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Material Point Method (MPM)

Material Point Method (MPM). Variational principle Particle discretization Grid interpolation. Wednesday, 10/2/2002. Lennard-Jones Potential. Handout: Molecular dynamics of simple systems Error, page 7. force. potential. Motion equations. Tensor expression:. Engineering expression:.

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Material Point Method (MPM)

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  1. Material Point Method (MPM) Variational principle Particle discretization Grid interpolation Wednesday, 10/2/2002

  2. Lennard-Jones Potential Handout: Molecular dynamics of simple systems Error, page 7 force potential

  3. Motion equations Tensor expression: Engineering expression:

  4. Discretization in Material Point Method (MPM) Solid line is an outline of the body analyzed. Black dots are the material points. Dashed lines show a regular, background grid for calculation.

  5. Motion equations (Variational form) : arbitrary spatial function

  6. Elastic Bar Dropping Acceleration due to gravity

  7. Particle Discretization?How to solve?

  8. Direct solution Solution:

  9. Variational Form : arbitrary spatial function

  10. Particle Discretization?

  11. Variational Equation Considering free ends at a and b

  12. Particle Discretization

  13. Spatial grid

  14. Shape function

  15. Grid Interpolation

  16. Grid Equation Since is arbitrary:

  17. Grid Equation (F=ma) External force Internal force Mass matrix

  18. Derivative of Shape Function

  19. Summary Variational principle Particle discretization Grid interpolation Next class: MPM procedure

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