超弹性材料中空穴的动态生成

本文在有限变形动力学的框架下研究了一种不可压超弹性材料圆柱体在表面突加均布拉伸载荷作用下空穴的动态生成问题.除一个相应于均匀变形状态的平凡解外,当外加载荷超过其临界值时,柱体内部还有空穴的突然生成,得到了空穴半径和表面载荷之间的一个精确的微分关系,证明了空穴随时间的演化是非线性的周期性振动.给出了空穴振动的相图、最大振幅、临界载荷及近似的周期.     

电活性聚合物圆柱壳静态与动态电压下的响应及稳定性

在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场.这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏.论文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题.采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程.给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏.同时,也讨论了厚度和边界条件对临界电压的影响.圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动.给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性.采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏.最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论.     

周期集中载荷作用下球形扁壳的非线性振动问题

本文用半解析法推导了周期集中载荷作用下,周边固定球形扁壳的非线性振动微分方程.然后用小参数法求出了非线性的非共振周期解和共振周期解.绘出了不同几何特征参数下的振幅——频率图.     

内聚爆炸载荷下热塑性中厚球壳的变形和层裂

考虑温度和损伤对材料参数的影响,计入温度和损伤对材料塑性变形发展的耦合作用,以本构关系的内变量理论为基础得到了热塑性本构关系的普适显式表达式以及增量形式的热塑性本构方程,结合在实际中有重要意义的内聚爆炸载荷作用下的球壳层裂问题,建立了含损伤热塑性球壳破裂问题的完备方程组,使用有限差分方法,完成了对问题的数值模拟,并对结果进行了分析。     

考虑横向剪切变形和旋转惯性的层合正交异性球壳的动态响应

本文建立了计及横向剪切变形的旋转惯性的复合材料轴对称层合圆柱正交异性球壳的运动方程。在此基础上，用有限差分法计算了球壳在轴对称动力载荷下的动态响应，并讨论了材料参数、结构参数和横向剪切变形的影响。     

柔韧扁球壳在静载荷作用下的非线性振动

本文研究了均布静载荷作用下柔韧扁球壳的非线性自由振动问题,其静力边值问题采用线性解,在此平衡构型的基础上,通过引入Ｇｒｅｅｎ函数,将动力协调方程及对应的边界条件转化为等的积分方程,并把摄动变分法于动力平衡方程的变分形式,得出其非线性固有频率和振幅间的二次近似特征关系。     

网架结构球节点的弹塑性计算和实验

本文用能量法和差分法对网架结构球节点(闭合的完全球壳),进行了弹塑性变形分析和塑性极限分析。用塑性形变理论获得了可以计算受环状集中载荷作用下球壳的弹塑性变形发展情况的方法,并得到较简单的有限形式的极限载荷公式。本文按实际工程尺寸进行了18个钢球壳受环状集中载荷作用的弹塑性实验,并将实验结果与理论计算结果进行了比较和讨论。实验结果与理论分析符合较好。     

考虑损伤效应的开孔浅球壳的非线性动力响应与动力屈曲

研究损伤对开孔浅球壳非线性动力响应与动力屈曲的影响.基于Talreja张量内变量损伤模型,建立了纤维增强复合材料板壳弯曲问题的损伤本构关系,导出了考虑损伤效应的具轴对称变形正交各向异性开孔浅球壳的非线性运动控制方程.对未知函数在空间域采用正交点配置法离散,时间域采用Newmark-β方法离散.数值结果表明,由于损伤导致结构刚度不断削弱,结构振幅增大而频率减小,结构的动力临界屈曲载荷降低.     

Bingham 流体中蛋白质气泡动力学特性研究

根据粘弹性蛋白质气泡有限变形的应力方程,利用Bingham流体的本构关系,得到Bingham流体中蛋白质气泡在内外压力差、弹性有限变形应力及粘性耗散产生的应力共同作用下内径的非线性振动方程.运用数值方法求解该方程,对蛋白质气泡有限变形的振动特性进行分析.研究了流体的静压力、Bingham流体的特性参数、蛋白质膜的粘弹性对蛋白质气泡振动特性的影响.结果表明,蛋白质气泡膜的振动具有非线性特性,降低气泡内外的压力差,振幅减小,振幅随时间衰减变慢,振动频率降低,平衡时气泡变形小,变形达到平衡时所需的时间也相对较短;增加Binghain流体的塑性粘度会使振幅衰减速度加快,频率降低,平衡时气泡变形小;增加蛋白质膜的粘弹性会抑制气泡的振动,增强气泡承受载荷的能力.     

