Authors:You Li; Xiao-Dong Niu; Hai-Zhuan Yuan; Adnan Khan; Xiang Li Pages: 995 - 1014 Abstract: In this paper, the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows, including inviscid LBFS I, viscous LBFS II, hybrid LBFS III and hybrid LBFS IV. Hybrid LBFS can automatically realize the switch between inviscid LBFS I and viscous LBFS II through introducing a switch function. The resultant hybrid WENO–LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS. We investigate the performance of WENO scheme based on four kinds of LBFS systematically. Numerical results indicate that the devopled hybrid WENO–LBFS scheme has high accuracy, high resolution and no oscillations. It can not only accurately calculate smooth solutions, but also can effectively capture contact discontinuities and strong shock waves. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0785-9 Issue No:Vol. 34, No. 6 (2018)

Authors:Qian-Long Xu; Ye Li; Zhi-Liang Lin Pages: 1015 - 1034 Abstract: A numerical model based on a boundary element method (BEM) is developed to predict the performance of two-body self-reacting floating-point absorber (SRFPA) wave energy systems that operate predominantly in heave. The key numerical issues in applying the BEM are systematically discussed. In particular, some improvements and simplifications in the numerical scheme are developed to evaluate the free surface Green’s function, which is a main element of difficulty in the BEM. For a locked SRFPA system, the present method is compared with the existing experiment and the Reynolds-averaged Navier–Stokes (RANS)-based method, where it is shown that the inviscid assumption leads to substantial over-prediction of the heave response. For the unlocked SRFPA model we study in this paper, the additional viscous damping primarily induced by flow separation and vortex shedding, is modelled as a quadratic drag force, which is proportional to the square of body velocity. The inclusion of viscous drag in present method significantly improves the prediction of the heave responses and the power absorption performance of the SRFPA system, obtaining results excellent agreement with experimental data and the RANS simulation results over a broad range of incident wave periods, except near resonance in larger wave height scenarios. It is found that the wave overtopping and the re-entering impact of out-of-water floating body are observed more frequently in larger waves, where these non-linear effects are the dominant damping sources and could significantly reduce the power output and the motion responses of the SRFPA system. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0792-x Issue No:Vol. 34, No. 6 (2018)

Authors:Xiao Chen; Gang Dong; Baoming Li Pages: 1035 - 1047 Abstract: The three-dimensional interactions of a perturbed premixed flame interface with a planar incident shock wave and its reflected shock waves are numerically simulated by solving the compressible, reactive Navier–Stokes equations with the high-resolution scheme and a single-step chemical reaction. The effects of the initial incident shock wave strength (Mach number) and the initial perturbation pattern of interface on the interactions are investigated. The distinct properties of perturbation growth on the flame interface during the interactions are presented. Our results show that perturbation growth is mainly attributed to the flame stretching and propagation. The flame stretching is associated with the larger-scale vortical flow due to Richtmyer–Meshkov instability while the flame propagation is due to the chemical reaction. The mixing properties of unburned/burned gases on both sides of the flame are quantitatively analyzed by using integral and statistical diagnostics. The results show that the large-scale flow due to the vortical motion always plays a dominating role during the reactive interaction process; however, the effect of chemistry becomes more important at the later stage of the interactions, especially for higher Mach number cases. The scalar dissipation due to the molecular diffusion is always small in the present study and can be negligible. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0783-y Issue No:Vol. 34, No. 6 (2018)

Authors:Toshiyuki Nakata; Ryusuke Noda; Shinobu Kumagai; Hao Liu Pages: 1048 - 1060 Abstract: Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0789-5 Issue No:Vol. 34, No. 6 (2018)

Authors:Yin Zhang; Feifei Gao; Zhiyue Zheng; Zhihai Cheng Pages: 1061 - 1071 Abstract: In an indentation test, the effective Young’s modulus of a film/substrate bilayer heterostructure varies with the indentation depth, a phenomenon known as the substrate effect. In previous studies investigating this, only the Young’s modulus of the film was unknown. Once the effective Young’s modulus of a film/substrate structure is determined at a given contact depth, the Young’s modulus of the film can be uniquely determined, i.e., there is a one-to-one relation between the Young’s modulus of the film and the film/substrate effective Young’s modulus. However, at times it is extremely challenging or even impossible to measure the film thickness. Furthermore, the precise definition of the layer/film thickness for a two-dimensional material can be problematic. In the current study, therefore, the thickness of the film and its Young’s modulus are treated as two unknowns that must be determined. Unlike the case with one unknown, there are infinite combinations of film thickness and Young’s modulus which can yield the same effective Young’s modulus for the film/substrate. An inverse problem is formulated and solved to extract the Young’s modulus and thickness of the film from the indentation depth-load curve. The accuracy and robustness of the inverse problem-solving method are also demonstrated. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0778-8 Issue No:Vol. 34, No. 6 (2018)

