Stability of caisson-type breakwater subjected to strong hydrodynamic impacts using discontinuous deformation analysis method

A numerical study using the Discontinuous Deformation Analysis (DDA) method is proposed to analyze the effect of the caisson sliding subjected to a hydrodynamic loading in the stability of the rear side of the caisson-type breakwater. The study takes into account the slope inclination of the breakwater as well as the contact between the armour units constituting the shoreward of the breakwater, where the contact stresses are imposed through a penalty method. A dimensionless displacement parameter, [Formula: see text], is defined to investigate the instability of armor units. The results of the simulation show that the shape of the armour units plays an important role in the stability of the breakwater, where the tetrapods and the acropods give better stability than the cubic shapes, with a clear superiority of the tetrapods. They also show that the reduction in the slope clearly contributes to the stability of caisson up to a slope of 1: 2, but below this ratio of 1: 2 this stability is no longer obvious. Furthermore, a new relation of the displacement of the armour units according to the slope is established.

Scaling of Thermal Positioning in Microscale and Nanoscale Bridge Structures

Heat transfer in a thermally positioned doubly clamped bridge is simulated to obtain a universal scaling for the behavior of microscale and nanoscale bridge structures over a range of dimensions, materials, ambient heat transfer conditions, and heat loads. The simulations use both free molecular and continuum models to define the heat transfer coefficient, h. Two systems are compared: one doubly clamped beam with a length of 100 μm, a width of 10 μm, and a thickness of 3 μm, and a second beam with a length of 10 μm, a width of 1 μm, and a thickness of 300 nm, in the air at a pressure from 0.01 Pa to 2 MPa. The simulations are performed for three materials: crystalline silicon, silicon carbide, and chemical vapor deposition (CVD) diamond. The numerical results show that the displacement and the response of thermally positioned nanoscale devices are strongly influenced by ambient cooling. The displacement depends on the material properties, the geometry of the beam, and the heat transfer coefficient. These results can be collapsed into a single dimensionless center displacement, δ* = δk/q″αl2, which depends on the Biot number and the system geometry. The center displacement of the system increases significantly as the bridge length increases, while these variations are negligible when the bridge width and thickness change. In the free molecular model, the center displacement varies significantly with the pressure at high Biot numbers, while it does not depend on cooling gas pressure in the continuum case. The significant variation of center displacement starts at Biot number of 0.1, which occurs at gas pressure of 27 kPa in nanoscale. As the Biot number increases, the dimensionless displacement decreases. The continuum-level effects are scaled with the statistical mechanics effects. Comparison of the dimensionless displacement with the thermal vibration in the system shows that CVD diamond systems may have displacements that are at the level of the thermal noise, while silicon carbide systems will have a higher displacement ratios.

The Dynamic Response of a Rotating Thick Piezoelectric Plate with Thermal Relaxations

Based on the generalized thermoelastic theory postulated by Green and Lindsay(G-L), the dynamic response of an infinite rotating piezoelectric plate subject to thermal shocks on both up and bottom surfaces was investigated. To avoid the calculation precision loss caused by the integral transform technique, the so-called direct finite element method was used to solve the governing equations in time domain directly. The distributions of the dimensionless temperature, stress, displacement and electric potential were presented graphically. The results show that the direct finite element method provides an effective way for achieving high calculation precision in solving the generalized piezoelectric-thermoelastic problem. The results also show that the rotation effect tends to decrease the dimensionless displacement and electric potential and barely affects the dimensionless temperature and stress.