variational Methods (Functionals and Extremization)
  43. 43 Variational Methods (Fundamental Lemma of Variational Calculus)
  44. 44 Variational Methods (Example - Shortest Path)
  45. 45 Variational Methods (Example - Surface of Revolution)
  46. 46 Variational Methods (First Integrals of the Euler-Lagrange Equation)
  47. 47 Variational Methods (Delta Operator)
  48. 48 Variational Methods (Natural Boundary Conditions)
  49. 49 Variational Methods (Functionals with Higher Order Derivatives)
  50. 50 Variational Methods (Functionals with Multiple Dependent Variables)
  51. 51 Variational Methods (Functionals with Multiple Independent Variables)
  52. 52 Variational Methods (Principle of Stationary Total Potential Energy)
  53. 53 Variational Methods (Potential Energy of an Elastic Body)
  54. 54 Variational Methods (Rayleigh-Ritz Method)
  55. 55 Variational Methods (Ritz Method and Finite Element Analysis)

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