Authors:Mingjie Cao; Haitao Ma; Peng Wei Pages: 1072 - 1083 Abstract: The stiffness spreading method (SSM) was initially proposed for layout optimization of truss structures, in which an artificial elastic material of low modulus is uniformly distributed in the design domain to create connections between discrete members. In this paper, a modified stiffness spreading method is proposed by replacing the artificial elastic material with auxiliary bars to connect real members of the truss structure. Since the background continuum mesh for the elastic material is no longer required, the computational cost is significantly reduced. Like SSM, the new method is advantageous in that an initial design may consist of disconnected bars allocated in the design domain, and mathematical programming methods can be applied for the efficient solution of the formulated optimization problem. A number of solution strategies are also developed to achieve more practical designs with lower computational cost. Numerical examples of both 2-D and 3-D truss structures are presented to demonstrate the feasibility, robustness and effectiveness of the proposed method. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0776-x Issue No:Vol. 34, No. 6 (2018)

Authors:Zunyi Duan; Jun Yan; Ikjin Lee; Jingyuan Wang; Tao Yu Pages: 1084 - 1094 Abstract: Fiber reinforced composite frame structure is an ideal lightweight and large-span structure in the fields of aerospace, satellite and wind turbine. Natural fundamental frequency is one of key indicators in the design requirement of the composite frame since structural resonance can be effectively avoided with the increase of the fundamental frequency. Inspired by the concept of integrated design optimization of composite frame structures and materials, the design optimization for the maximum structural fundamental frequency of fiber reinforced frame structures is proposed. An optimization model oriented at the maximum structural fundamental frequency under a composite material volume constraint is established. Two kinds of independent design variables are optimized, in which one is variables represented structural topology, the other is variables of continuous fiber winding angles. Sensitivity analysis of the frequency with respect to the two kinds of independent design variables is implemented with the semi-analytical sensitivity method. Some representative examples in the manuscript demonstrate that the integrated design optimization of composite structures can effectively explore coupled effects between structural configurations and material properties to increase the structural fundamental frequency. The proposed integrated optimization model has great potential to improve composite frames structural dynamic performance in aerospace industries. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0784-x Issue No:Vol. 34, No. 6 (2018)

Authors:Wei Qiu; Lulu Ma; Qiu Li; Huadan Xing; Cuili Cheng; Ganyun Huang Pages: 1095 - 1107 Abstract: The requirement of stress analysis and measurement is increasing with the great development of heterogeneous structures and strain engineering in the field of semiconductors. Micro-Raman spectroscopy is an effective method for the measurement of intrinsic stress in semiconductor structures. However, most existing applications of Raman-stress measurement use the classical model established on the (001) crystal plane. A non-negligible error may be introduced when the Raman data are detected on surfaces/cross-sections of different crystal planes. Owing to crystal symmetry, the mechanical, physical and optical parameters of different crystal planes show obvious anisotropy, leading to the Raman-mechanical relationship dissimilarity on the different crystal planes. In this work, a general model of stress measurement on crystalline silicon with an arbitrary crystal plane was presented based on the elastic mechanics, the lattice dynamics and the Raman selection rule. The wavenumber-stress factor that is determined by the proposed method is suitable for the measured crystal plane. Detailed examples for some specific crystal planes were provided and the theoretical results were verified by experiments. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0797-5 Issue No:Vol. 34, No. 6 (2018)

Authors:H. X. Wu; Y. Liu; X. C. Zhang Pages: 1108 - 1123 Abstract: Theoretical analysis and numerical simulation methods were used to study the in-plane crushing behavior of single-cell structures and regular and composite honeycombs. Square, hexagonal, and circular honeycombs were selected as honeycomb layers to establish composite honeycomb models in the form of composite structures and realize the complementary advantages of honeycombs with type I and type II structures. The effects of honeycomb layer arrangement, plastic collapse strength, relative density, and crushing velocity on the deformation mode, plateau stress, load uniformity, and energy absorption performance of the composite honeycombs were mainly considered. A semi-empirical formula for plateau stress and energy absorption rate per unit mass for the composite honeycombs was developed. The results showed that the arrangement mode of honeycomb layers is an important factor that affects their mechanical properties. Appropriately selecting the arrangement of honeycomb layers and the proportion of honeycomb layers with different structures in a composite honeycomb can effectively improve its load uniformity and control the magnitude of plateau stress and energy absorption capacity. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0798-4 Issue No:Vol. 34, No. 6 (2018)

