Reference : Meshfree methods for shear-deformable structures based on mixed weak forms |

Scientific congresses, symposiums and conference proceedings : Unpublished conference | |||

Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Multidisciplinary, general & others | |||

Computational Sciences | |||

http://hdl.handle.net/10993/17084 | |||

Meshfree methods for shear-deformable structures based on mixed weak forms | |

English | |

Hale, Jack [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit > ; Imperial College London > Department of Aeronautics] | |

24-Jul-2014 | |

Yes | |

Yes | |

International | |

PhD Olympiad at the 11th. World Congress on Computational Mechanics | |

20-07-2013 to 25-07-2013 | |

Barcelona | |

Spain | |

[en] meshfree ; mixed forms ; shear-deformable ; beams ; plates | |

[en] Similarly to the finite element method, meshfree methods must be carefully designed to overcome the shear-locking problem when discretising the shear-deformable structural theories.
Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed variational form, where the shear stress is treated as an independent variational quantity in addition to the usual displacements. Because of its sound mathematical underpinnings this is the methodology I have chosen to solve the shear-locking problem when using meshfree basis functions. In this talk I will discuss the mathematical origins of the shear-locking problem and the applicability of the celebrated LBB stability condition for designing well-behaved mixed meshfree approximation schemes. I will show results from two new formulations that demonstrate the effectiveness of this approach. The first method is a meshfree formulation for the Timoshenko beam problem that converges to a classic inf-sup stable finite element method when using Maximum- Entropy basis functions. The second method is a generalised displacement meshfree method for the Reissner- Mindlin problem where the shear stress is eliminated prior to the solution of the linear system using a local patch-projection technique, resulting in a linear system expressed in terms of the original displacement unknowns only. Stability is ensured by using a stabilised weak form which is necessary due to the loss of kernel coercivity for the Reissner-Mindlin problem. | |

Imperial College London | |

EPSRC | |

Researchers | |

http://hdl.handle.net/10993/17084 | |

http://orbilu.uni.lu/handle/10993/12057 |

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