A microstructure-dependent piezoelectric beam model was developed using a variational formulation, which is based on the modified strain gradient theory and the Timoshenko beam theory. The new model contains three material length scale parameters and can capture the size effect, unlike the classical beam theory. To illustrate the new piezoelectric beam model, the static bending and the free vibration problems of a simply supported beam are numerically solved. These results may be useful in the analysis and design of smart structures that are constructed from piezoelectric materials.

A 3-D numerical model, based on the Navier-Strokes equations and the RNG k-ε turbulence closure, for studying hydrodynamic drag on a swimmer with wave-making resistance taken into account is established. The volume of fluid method is employed to capture the undulation of the free surface. The simulation strategy is evaluated by comparison of the computed results with experimental data. The computed results are in good agreement with data from mannequin towing experiments. The effects of the swimmer's head position and gliding depth on the drag force at different velocities are then investigated. It is found that keeping the head aligned with the body is the optimal posture in streamlined gliding. Also wave-making resistance is significant within 0.3 m depth from the free surface.

Marine geological disasters, such as seabed liquefactions, submarine landslides, debris flows and turbidity currents, are all closely related to the accumulation of wave-induced excess pore pressure in the seabed. Due to the limitations of physical model experiment and in-situ observations, numerical analysis has become an important method to explore the microscopic mechanism of the accumulation of excess pore pressure. Based on the discrete element porous density flow method, we simulated the changing process of excess pore pressure in seabed sediment in this study, comparing with laboratory flume experiment. The simulation results reproduce the changing process of excess pore pressure in the laboratory flume experiment. The excess pore pressure occurs in the surface of seabed and gradually transfers to the deep layer, tending to a stable value. Thus, the discrete element porous density flow method is well suitable for simulating the accumulation of wave-induced excess pore pressure. Furthermore, the method constitutes a promising tool to study the microscopic mechanism of seabed liquefaction.