Authors:Nuttawit Wattanasakulpong; Arisara Chaikittiratana; Sacharuck Pornpeerakeat Pages: 1124 - 1135 Abstract: In this paper, vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory. The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs. The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams. The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton’s principle, which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions. Based on the numerical experiments, it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0770-3 Issue No:Vol. 34, No. 6 (2018)

Authors:J. Chen; Y. X. Guo; F. X. Mei Pages: 1136 - 1144 Abstract: A large proportion of constrained mechanical systems result in nonlinear ordinary differential equations, for which it is quite difficult to find analytical solutions. The initial motions method proposed by Whittaker is effective to deal with such problems for various constrained mechanical systems, including the nonholonomic systems discussed in the first part of this paper, where in addition to differential equations of motion, nonholonomic constraints apply. The final equations of motion for these systems are obtained in the form of corresponding power series. Also, an alternative, direct method to determine the initial values of higher-order derivatives \({\ddot{q}}_0 ,{{\dddot{q}{} }}_{\!0} ,\ldots \) is proposed, being different from that of Whittaker. The second part of this work analyzes the stability of equilibrium of less complex, nonholonomic mechanical systems represented by gradient systems. We discuss the stability of equilibrium of such systems based on the properties of the gradient system. The advantage of this novel method is its avoidance of the difficulty of directly establishing Lyapunov functions aimed at such unsteady nonlinear systems. Finally, these theoretical considerations are illustrated through four examples. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0768-x Issue No:Vol. 34, No. 6 (2018)

Authors:Ji-Yang Zhou; Guang-Yu Lu; Guo-Ping Cai; Guang-Qiang Fang; Liang-Liang Lv; Jun-Wei Shi Pages: 1145 - 1155 Abstract: Planar phased-array satellite antennas deform when subjected to external disturbances such as thermal gradients or slewing maneuvers. Such distortion can degrade the coherence of the antenna and must therefore be eliminated to maintain performance. To support planar phased-array satellite antennas, a truss with diagonal cables is often applied, generally pretensioned to improve the stiffness of the antenna and maintain the integrity of the structure. A new technique is proposed herein, using the diagonal cables as the actuators for static shape adjustment of the planar phased-array satellite antenna. In this technique, the diagonal cables are not pretensioned; instead, they are slack when the deformation of the antenna is small. When using this technique, there is no need to add redundant control devices, improving the reliability and reducing the mass of the antenna. The finite element method is used to establish a structural model for the satellite antenna, then a method is introduced to select proper diagonal cables and determine the corresponding forces. Numerical simulations of a simplified two-bay satellite antenna are first carried out to validate the proposed technique. Then, a simplified 18-bay antenna is also studied, because spaceborne satellite antennas have inevitably tended to be large in recent years. The numerical simulation results show that the proposed technique can be effectively used to adjust the static shape of planar phased-array satellite antennas, achieving high precision. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0790-z Issue No:Vol. 34, No. 6 (2018)

Authors:Shaoxiong Yang; Lucy T. Zhang; Cheng Hua; Yunqiao Liu; Jingdong Tang; Xiaobo Gong; Zonglai Jiang Pages: 1156 - 1166 Abstract: Mechanical stimuli play critical roles in cardiovascular diseases, in which in vivo stresses in blood vessels present a great challenge to predict. Based on the structural–thermal coupled finite element method, we propose a thermal expansion method to estimate stresses in multi-layer blood vessels under healthy and pathological conditions. The proposed method provides a relatively simple and convenient means to predict reliable in vivo mechanical stresses with accurate residual stress. The method is first verified with the opening-up process and the pressure-radius responses for single and multi-layer vessel models. It is then applied to study the stress variation in a human carotid artery at different hypertension stages and in a plaque of vascular stenosis. Our results show that specific or optimal residual stresses exist for different blood pressures, which helps form a homogeneous stress distribution across vessel walls. High elastic shear stress is identified on the shoulder of the plaque, which contributes to the tearing effect in plaque rupture. The present study indicates that the proposed numerical method is a capable and efficient in vivo stress evaluation of patient-specific blood vessels for clinical purposes. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0780-1 Issue No:Vol. 34, No. 6 (2018)

