Jae Woo Jeong, Miami University, Hamilton Ohio |

Isogeometric analysis of plates with cracks |

ABSTRACT: The mapping techniques for isogeometric analysis, introduced by Jeong et al. (2013), is an effective method for dealing with crack singularities of elliptic boundary value problems. In some sense, the mapping techniques is similar to the Method of Auxiliary Mapping(MAM), introduced by Babuska and Oh (1990), for conventional Finite Element Methods(FEM). However, unlike MAM, the mapping techniques make it possible to independently control the radial and angular direction of the function to be approximated as far as the point singularities are concerned.The vertical displacement of a thin plate is governed by a fourth order elliptic equation and thus the approximation functions for numerical solutions are required to have continuous partial derivatives. Hence, the conventional FEM has difficulties to solve the fourth order problems. In order to deal a plate problem with crack effectively, the approximation functions must be smooth except at the crack tip and have singularity at the crack. In this talk, I will discuss recent results and ongoing works on isogeometric analysis, including a way to construct such approximation functions. |

# Wednesday, Aug 21 at 11:00am in the conference room

Categories: Fall 2013