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Introduction to Meshfree Method

Introduction to Meshfree Method. Speaker ： Yu-Ling Chen Date ： 2013/06/13. National Taiwan Ocean University Department of Systems Engineering & Naval Architecture. Moving Least-squares Approximation(MLS). x. a. a. x=s.

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Introduction to Meshfree Method

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  1. Introduction to Meshfree Method Speaker：Yu-Ling Chen Date：2013/06/13 National Taiwan Ocean University Department of Systems Engineering & Naval Architecture

  2. Moving Least-squares Approximation(MLS) x a a x=s Discrete Element Method(DEM) first employed MLS in the construction of “meshfree” discrete eq. Consider 1-D domain

  3. Discrete Reprod (RK) Approximation

  4. Exact Reproduction of basis function

  5. Use the Reproducing Kernel Approximation to approximate the following functions • (1) • (2)

  6. RK shape function-discrete point=11 support size=2

  7. RK shape function-discrete point=21 support size=2

  8. RK shape function-discrete point=31 support size=2

  9. RK shape function-discrete point=11 support size=2.001

  10. RK shape function-discrete point=21 support size=2.001

  11. RK shape function-discrete point=31 support size=2.01

  12. RK shape function-discrete point=11 support size=3.001

  13. RK shape function-discrete point=21 support size=4

  14. RK shape function-discrete point=31 support size=4

  15. RK shape function-discrete point=11 support size=2

  16. RK shape function-discrete point=21 support size=2

  17. RK shape function-discrete point=31 support size=2

  18. RK shape function-discrete point=11 support size=2.001

  19. RK shape function-discrete point=21 support size=2.001

  20. RK shape function-discrete point=31 support size=2.001

  21. RK shape function-discrete point=11 support size=3.001

  22. RK shape function-discrete point=21 support size=3.001

  23. RK shape function-discrete point=31 support size=3.001

  24. References 結論: 由以上圖表得知support size在1,2階時，設定為大於等於2就可以貼近解析解。但在第3階時，support size為2時反而離散，如果大於2時就可以貼近解析解。因此由以上得知階數越高並不代表精度可以更高。

  25. Thanks for your listening!

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