Finite element modelling of transfer plates in tall buildings.

摘要

In this thesis, a systematic study is presented for the development of a new flat shell element that is tailored to the analysis of transfer plates that connecting to frame structures and shear walls/core walls. To develop this flat shell element, an eight-node arbitrary quadrilateral membrane element with drilling degrees of freedom is first derived. The reason of introducing drilling degrees to both corner and mid nodes of the element is to achieve the mesh with a more reasonable element aspect ratio. Moreover, incorporating drilling degrees to the mid nodes of the element will lead to the finite element formulation that includes higher-order shape functions, which is needed when modelling the complex in-plane structural behaviour of the transfer plates.; A new Reissner-Mindlin plate element is then developed, in which the boundary segment interpolation using Timoshenko's beam function is employed for derivation. This analytical interpolation can ensure that the high accuracy and efficiency of modelling the bending stiffness of a transfer plate are obtained when using the proposed Reissner-Mindlin plate element. Moreover, an independent shear strain approximation is used in deriving the proposed element; thus the problem of shear locking can effectively be removed.; By integrating the proposed arbitrary quadrilateral membrane element with drilling degrees and the new Reissner-Mindlin plate element, the development of an eight-node flat shell element with six degrees of freedom at each node is presented. The procedure of integration and derivation for the proposed flat shell element is based on the fact that for a flat shell the in-plane displacements prescribed for the in-plane forces will have no effect on the out-of-plane displacements prescribed for the out-of-plane forces, and vice versa. This eight-node flat shell element is developed and tailored to the analysis of transfer plates that are connected to frame structures and shear walls/core walls in tall buildings.; The study of the thesis is further extended from the static analysis of transfer plates to cover the dynamic analysis of plate structures using a new space-time finite element. This space-time finite element is developed based on the proposed unconventional Hamilton's variational principle and is derived using the new Reissner-Mindlin plate element for spatial domain discretization. It has been shown that the proposed space-time finite element can provide an unconditionally stable, higher-order and accurate algorithm for the dynamic analysis of plate structures. (Abstract shortened by UMI.)