A two-dimensional model for linear elastic thick shells

In this paper, a two-dimensional model for linear elastic thick shells is deduced from the three-dimensional problem of a shell thickness 2ε, ε > 0. From different scalings on the tangent and normal components of the displacement u^ε as widely used in recent works, the limit displacement appears to be Kirchhoff–Love displacement of a different type. It contains additional terms to those found in the Reissner–Mindlin model and satisfies more general equations containing the classical terms found in the literature and some new terms related to the third fundamental form. Such terms could not be well handled in the usual framework. Shear stresses across the thickness are also computed. This model appears to be appropriate to handle stiffened shells which, in fact, cannot be considered uniformly as shallow shells. As a by-product it also lays the mathematical background to justify the Reissner–Mindlin model for plates and will probably contribute to a better understanding of the locking phenomenon encountered in computational mechanics.     

Flattened Brazilian Disc Method for Determining the Dynamic Tensile Stress-Strain Curve of Low Strength Brittle Solids

An indirect tensile testing method is proposed to measure the full dynamic tensile stress-strain curve of low strength brittle solids. In this method, the flattened-Brazilian disc (FBD) sample is loaded by modified split Hopkinson pressure bars (SHPB) system. Low amplitude dynamic forces were measured with a pair of piezoelectric force transducers embedded in the incident bar and the transmitted bar. The evolution of tensile stress at the center of the disc sample was determined through finite element analyses using the measured stress in SHPB as inputs. In a traditional Brazilian test, a strain gauge is mounted at the center of the specimen to measure the tensile strain, which is difficult to apply for low strength brittle materials. Thus, two types of non-contact methods, the Digital Image Correlation (DIC) technique and the Laser Gap Gauge (LGG), were used to measure the strain. The DIC method was used to monitor the displacement and the strain map of the specimen during the test, from which the strain at the center of the specimen can be obtained. The accuracy of the DIC results was assessed, and the displacement and strain uncertainties of our system were 0.003 mm and 0.003, respectively. LGG was used to monitor the expansion of the disc perpendicular to the loading axis, from which the average tensile strain is deduced. The numerical simulation revealed that the tensile strain at the center of the specimen is proportional to the average tensile strain and that the ratio is not sensitive to the material elastic parameters. The strain measured through LGG was compared with that measured by the DIC method using photos captured with a synchronized high-speed camera. The result of the LGG method was 20 % smaller than that of the DIC process. However, the latter was limited by the number of frames of the high-speed camera. The feasibility of this methodology was demonstrated using a polymer-bonded explosive (PBX).     

Simulating the fluid forces and fluid-elastic instabilities of a clamped–clamped cylinder in turbulent axial flow

In this paper, the fluid forces and the dynamics of a flexible clamped–clamped cylinder in turbulent axial flow are computed numerically. In the presented numerical model, there is no need to tune parameters for each specific case or to obtain coefficients from experiments. The results are compared with the dynamics measured in experiments available in the literature. The specific case studied here consists of a silicone cylinder mounted in axial water flow. Computationally it is found that the cylinder loses stability first by buckling. The threshold for buckling is in quantitative agreement with experimental results and weakly nonlinear theory. At higher flow speed a fluttering motion is predicted, in agreement with experimental results. It is also shown that even a small misalignment between the flow and the structure can have a significant impact on the dynamical behavior. To provide insight in the results of these fluid–structure interaction simulations, forces are computed on rigid inclined and curved cylinders, showing the existence of two different flow regimes. Furthermore it is shown that the inlet turbulence state has a non-negligible effect on these forces and thus on the dynamics of the cylinder.     

Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number

The flow-induced vibrations of two elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement are studied numerically at Re=160. A four-step semi-implicit Characteristic-based split (4-SICBS) finite element method is developed under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. For the computational code verification, two benchmark problems are examined in the laminar region: flow-induced vibration of an elastically mounted cylinder having two degrees of freedom and past two stationary ones in tandem arrangement. Regarding the two-cylinder VIVs in shear flow, the computation is conducted with the cylinder reduced mass M_r=2.5π and the structural damping ratio ξ=0.0. The effects of some key parameters, such as shear rate (k=0.0, 0.05, 0.1), reduced velocity (U_r=3.0–18.0) and spacing ratio (L_x/D=2.5, 3.5, 4.5, 8.0), are demonstrated. It is observed that the shear rate and reduced velocity play an important role in the VIVs of both cylinders at various center-to-center distances. Additionally, in comparison with the single cylinder case, a further study indicated that the gap flow has a significant impact on such a dynamic system, leading it to be more complex. The results show that, the performances of ‘dual-resonant’ are discovered in the shear flow. A valley is formed in transverse oscillation amplitude of DC for each spacing ratio when U_r is about 6.0. For the X–Y trajectories of the circular cylinders, figure-eight, figure-O and oval shape are obtained. Finally, the interactions between cylinders are revealed, together with the wake-induced vibration (WIV) mechanism underlying the oscillation characteristics of both cylinders exposed to shear flow. Besides, the “T+P” wake pattern is discovered herein.     

