Archery simulation

The problem of bow shooting is considered. Its solution is obtained in the quasistatic approximation when it is assumed that, at the successive instants of time, the limbs of a bow reach near-equilibrium states. Some dependencies of the initial arrow velocity on all basic physical parameters of the bow are obtained.     

The static deformation of the asymmetric Japanese bow: modelling bow asymmetries with the elastica theory

Meccanica - The static deformation of symmetric bow limbs has been widely studied in the last century. However, asymmetries in shape and length which correspond to a more realistic situation, have...     

A HIGH-ORDER RIGID-FLEXIBLE COUPLING MODEL OF A ROTATING FLEXIBLE BEAM UNDER LARGE DEFORMATION

对在平面内做大范围转动的中心刚体-柔性梁系统的刚柔耦合建模理论进行了深入研究,建立了系统的高次耦合动力学模型. 该动力学模型考虑了柔性梁横向弯曲变形和纵向伸长变形,且在纵向位移中计及由于横向变形而引起的纵向缩短项,即非线性耦合变形项,并保留了与非线性耦合项相关的一些高阶项,最终得到了系统的高次刚柔耦合动力学方程. 由此得到的动力学方程不仅能适用于柔性梁的小变形问题,也同样适用于大变形问题,弥补了一次近似耦合模型在处理柔性梁大变形问题上的不足. 通过与绝对节点坐标法以及一次近似耦合模型的对比验证了高次耦合模型的正确性.     

基于径向基点插值法的旋转Mindlin板高次刚柔耦合动力学模型

将无网格径向基点插值法(radial point interpolation method,RPIM)用于中心刚体?旋转柔性板的动力学分析.基于浮动坐标系方法和一阶剪切变形理论即Mindlin板理论,考虑剪切变形的影响,并计入板面内变形的非线性耦合变形项,采用径向基点插值法描述板的变形场,保留动能中有关非线性耦合变形项...     

旋转悬臂梁的刚柔耦合动力学建模与频率分析

对固结于转动刚体上外接柔性梁的刚柔耦合动力学建模和频率特性进行了研究,在精确描述柔性梁非线性变形的基础上,利用Hamilton变分原理和假设模态法,在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下,推导出考虑"动力刚化"项的一次近似耦合模型。首先忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型做无量纲化处理,分析梁固有频率对模态截断数的依赖性;其次研究在一次近似简化模型和零次近似简化模型下,调谐角速度与共振现象的关系;最后分析一次近似耦合模型的动力特性。研究发现,为保证计算的精度,模态截断数应随无量纲角速度的增大而增加,合理的模态截断数具有收敛值;一次近似简化模型下悬臂梁横向弯曲振动不存在共振调谐角速度,一次耦合模型下柔性梁并没有出现屈曲失稳现象。现有典型文献的相关结论是值得商榷的。     

Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression

The size dependent deformation of Cu single crystal micropillars with thickness ranging from 0.2 to 2.5 μm subjected to uniaxial compression is investigated using a Multi-scale Dislocation Dynamics Plasticity (MDDP) approach. MDDP is a hybrid elasto-viscoplastic simulation model which couples discrete dislocation dynamics at the micro-scale (software micro3d) with the macroscopic plastic deformation. Our results show that the deformation field in these micropillars is heterogeneous from the onset of plastic flow and is confined to few deformation bands, leading to the formation of ledges and stress concentrations at the surface of the specimen. Furthermore, the simulation yields a serrated stress–strain behavior consisting of discrete strain bursts that correlates well with experimental observations. The intermittent operation and stagnation of discrete dislocation arms is identified as the prominent mechanism that causes heterogeneous deformation and results in the observed macroscopic strain bursts. We show that the critical stress to bow an average maximum dislocation arm, whose length changes during deformation due to pinning events, is responsible for the observed size dependent response of the single crystals. We also reveal that hardening rates, similar to that shown experimentally, occur under relatively constant dislocation densities and are linked to dislocation stagnation due to the formation of entangled dislocation configuration and pinning sites.     

具有内域的双层加筋圆柱壳动响应特性简

采用外域双渐近法模拟外部流体域,内域双渐近法模拟内部流体域,采用非线性有限元软件ABAQUS 模拟结构,建立流固耦合数值模型并验证了其有效性. 利用建立的数值模型研究内部流体对双层加筋圆柱壳动响应的影响. 研究结果表明：一阶双渐近的解在中后期振荡周期变短、幅值变小,而二阶双渐近的解与解析解吻合良好;内部流体的存在减弱了双层加筋圆柱壳外壳的塑性变形,对其内壳塑性变形的影响较小;内部流体的存在减弱了双层加筋圆柱壳的速度响应.     