内含弹性介质功能梯度压电球壳的径向振动调控

针对内含弹性介质的功能梯度压电球壳的径向振动问题,利用变量替换技术,求得了解析解。该解适用于材料参数沿厚度按幂律变化且密度的梯度指标可与其它物理量的梯度指标不同的功能梯度压电球壳,克服了以往分析中所有材料参数梯度指标均假设为相等的局限。数值结果表明,功能梯度压电球壳的径向振动特性可利用材料参数梯度指标和内部弹性介质的刚度进行有效调控。     

Dynamical formation of cavity in a composed hyper-elastic sphere

The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile land was obtained. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.     

Poynting oscillations of a rigid disk supported by a neo-Hookean shaft

Simultaneous axial and torsional oscillations of a rigid disk attached to an elastomeric shaft are investigated. Five cases are solved exactly. The uncoupled, small amplitude axial and torsional oscillations of the disk are investigated for neo-Hookean and Mooney-Rivlin shafts with static stretch. The finite torsional vibration of the load superimposed on a static stretch of the shaft is studied for the Mooney-Rivlin model. Solutions for both small and finite amplitude, uniaxial vibrations of the body superimposed on a pretwisted neo-Hookean shaft with static stretch are derived. Simple bounds on the period for the finite motion are provided; and various universal frequency relations for neo-Hookean and Mooney-Rivlin materials are identified.Finally, the main problem of finite, uniaxial vibrations accompanied by a small twisting motion is studied for the neo-Hookean model. The exact periodic solution for the axial response is obtained; and the coupled, small torsional motion is then determined by Hill's equation. A stability criterion for the Mathieu-Hill equation is used to obtain stability maps in a physical parameter space. Geometrical conditions sufficient for universal stability of the motion are read from this graph. Instability of the torsional oscillation, the beating phenomenon and exchange of energies, and the relation of the stability diagram to amplitude bounds on the uncoupled, linearized motion sufficient to assure universal stability predicted for small amplitude vibrations, are discussed and described graphically with the aid of a numerical model. It is shown that an unstable configuration may be stabilized by increasing the diameter of the disk.     

单轴拉伸过程中双相不锈钢局部微观变形行为的细观力学有限元分析

针对双相不锈钢中奥氏体相和铁素体相分别展开了纳米压痕实验,并通过有限元反演得到两相各自的拉伸应力-应变关系,利用Voronoi Tessellation法生成代表性的微结构体积单元,对双相不锈钢的单轴拉伸行为进行了有限元仿真和模拟,研究了双相不锈钢在拉伸过程中的局部应力、应变分布和演化规律．结果表明,利用Voronoi Tessellation法建立单元模型,结合本文通过纳米压痕实验获取的两相力学性能参数,可以很好地模拟双相不锈钢的整体单拉行为,奥氏体比铁素体软,拉伸载荷下双相不锈钢的应变集中在奥氏体中,应力集中在铁素体中;局部应力应变的分布特征与两相分布特征和晶粒形状有关,最大应变值主要集中在奥氏体晶粒狭长且尖锐的区域,而最大应力则主要发生在铁素体晶粒狭长和尖锐的区域;对于奥氏体和铁素体晶粒占比相当的双相不锈钢,其虽然可以具有较为综合的宏观力学性能,但是其微观应力集中的区域和应力最大值相对较大．研究成果为进一步揭示双相不锈钢局部失效机理奠定了基础．     

Finite amplitude,horizontal motion of a load symmetrically supported between isotropic hyperelastic springs

The undamped, finite amplitude horizontal motion of a load supported symmetrically between identical incompressible, isotropic hyperelastic springs, each subjected to an initial finite uniaxial static stretch, is formulated in general terms. The small amplitude motion of the load about the deformed static state is discussed; and the periodicity of the arbitrary finite amplitude motion is established for all such elastic materials for which certain conditions on the engineering stress and the strain energy function hold. The exact solution for the finite vibration of the load is then derived for the classical neo-Hookean model. The vibrational period is obtained in terms of the complete Heuman lambda-function whose properties are well-known. Dependence of the period and hence the frequency on the physical parameters of the system is investigated and the results are displayed graphically.     

