Authors:W. T. Liu; P. N. Sun; F. R. Ming; A. M. Zhang Pages: 601 - 613 Abstract: Smoothed particle hydrodynamics (SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse (mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process, conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems. PubDate: 2018-08-01 DOI: 10.1007/s10409-017-0739-7 Issue No:Vol. 34, No. 4 (2018)

Authors:Wen-Geng Zhao; Hong-Wei Zheng; Feng-Jun Liu; Xiao-Tian Shi; Jun Gao; Ning Hu; Meng Lv; Si-Cong Chen; Hong-Da Zhao Pages: 623 - 631 Abstract: An efficient high-order numerical method for supersonic reactive flows is proposed in this article. The reactive source term and convection term are solved separately by splitting scheme. In the reaction step, an adaptive time-step method is presented, which can improve the efficiency greatly. In the convection step, a third-order accurate weighted essentially non-oscillatory (WENO) method is adopted to reconstruct the solution in the unstructured grids. Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids, while high order accuracy can be achieved in the smooth region. In addition, the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method. PubDate: 2018-08-01 DOI: 10.1007/s10409-018-0756-1 Issue No:Vol. 34, No. 4 (2018)

Authors:Hai-Sheng Zhao; Yao Zhang; Seng-Tjhen Lie Pages: 676 - 688 Abstract: Considerations of nonlocal elasticity and surface effects in micro- and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short, explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation. PubDate: 2018-08-01 DOI: 10.1007/s10409-018-0751-6 Issue No:Vol. 34, No. 4 (2018)

Authors:Yuwei Zhang; Zhansheng Guo Pages: 706 - 715 Abstract: Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithium-ion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles \((\hbox {LiMn}_{2}\hbox {O}_{4})\) by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling. PubDate: 2018-08-01 DOI: 10.1007/s10409-018-0764-1 Issue No:Vol. 34, No. 4 (2018)

Authors:Q. Zhang; X. P. Zhang; P. Q. Ji Pages: 716 - 727 Abstract: The Brazilian test is a widely used method for determining the tensile strength of rocks and for calibrating parameters in bonded-particle models (BPMs). In previous studies, the Brazilian disc has typically been trimmed from a compacted rectangular specimen. The present study shows that different tensile strength values are obtained depending on the compressive loading direction. Several measures are proposed to reduce the anisotropy of the disc. The results reveal that the anisotropy of the disc is significantly influenced by the compactibility of the specimen from which it is trimmed. A new method is proposed in which the Brazilian disc is directly generated with a particle boundary, effectively reducing the anisotropy. The stiffness (particle and bond) and strength (bond) of the boundary are set at less than and greater than those of the disc assembly, respectively, which significantly decreases the stress concentration at the boundary contacts and prevents breakage of the boundary particle bonds. This leads to a significant reduction in the anisotropy of the disc and the discreteness of the tensile strength. This method is more suitable for carrying out a realistic Brazilian test for homogeneous rock-like material in the BPM. PubDate: 2018-08-01 DOI: 10.1007/s10409-018-0754-3 Issue No:Vol. 34, No. 4 (2018)

Authors:Qiping Xu; Jinyang Liu Pages: 744 - 753 Abstract: Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate formulation (ANCF) beam element employs cubic interpolation in the longitudinal direction and linear interpolation in the transverse direction, whereas it cannot accurately describe the large bending deformation. On this account, a novel modeling method for studying the dynamic behavior of nonlinear materials is proposed in this paper. In this formulation, a higher-order beam element characterized by quadratic interpolation in the transverse directions is used in this investigation. Based on the Yeoh model and volumetric energy penalty function, the nonlinear elastic force matrices are derived within the ANCF framework. The feasibility and availability of the Yeoh model are verified through static experiment of nonlinear incompressible materials. Furthermore, dynamic simulation of a silicone cantilever beam under the gravity force is implemented to validate the superiority of the higher-order beam element. The simulation results obtained based on the Yeoh model by employing three different ANCF beam elements are compared with the result achieved from a commercial finite element package as the reference result. It is found that the results acquired utilizing a higher-order beam element are in good agreement with the reference results, while the results obtained using a lower-order beam element are different from the reference results. In addition, the stiffening problem caused by volumetric locking can be resolved effectively by applying a higher-order beam element. It is concluded that the proposed higher-order beam element formulation has satisfying accuracy in simulating dynamic motion process of the silicone beam. PubDate: 2018-08-01 DOI: 10.1007/s10409-018-0759-y Issue No:Vol. 34, No. 4 (2018)

Authors:Jiabei Shi; Zhuyong Liu; Jiazhen Hong Pages: 769 - 780 Abstract: Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model. PubDate: 2018-08-01 DOI: 10.1007/s10409-018-0763-2 Issue No:Vol. 34, No. 4 (2018)

Authors:Wei Qiu; Lulu Ma; Qiu Li; Huadan Xing; Cuili Cheng; Ganyun Huang 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: 2018-09-21 DOI: 10.1007/s10409-018-0797-5

Authors:Lang Li; Zhenyu Zhao; Rui Zhang; Bin Han; Qiancheng Zhang; Tian Jian Lu Abstract: Dual-level stress plateaus (i.e., relatively short peak stress plateaus, followed by prolonged crushing stress plateaus) in metallic hexagonal honeycombs subjected to out-of-plane impact loading are characterized using a combined numerical and analytical study, with the influence of the strain-rate sensitivity of the honeycomb parent material accounted for. The predictions are validated against existing experimental measurements, and good agreement is achieved. It is demonstrated that honeycombs exhibit dual-level stress plateaus when bucklewaves are initiated and propagate in cell walls, followed by buckling and progressive folding of the cell walls. The abrupt stress drop from peak to crushing plateau in the compressive stress versus strain curve can be explained in a way similar to the quasi-static buckling of a clamped plate. The duration of the peak stress plateau is more evident for strain-rate insensitive honeycombs. PubDate: 2018-09-20 DOI: 10.1007/s10409-018-0800-1