具有内域的双层加筋圆柱壳动响应特性

采用外域双渐近法模拟外部流体域,内域双渐近法模拟内部流体域,采用非线性有限元软件ABAQUS 模拟结构,建立流固耦合数值模型并验证了其有效性. 利用建立的数值模型研究内部流体对双层加筋圆柱壳动响应的影响. 研究结果表明:一阶双渐近的解在中后期振荡周期变短、幅值变小,而二阶双渐近的解与解析解吻合良好;内部流体的存在减弱了双层加筋圆柱壳外壳的塑性变形,对其内壳塑性变形的影响较小;内部流体的存在减弱了双层加筋圆柱壳的速度响应.      

Magnetohydrodynamic description of the process of collision of a solar wind shock perturbation with the bow shock

The interaction of the solar wind oblique shock wave with the bow shock front ahead of the earth's magnetosphere is considered in an ideal MHD approximation. It is shown that as the impinging shock wave propagates along the bow front, the pattern of the emerging flow is qualitatively and quantitatively modified, being asymmetrical on the flanks. The effect of the interplanetary magnetic field orientation and the obliqueness of the arriving solar wind shock wave on this process is studied. It is shown that sharp nonlinear restructurings may occur, with neighboring, oppositely poled current layers emerging somewhere on the flanks. Alfvén discontinuities and slow waves play a significant part in this process. The emerging current layers may account for the fact that only some solar wind shock waves are geoeffective.     

扑翼柔性及其对气动特性的影响

以往对扑翼气动特性的研究基本上都是基于简单的匀速刚性模型,但是通过大量观察不同飞鸟的扑翼动作发现,该模型与鸟翼的实际扑动还有很大差别。鸟翼不但上扑段和下扑段所需时间不同,而且在扑动过程中,鸟翼的形状无论沿弦向或展向都存在着相当大的柔性变形。本文在原有匀速刚性模型的基础上,加入了扑动速率变化和形状变化的影响,得出新的变速柔性扑翼分析模型,使之更接近鸟翼柔性扑动的真实情况。通过对比计算发现,柔性变形对扑翼的升力与推力都有着显著影响,如果控制得当,柔性变形能大大改善扑翼的气动性能。     

旋转薄板的一种高次动力学模型与频率转向

对固结于转动刚体上柔性薄板的刚柔耦合动力学和频率转向特性进行了深入研究,建立了系统的高次刚柔耦合动力学模型,该动力学模型计入了由于横向变形而引起的面内纵向缩短项,即非线性耦合变形量,并且完整保留了与非线性耦合变形量相关的所有项. 研究表明,高次耦合模型不仅适用于小变形问题,而且还适用于大变形问题,弥补了一次近似耦合模型在处理大变形问题上的不足. 旋转悬臂薄板相邻两阶模态间既有柔和的频率转向现象也有剧烈的频率转向现象. 柔和的频率转向伴随着的振型转换的过程是连续的,而剧烈的频率转向伴随着的振型转换的过程则是不连续的. 相隔多阶模态间存在传递性频率转向,并伴随着振型转移.      

Mechanics of physisorption on elastomer surface

Mechanical aspects of physisorption on elastomeric substrates are studied via a continuum model in combination with the Lennard-Jones potential. In light of the incompressibility of elastomers, it is shown that the presence of a zero-dimensional adsorbate gives rise to a distributed force on the surface of the substrate. The induced surface deformation is determined, and the adsorption force and energy which depend on the substrate stiffness are derived. The results are then used to examine mutual interaction between two like adsorbates with small spacing, showing complicated attraction and repulsion arising from elastic deformation of the substrate. The dipole and quadruple moments of an adsorbate are also calculated, and the multipole approximation is adopted to quantify the interaction when the two adsorbates are separated remotely.     

Comparison of slamming and whipping loads by fully coupled hydroelastic analysis and experimental measurement

This paper proposes a numerical method for analyzing whipping using a fully coupled hydroelastic model. The numerical analysis method utilizes a 3-D Rankine panel method, 1-D/3-D finite element methods, and a 2-D generalized Wagner model, which are strongly coupled in the time domain. The computational results were compared with those of a model test of an 18 000-TEU containership. The slamming pressures and whipping responses to regular waves for bow flare and stern slamming were compared. Furthermore, the slamming pressure was decomposed into its dynamic and static components. The numerical and experimental models produced similar results. In addition, the effects of the discretization and geometric approximation of the 2-D slamming sections were investigated.     

Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow

A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory. The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow.     

The reptation model with segmental stretch

The Doi-Edwards model with segmental stretch and a non-linear finitely extensible spring law is described and examined in simple flow situations where analytic results are derivable; namely oscillatory flow and steady state flow at high deformation rates. The model is shown to be consistent with the Bueche-Ferry hypothesis in fast large strain unidirectional flows but to violate this rule in small strain reversing flows. The discrepancy is identified with a preaveraging approximation used to describe the relative tube-chain velocity. Experimentally verifiable scaling rule for the birefringence as a universal function of a planar flow-type parameter and deformation rate are identified. Sensitivity to the extensional flow character, absent in the original tube model, manifests itself with the introduction of segmental stretch. Although the model generates a non-separable memory function kernel the deformation dependence of the memory function is quantitatively shown to have negligible impact on the predicted theological properties relative to the original Doi-Edwards model. With this simplification, relatively uncomplicated approximations to the segmental stretch model can be deduced.     

