Keywords: space-time finite element, transfer plate, dynamic analysis.

Finite element methods have been widely used to solve time-dependent problems for transfer structures. Most procedures have been based upon semi-discretisations; i.e. the spatial domain is discretised using finite elements, producing a system of ordinary differential equations in time which in turn is discretised using finite difference methods. These procedures have been particularly successful in solving structural dynamics analysis for plates, frames and trusses.

However, one disadvantage of the semi-discrete approaches is the difficulty in designing algorithms that accurately capture discontinuities or sharp gradients in the solution. Another disadvantage of semi-discrete methods is the difficulty of employing adaptive mesh techniques. Since, for semi-discrete methods, the spatial domain is discretised first and then the temporal discretisation is used for the resultant set of ordinary differential equations, the corresponding space-time discretisation is structured. The space-time discretisation arising from the semi-discrete approach consists of rectangular sub-domains of the space-time domain. By contrast, space-time finite element methods, in which the spatial and temporal domain are simultaneously discretised, accommodate unstructured meshes in the space-time domain. This mesh may be considered to arise from an adaptive mesh refinement strategy in which both spatial and temporal refinement can occur to accurately capture the stress waves, stress concentrations, etc. In regions where the solution is smooth, the mesh is relatively coarse, while a finer mesh is employed near the stress wave fronts. Thus, an accurate solution may be obtained without resorting to a uniformly refined (and computationally expensive) mesh.

In this paper, a new space-time finite element formulation for dynamic analysis of transfer plates is presented [1]. The method is based on an unconventional Hamilton variational principle. The stability and convergence of this formulation are demonstrated. The results of the proposed method are compared with the results of the methods Newmark-beta and Wilson-theta. The results show that the proposed space-time finite element method exhibits the improved accuracy and precision in the dynamic analysis.

1

H. Zhang, "Finite element modelling of transfer plates in tall buildings", PhD thesis of the Hong Kong University of Science and Technology, 2004.

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