1 / 18

Material Point Method Grid Equations

Explore the use of equations and mass matrices in the analysis of an elastic bar dropping due to gravity. Understand the principles of grid methods and variational forms in particle discretization on Monday, 10/7/2002. Delve into the concept of lumped mass matrices and their role in modeling accelerations and forces. Learn about the compactness of grid mass matrices and the differentiation between mass matrices and lumped mass matrices in bar dropping scenarios.

rpolly
Download Presentation

Material Point Method Grid Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related