非惯性系下柔性悬臂梁的振动主动控制

采用变结构控制方法对非惯性系下柔性悬臂梁的振动主动控制进行研究．重点通过算例揭示一次近似模型与传统的零次近似模型的巨大差异，以及变结构方法在控制非惯性系下柔性悬臂梁的稳态振动的有效性．结果表明，当大范围旋转运动角速度较大时，传统零次近似模型不能对动力系统进行正确的数学描述；变结构控制方法能够使得非惯性系下梁的稳态振动得到完全镇定，且该方法对转动角速度变化具有较好的鲁棒性；采用零次近似模型进行控制设计的控制效果将在某一临界角速度条件下出现失效，该临界角速度值大于静止悬臂梁的基频．     

A higher order model for thin-walled structures with deformable cross-sections

A higher order model for the analysis of linear, prismatic thin-walled structures that considers the cross-section warping together with the cross-section in-plane flexural deformation is presented in this paper. The use of a one-dimentional model for the analysis of thin-walled structures, which have an inherent complex three-dimensional (3D) behaviour, can only be successful and competitive when compared with shell finite element models if it fulfills a twofold objective: (i) an enrichment of the model in order to as accurately as possible reproduce its 3D elasticity equations and (ii) the definition of a consistent criterion for uncoupling the beam equations, allowing to identify structural deformation modes.The displacement field is approximated through a linear combination of products between a set of linear independent functions defined over the cross-section and the associated weights only dependent on the beam axis; this approximation is not constrained by any ab initio kinematic assumptions. Towards an efficient application of the approximation procedure, the cross-section is discretized into thin-walled elements, being the displacement field approximated for each element independently of the displacement direction. The approximation is thus hp refined enhancing the “capture” of the 3D structural mechanics of thin-walled structures. The beam model governing equations are obtained through the integration over the cross-section of the corresponding elasticity equations weighted by the cross-section global approximation functions.A criterion for uncoupling the beam governing equations is established, allowing to (i) retrieve the classic equations of the thin-walled beam theory both for open and closed sections and (ii) derive a set of uncoupled deformation modes representing higher order effects. The criterion is based on the solution of the polynomial eigenvalue problem associated with the beam differential equations, allowing to quantify the Saint-Venant principle for thin-walled structures. In fact, the solution of the non linear eigenvalue problem yields a twelve fold null eigenvalue (representing polynomial solutions) that are verified to represent beam classic solutions and sets of pairs and quadruplets of non-null eigenvalues corresponding to higher order modes of deformation.     

降落伞膜索非线性有限元模拟

用膜单元和索单元模拟降落伞织物绳索系统,基于完全拉格朗日格式的非线性有限元方法编程计算降落伞的结构动力学特性。采用增量与迭代混合方法改善非线性计算的收敛特性并结合HHT隐式时间推进方法减小整体迭代计算量。使用修正应力应变张量导数的方法模拟膜单元单向应力状态并针对膜单元和索单元分别进行了非线性有限元计算验证。最后针对C-9型降落伞建立三维有限元模型,根据设定流速对伞衣施加均匀压强载荷,将模拟展开的结果与使用相同模型、不同方法商业软件的文献进行对比,显示了隐式非线性有限元方法模拟降落伞膜索系统大变形动力学的能力。     

Analysis of structural behavior during collision event accounting for bow and side structure interaction

The main goal of this study was to investigate the effects of selected ship collision parameter values on the characteristics of the absorbed energy in several ship collision scenarios.Non-linear simulations were performed using a finite element method(FEM)to obtain virtual experiment data.In the present research,the size of the side damage from a collision phenomenon were measured and used to verify the numerical configuration together with the calculation results using an empirical equation.Parameters in the external dynamics of a ship collision such as the location of the contact point and velocity of the striking ship were taken into consideration.The internal energy and deformation size on the side structure were discussed further in a comparative study.The effects of the selected parameters on several structural behaviors,namely energy,force,and damage extent were also observed and evaluated in this section.Stiffener on side hull was found to contribute significantly into resistance capability of the target ship against penetration of the striking bow.Remarkable force during penetration was observed to occur when inner shell was crushed as certain velocity was applied in the striking bow.     

A lattice-based model of the kinetics of twin boundary motion

In this paper we derive a macroscopic kinetic law for twin boundary motion from a lattice dynamical model. The model is developed for compound and type-1 twins and it is explicitly illustrated for a Cu-Al-Ni shape memory alloy. The governing multiple-well energy is calculated using an effective interatomic potential; a Frenkel-Kontorowa type model is developed for the dynamics at the lattice scale; and a quasi-continuum approximation is used to determine the continuum-scale kinetics. The model predicts that compound twins in the Cu-Al-Ni shape memory alloy are an order of magnitude more mobile than type-1 twins which is consistent with experimental observations.