Three-dimensional water entry of a solid body: A particle image velocimetry study

Understanding and predicting the hydrodynamic loading experienced by a solid body during water impact is critical for researchers and practitioners in naval engineering. While two-dimensional (2D) water entry problems have been extensively investigated, experimental data on 3D fluid–structure interactions during water impact are rather limited. Here, particle image velocimetry (PIV) is utilized to study the free fall vertical impact of a solid body, modeling a ship hull, on an otherwise quiescent fluid. Planar PIV is used to measure the velocity field on multiple cross-sections along the length and width of the model. These data are combined to infer the 3D velocity field in the entire fluid. The 3D velocity field is then utilized to reconstruct the pressure field by integrating the incompressible 3D Navier–Stokes equations in a time-varying domain, where both the free surface and the fluid–solid interface evolve in time. By evaluating the pressure field on the wetted surface of the model, we estimate the hydrodynamic loading during water entry. Experimental results demonstrate the central role of 3D effects on both the flow physics and the hydrodynamic loading. As the cross-sectional velocity decreases away from the mid-span, we observe a robust increase in the axial velocity component. This translates into a complex spatio-temporal dependence of the hydrodynamic loading, which is initially maximized in the vicinity of the pile-up and later increases toward the keel. Due to the deceleration of the model during the impact and the increase in the wetted surface, the hydrodynamic loading close to the mid-span in the early stage of the impact is considerably larger than the ends. The 3D flow physics is used to study the energy imparted to the fluid during the impact, which we find to be mostly transferred to the risen water, consisting of the pile-up region and the spray jet. Our methodology can be implemented for the analysis of other solid bodies with multiple geometric curvatures, and our experimental results can be utilized for the validation of 3D mathematical models of water entry.     

Evolution of mesoscopic granular clusters in comminution systems: a structural mechanics model of grain breakage and force chain buckling

A major scientific challenge in establishing a micromechanics theory for complex materials is the characterisation and modelling of emergent mesoscopic phenomena. This study demonstrates the key elements of a structural mechanics approach to the modelling of mesoscopic dissipative phenomena in comminution systems where grain breakage and force chain buckling coexist. Given the many degrees of freedom in these systems, there are multitude of possible configurations and configurational transitions accessible even for a small particle cluster (e.g. a particle and its immediate neighbours). Here, we develop a model of the evolution of a 6-particle cluster undergoing breakage and force chain buckling, in sequence. The analysis lays bare the intricate connections between the contact topology, the relative kinematics arising from the interactions of particles at the bonded versus non-bonded contacts, and the collective dynamics of these interactions as the cluster is monotonically compressed under confinement. The stress-displacement response profiles at the cluster scale exhibit qualitatively similar properties to those seen in macroscopic assemblies under confined compression. A parametric analysis is undertaken to explore the effects of grain-scale resistances to breakage and buckling with respect to the overall force-displacement behaviour of the granular cluster. The study casts light on open problems for future research into the micromechanics of emergent cluster behaviour germane to comminution systems.     

A novel mesh-free poly-cell Galerkin method

A novel numerical method is explored and named as mesh-free poly-cell Galerkin method. An improved moving least-square （MLS） scheme is presented, which can avoid the matrix inversion in standard MLS and can be used to construct shape functions possessing delta Kronecher property. A new type of local support is introduced to ensure the alignment of integral domains with the cells of the back-ground mesh, which will reduce the difficult in integration. An intensive numerical study is conducted to test the accuracy of the present method. It is observed that solutions with good accuracy can be obtained with the present method.     

Experimental study of near-wall turbulent characteristics in an open-channel with gravel bed using an acoustic Doppler velocimeter

This experimental study investigated the mean velocity profiles, skin friction and turbulent characteristics of a gravel bed over a wide range of roughness using an acoustic Doppler velocimeter (ADV). The median diameter of bed material ranged from 2 to 40 mm, and the normalized roughness heights ranged from 47 to 4,881 mm. The flow regime was fully developed turbulence with a Reynolds number in the range of 4.2 × 10⁴–9.86 × 10⁴. All velocity curves exhibited logarithmic distributions, and the log-law region was influenced greatly by both the roughness and the Reynolds number. Moreover, the roughness of the gravel bed exerted a strong effect on Reynolds stress, and the turbulence tended towards isotropic with increasing roughness. Using statistical analyses, the third-order turbulence moments, sweep, and ejection motions were also examined. The results of this experimental analysis present a contrast to the classical wall similarity hypothesis.