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Material Point Method Grid Equations

Material Point Method Grid Equations. Mass matrix Lumped mass matrix. Monday, 10/7/2002. Elastic Bar Dropping. Acceleration due to gravity. Variational Form.  : arbitrary spatial function. Particle Discretization?. Grid Equations of Motion. External force. Internal force. Mass matrix.

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Material Point Method Grid Equations

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  1. Material Point MethodGrid Equations Mass matrix Lumped mass matrix Monday, 10/7/2002

  2. Elastic Bar Dropping Acceleration due to gravity

  3. Variational Form : arbitrary spatial function

  4. Particle Discretization?

  5. Grid Equations of Motion External force Internal force Mass matrix Shape function between node n and particle p:

  6. Shape Functions (1D)

  7. Elastic Bar Dropping (coordinates) Particles: Nodes:

  8. Elastic Bar Dropping (particle mass) Mass density: Cross section area:

  9. Elastic Bar Dropping (mass matrix) Mass matrix

  10. Elastic Bar Dropping (grid mass) Mass matrix

  11. Grid mass (1,1)

  12. Grid mass (1,2)

  13. Grid mass (2,1)

  14. Grid mass (2,2)

  15. Grid equations

  16. Mass matrix Compact mass matrix: Only matrix elements close to diagonal are not zero.

  17. Lumped Mass Matrix Lumped grid mass :

  18. Mass matrix vs. lumped mass matrix

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