Authors:Yu-Cheng Lo; Liu Wang Pages: 1167 - 1173 Abstract: A bulging intervertebral disc (IVD) occurs when pressure on a spinal disc damages the once healthy disc, causing it to compress or change its normal shape. In medicine, most attention has been paid clinically to diagnosis of and treatment for such problems, which little effect has been made to understand such issues from a mechanics perspective, i.e., the bulging deformation of the soft IVD induced by excessive compressive load. We report herein a simple elasticity solution to understand the bulging disc issue. For simplicity, the soft IVD is modeled as an incompressible circular composite layer consisting of an inner nucleus and outer annulus, sandwiched between two vertebral segments which are much stiffer than the IVD and can be treated as rigid bodies. Without adopting any assumptions regarding prescribed displacements or stresses, we obtained the stress and displacement fields within the composite layer when a certain compressive stain is applied via an asymptotic approach. This asymptotic approach is very simple and accurate enough for prediction of the bugling profile of the IVD. We also performed finite-element modeling (FEM) to validate our solutions; the predicted stress and displacement fields inside the composite are in good agreement with the FEM results. PubDate: 2018-12-01 DOI: 10.1007/s10409-018-0788-6 Issue No:Vol. 34, No. 6 (2018)

Authors:L. M. Lin; S. Y. Shi; Y. X. Wu Abstract: In the present paper, physical mechanism responsible for origin of streamwise vortices in mode A appeared in the three-dimensional (3-D) wake transition of a square-section cylinder is investigated. Direct numerical simulations at a Reynolds number of 180 firstly show that such streamwise vorticity is not originated from lateral surfaces. Then through the analysis of local flow field in the immediate neighborhood of rear surface, based on the theory of vortex-induced vortex, a new physical mechanism is identified. At first, the vertical vorticity on rear surface is generated by the intrinsic three-dimensional instability with the same instability wavelength of mode A. Then the streamwise vorticity at a specific sign is induced by such vertical vorticity, convected and concentrated in the shear layers. Finally, streamwise vortices are formed and shed with alternatively shedding spanwise vortices in the near wake. Moreover, the effect of induced spanwise vorticity on original two-dimensional (2-D) spanwise vorticity is also presented in detail. PubDate: 2018-12-11 DOI: 10.1007/s10409-018-0818-4

Authors:Junfeng Ou; Zhigang Zhai Abstract: Interaction of a planar shock wave with a discontinuous \(\hbox {SF}_6\) elliptic gas cylinder surrounded by air is investigated. Special attention is given to the effects of aspect ratio on wave pattern, interface evolution, and material mixing. An ideal discontinuous two-dimensional gas cylinder is created by the soap film technique in experiments, and the shocked flow is captured by schlieren photography combined with a high-speed video camera. The surface of the gas cylinder is clear enough to observe the shock motions, and the distinct interface boundaries allow us to extract more details. As aspect ratio varies, the shock focusing process is quite different. For the prolate gas cylinder, an inward jet is produced although an internal shock focusing firstly occurs. The inward jet has never been observed in membraneless prolate ellipse experiments probably because the inward jet is so faint due to less vorticity generation on membraneless interface that it is difficult to be observed. For the oblate gas cylinder, a secondary vortex pair, which has not been described clearly in previous work, is derived from the downstream interface. The material lines at early stages are extracted from experiments, which grow faster as aspect ratio increases. The interfacial area, the mean volume fraction and the mixing rate are presented from computations, and the results show that the increase of aspect ratio promotes the mixing between gases. PubDate: 2018-12-10 DOI: 10.1007/s10409-018-0819-3

