A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.

A substructure approach is used to estimate the stiffness and damping coefficients of structures from measurement of dynamic responses. The structures are decomposed into smaller subsystems for which state and observation equations are formulated and solved by the method of extended Kalman filter with a weighted global iteration algorithm. Substructural identification methods with and without overlapping members are proposed. In both methods, the convergence of the structural parameters to the optimal values is improved significantly with less computation time as compared to a complete structural approach. Numerical simulation studies are performed for three types of structures, namely a shear building, a plane frame building and a plane truss bridge. The effects of measurement noise and response observations required for identification of system parameters are also investigated.

SUMMARYA new Lagrangian particle method called the consistent particle method (CPM), which solves the NavierStokes equations in a semi-implicit time stepping scheme, is proposed in this paper. Instead of using kernel function as in some particle methods, partial differential operators are approximated in a way consistent with Taylor series expansion. A boundary particle recognition method is applied to help define the changing liquid domain. The incompressibility condition of free surface particles is enforced by an adjustment scheme. With these improvements, the CPM is shown to be robust and accurate in long time simulation of free surface flow particularly for smooth pressure solution. Two types of free surface flow problems are presented to verify the CPM, that is, two-dimensional dam break and liquid sloshing in a rectangular tank. In the dam break example, the CPM solutions of pressure and wave elevation are in good agreement with published experimental results. In addition, an experimental study of water sloshing in tank on a shake table was conducted to verify the CPM solutions.

The concept of fractional derivatives is employed in the formulation of a stress-strain relationship for elastomers. An oscillator consisting of a mass and a 'fractional' Kelvin element is used to model elastomeric bearings used in base isolation systems. Efficient numerical multi-step schemes are developed for the dynamic analysis of a single-degree-offreedom 'fractional oscillator' in the time domain. Numerical examples show that these multi-step schemes are in good agreement with the Laplace and Fourier solutions. When applied to shaking table tests of a base-isolated bridge deck, the fractional derivative model is found to agree well with the experimental results. *Lecturer. +Professor of Civil Engineering.

SUMMARYThis paper presents a new approach, called the moving element method, for the dynamic analysis of train-track systems. By discretizing the rail beam on viscoelastic foundation into elements that ' ow' with the moving vehicle, the proposed method eliminates the need for keeping track of the vehicle position with respect to the track model. The governing equations are formulated in a co-ordinate system travelling at a constant velocity, and a class of conceptual elements (as opposed to physical elements) are derived for the rail beams. In the numerical study, four cases of moving vehicle are presented taking into consideration the e ects of moving load and rail corrugation. The method is shown to work for varying vehicle velocity and multiple contact points, and has several advantages over the ÿnite element method. The numerical solutions compare favourably with the results obtained by alternative methods.

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