A Timoshenko beam finite element suitable for vehicle-track vibration analysis is proposed and is applied to a jointed railway track. In several simulation models, the track vibration excited by a train running on the rail is formulated as a dynamic problem where a sequence of concentrated loads moves on the discretely supported Timoshenko beam. The external force is then defined by the concentrated load. The Timoshenko beam subjected to concentrated loads deforms with the slope discontinuity at the loading points. This deformation cannot be represented by the usual finite elements, which causes the fictitious responses of the beam. The present finite element model removes the undesirable response by completely modelling the slope discontinuity. This is achieved by the TIM7 element with the piecewise-linear hat functions. The jointed track model constructed by this finite element is employed to predict the impulsive wheel-track contact force excited by the wheel passage on rail joints. The rail joints with fishplates are of great concern to track deterioration, the settlement of ballast track and the failure of track components. In the present paper the effects of train speed and gap size of the joints on the impact force are assessed from simulation results.

SUMMARYA boundary element method is developed for the topology optimization problem. The topological change is captured using the level set method. The level set function which is defined by signed distance from the boundary contour is assigned to fixed grid points. Boundary elements are developed along the zero contour of the level set function. The design sensitivity analysis is performed for the boundary element equation, and then the boundary velocity is obtained. The velocity field which leads the level set function to optimal material distribution is obtained by the extension of the boundary velocity. Numerical examples show that the proposed method is valid for the topology optimization problems.

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SUMMARYA practical strategy is developed to determine the optimal threshold parameter for wavelet-based boundary element (BE) analysis. The optimal parameter is determined so that the amount of storage (and computational work) is minimized without reducing the accuracy of the BE solution. In the present study, the Beylkin-type truncation scheme is used in the matrix assembly. To avoid unnecessary integration concerning the truncated entries of a coe cient matrix, a priori estimation of the matrix entries is introduced and thus the truncated entries are determined twice: before and after matrix assembly. The optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors. These errors are estimated in the residual sense. For Laplace problems the discretization error is, in particular, indicated with the potential's contribution c to the residual norm R used in error estimation for mesh adaptation. Since the normalized residual norm c = u (u: the potential components of BE solution) cannot be computed without main BE analysis, the discretization error is estimated by the approximate expression constructed through subsidiary BE calculation with smaller degree of freedom (DOF). The matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with O(N 1+ ) (06 ¡1) non-zero entries. Although the quasi-optimal memory requirements and complexity are not attained, the compression rate of a few per cent can be achieved for N ∼ 1000.

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