Authors:Yaohong Suo; Fuqian Yang Abstract: Diffusion-induced deformation during electrochemical cycling plays an important role in determining structural durability of the electrodes in lithium-ion batteries. In this work, we investigate the coupling between diffusion and stress in the boundary conditions of a bilayer electrode, and analyze the evolution of the lithium concentration and stress. Numerical simulations are performed under four different combinations of the boundary conditions between diffusion and mechanical deformation. The stress distributes uniformly in the bilayer electrode for all four cases. The concentration of lithium at the interface is discontinuous for the cases with fixed boundary conditions and is continuous for the cases with a surface at stress-free state. For the bilayer electrode fixed at both surfaces, the magnitude of the stress in the bilayer electrode increases with the increase of the diffusion time. This study reveals the importance of incorporating the coupling between diffusion and stress in the boundary condition in the analysis of the structural durability of lithium-ion batteries and in the design of multilayered and/or gradient electrodes. PubDate: 2018-12-04 DOI: 10.1007/s10409-018-0817-5

Authors:Y. C. Zhang; Y. J. Liang; S. T. Liu; Y. D. Su Abstract: Triangular lattice metamaterials composed of bi-layer curved rib elements (called the Lehman–Lakes lattice) possess unbounded thermal expansion, high stiffness and impossibility of thermal buckling, which are highly desirable in many engineering structural applications subjected to large fluctuations in temperature. However, the requirement of such lattice metamaterial is that it must be a hinged joint in order to achieve the bending deformation upon heating freely, which directly leads to poor manufacturability, especially in small dimensions. In this study, a new design of dual-constituent triangular lattice metamaterial (DTLM) with good manufacturability is proposed to achieve the identical unbounded thermal expansion. In this lattice, a special bi-layer curved rib element where layer one is partially covered by layer two is presented, where the hinge joints are not necessary because the flexural rigidity in the single-layer part is much smaller than that in the bi-layer part, and the desirable thermal bending deformation can be achieved. A sample fabricated by additive manufacturing is given in order to show the good manufacturability; simultaneously, the multifunctional performance of the tailored DTLM with zero, large positive or negative coefficient of thermal expansion (CTE) can remain excellent, as well as the Lehman–Lakes lattice. Examples illustrate that the DTLM with zero CTE has about 34.2% improvement in stiffness and meanwhile has 17% reduction in weight compared with the Lehman–Lakes lattice. The stiffness of the DTLM has a moderate reduction when achieving the same large positive or negative CTE. In addition, the thermomechanical properties of the DTLM are given by the closed-form analytical solution and their effectiveness is verified by the detailed numerical simulation. PubDate: 2018-11-27 DOI: 10.1007/s10409-018-0811-y

Authors:Y. Peng; H. Wu; Q. Fang; X. Z. Kong Abstract: A modified spherical cavity-expansion model is developed in this paper. (1) We introduce a piecewise hyperbolic yield criterion suitable for pressure less than fc/3 to describe the mechanical behavior in the elastic region for the elastic–plastic response and modify the crack occurrence condition for the elastic–cracked–plastic response. (2) The hyperbolic yield criterion and a piecewise equation of state (EOS) are adopted for a better description of the plastic behavior of concrete material. Then, the modified model is validated by several projectile penetration tests in both the normal strength concrete (NSC) and ultra-high performance cement-based composite (UHPCC) targets. Finally, the hydrostatic pressure of the targets under rigid ogive-nosed projectile penetrations is found to be nearly within (0, 1.6 GPa), which usually exceeds the range that the shear strength-pressure test data covered. The influence of yield criterion on depth of penetration is discussed and it is recommended that the pressure should arrive at least 400 MPa in the related triaxial compression tests. PubDate: 2018-11-27 DOI: 10.1007/s10409-018-0815-7

Authors:Xiangwei Dong; Jianlin Liu; Sai Liu; Zengliang Li Abstract: Numerical simulation of the morphology of a droplet deposited on a solid surface requires an efficient description of the three-phase contact line. In this study, a simple method of implementing the contact angle is proposed, combined with a robust smoothed particle hydrodynamics multiphase algorithm (Zhang 2015). The first step of the method is the creation of the virtual liquid–gas interface across the solid surface by means of dummy particles, thus the calculated surface tension near the triple point serves to automatically modulate the dynamic contact line towards the equilibrium state. We simulate the evolution process of initially square liquid lumps on flat and curved surfaces. The predictions of droplet profiles are in good agreement with the analytical solutions provided that the macroscopic contact angle is accurately implemented. Compared to the normal correction method, the present method is straightforward without the need to manually alter the normal vectors. This study presents a robust algorithm capable of capturing the physics of the static wetting. It may hold great potentials in bio-inspired superhydrophobic surfaces, oil displacement, microfluidics, ore floatation, etc. PubDate: 2018-11-27 DOI: 10.1007/s10409-018-0812-x