Authors:Chein-Shan Liu; Bo-Tong Li Abstract: A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex non-smooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix \({{\varvec{A}}}:=[a_{ij}]\) , \(a_{ij}=0\) if \(i+j\) is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of \({{\varvec{A}}}\) can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of \({{\varvec{A}}}\) . We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces. PubDate: 2018-09-18 DOI: 10.1007/s10409-018-0799-3

Authors:L. M. Lin; S. Y. Shi; X. F. Zhong; Y. X. Wu Abstract: As reported in a previous work by Lin et al. (Acta Mech Sin, 2018. https://doi.org/10.1007/s10409-018-0758-z), an interesting phenomenon was discovered based on the analysis of wavy vortex and vorticity distribution in the shear layers and near wake of a peak-perforated conic shroud, and two sign laws were summarized. In the present paper, the theory of a vortex-induced vortex is introduced to explore mechanisms in a wavy vortex and applicable sign laws for uniform and incompressible flow past a fixed bluff body. Based on the analysis of the nearest-wall flow, two vortex-induced models for streamwise and vertical vortex pairs, respectively, are proposed under two boundary cases, denoting the induced vorticity introduced or distributed on and near the walls. As a result, the first sign law, for only streamwise and vertical components of vorticity, and the second sign law, for three components of vorticity, are obtained under their own particular conditions. The first sign law reveals the intrinsic physical relationship between streamwise and vertical vorticities, independent of the distribution of spanwise vortices in the whole flow field. It is also confirmed that the spanwise vortices, as well as the shear layers and wake width, distributed wavily across the span, are attributed to the introduced streamwise or vertical vortices. The two sign laws for vorticity are independent of the disturbed spanwise wavelength and the Reynolds number. Through the analysis of flow past the conic shroud, the two sign laws are successfully used to summarize typical spacial distributions of vorticity in three flow regions: on and near the front cylinder surfaces, the separated shear layers and the near wake. PubDate: 2018-09-10 DOI: 10.1007/s10409-018-0793-9

Authors:Qian-Long Xu; Ye Li; Zhi-Liang Lin 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: 2018-09-10 DOI: 10.1007/s10409-018-0792-x

Authors:Mengmeng Zhou; Huimin Xie; Luming Li Abstract: Thermal barrier coatings (TBCs) are widely applied in thermal components to protect metallic components. Owing to the complex layered structure of TBCs and difficult preparation of coating, the mechanical characterization of TBCs should be of primary importance. With regard to TBCs, this study deals with the constitutive parameters identification of bi-material. Considering the complex construction and boundary of bi material, the virtual fields method (VFM) was employed in this study. A methodology based on the optimized virtual fields method combined with moiré interferometry was proposed for the constitutive parameters identification of bi-material. The feasibility of this method is verified using simulated deformation fields of a two-layer material subjected to three point bending loading. As an application, the deformation fields of the TBC specimens were measured by moiré interferometry. Then, the mechanical parameters of the coating were identified by the proposed method. The identification results indicate that Young’s modulus of the TBC top coating is 89.91 GPa, and its Poisson’s ratio is 0.23. PubDate: 2018-08-29 DOI: 10.1007/s10409-018-0787-7

Authors:Milad Saadatmand; Alireza Shooshtari Abstract: In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Kármán plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlinear frequency response (F–R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases: (1) semi-linear vibration; (2) weakly nonlinear vibration; (3) highly nonlinear vibration, are validated by comparing with the numerical solutions. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano/microelectromechanical transducers such as microphones and pressure sensors. PubDate: 2018-08-28 DOI: 10.1007/s10409-018-0794-8

Authors:Yu-Cheng Lo; Liu Wang 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: 2018-08-14 DOI: 10.1007/s10409-018-0788-6

Authors:Arash Shahbaztabar; Koosha Arteshyar Abstract: We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated. PubDate: 2018-08-13 DOI: 10.1007/s10409-018-0796-6

Authors:Ji-Yang Zhou; Guang-Yu Lu; Guo-Ping Cai; Guang-Qiang Fang; Liang-Liang Lv; Jun-Wei Shi 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: 2018-08-10 DOI: 10.1007/s10409-018-0790-z

Authors:Li-Jie Wu; Han-Wen Song Abstract: An approach is proposed to estimate the transfer function of the periodic structure, which is known as an absorber due to its repetitive cells leading to the band gap phenomenon. The band gap is a frequency range in which vibration will be inhibited. A transfer function is usually performed to gain band gap. Previous scholars regard estimation of the transfer function as a forward problem assuming known cell mass and stiffness matrices. However, the estimation of band gap for irregular or complicated cells is hardly accurate because it is difficult to model the cell exactly. Therefore, we treat the estimation as an inverse problem by employing modal identification and curve fitting. A transfer matrix is then established by parameters identified through modal analysis. Both simulations and experiments have been performed. Some interesting conclusions about the relationship between modal parameters and band gap have been achieved. PubDate: 2018-08-10 DOI: 10.1007/s10409-018-0781-0

Authors:You Li; Xiao-Dong Niu; Hai-Zhuan Yuan; Adnan Khan; Xiang Li 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: 2018-08-09 DOI: 10.1007/s10409-018-0785-9

Authors:Toshiyuki Nakata; Ryusuke Noda; Shinobu Kumagai; Hao Liu 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: 2018-08-01 DOI: 10.1007/s10409-018-0789-5