爆炸载荷特征参数对无限长圆柱壳弹性动态响应的影响

采用含有三角脉冲载荷和准静压载荷的爆炸载荷加载,利用单自由度模型对无限长圆柱壳体（即等效平面应变圆环）的弹性动态响应进行了力学分析,获得了径向位移响应解析解及准静压阶段弹性响应振幅的解析解。基于所得解析解,通过控制变量法分析了载荷压力及载荷分界点时刻（即三角脉冲载荷与准静压载荷作用的分界点时刻）对径向位移最大值、准静压阶段弹性响应振幅的影响规律,更加深入地研究了爆炸载荷对结构响应的影响。本文主要从准静压幅值与三角脉冲峰值的比值以及载荷分界点时刻两个主要特征参数入手,结合结构的呼吸振动频率来研究爆炸载荷对无限长圆柱壳弹性动态响应的影响。在研究中发现存在临界时刻:当载荷分界点时刻早于临界时刻时,径向位移最大值出现在准静压阶段;当载荷分界点时刻晚于临界时刻时,获得了便于直观判断径向位移达到最大值时所处载荷阶段的分区图。基于前述解析解的分析,还获得了不同影响因素导致的振幅变化的单调性分区图,便于判别载荷压力的变化所致的准静压阶段振幅的增减趋势。通过研究获得的爆炸压力载荷对结构响应的影响规律,可为爆炸容器设计以及结构防护基础研究提供参考。     

风机叶片涂层雨蚀研究

研究了风电叶片在雨水冲击下的失效过程,利用有限元方法建立雨水冲击的数值模型,分析了雨滴的冲击角度、直径、涂层性能等对涂层受力的影响,并对双雨滴及四雨滴耦合模型进行了研究。结果表明:风雨耦合流场中叶片最大载荷在叶尖处,涂层的冲击受力与雨滴冲击角度和雨滴直径的大小呈正相关。低模量涂层能大幅降低涂层受冲击时的拉伸应力,小幅增加其压缩应力。同一平面内的双雨滴耦合时,拉伸应力受影响的范围较大,压缩应力受影响的范围较小。不同高度差下的双雨滴耦合中,随着高度差的增大,材料拉伸和压缩应力都呈现先增后减的趋势,其中压缩应力随高度差的变化幅度明显大于拉伸应力。四雨滴耦合时压缩应力对间距的变化更加敏感。涂层失效的过程主要为:涂层表面拉应力疲劳产生微裂纹;液压渗透引起裂纹扩展,涂层质量减少,表面粗糙度增加;表面小范围破坏后形成的凹面结构促进涂层的失效。     

气管的非线性弯曲力学性能研究1)

研究了人工气管和生物气管拉伸和弯曲的力学性能及仿真方法。根据气管拉伸实验数据,拟合建立了人工气管的线弹性和生物气管的非线性幂函数本构模型,其与实验的最大误差为18.8%。根据非线性弯曲理论,建立了气管大变形的弯曲变形方程,并得到了其解析解,计算的弯曲载荷与实验的最大误差为8.7%。基于显式有限元法提出了气管弯曲变形的有限元仿真方法,犬气管的弯曲角度的有限元计算结果与实验的误差为3%。     

Accurate Higher-Order Analytical Approximate Solutions to Large-Amplitude Oscillating Systems with a General Non-Rational Restoring Force

A new approximate analytical approach for accurate higher-order nonlinear solutions of oscillations with large amplitude is presented in this paper. The oscillatory system is subjected to a non-rational restoring force. This approach is built upon linearization of the governing dynamic equation associated with the method of harmonic balance. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. This approach also explores large parameter regions beyond the classical perturbation methods which in principle are confined to problems with small parameters. It has significant contribution as there exist many nonlinear problems without small parameters. Through some examples in this paper, we establish the general approximate analytical formulas for the exact period and periodic solution which are valid for small as well as large amplitudes of oscillation.     

Bending of corrugated thick rectangular plates

An approximate analytical solution describing the bending of hinged corrugated thick plates is obtained using the second variant of the boundary shape perturbation method and taking into account the first three approximations. The effect of the shape of the boundary surfaces in the zone of maximum external load on the magnitude and nonlinear variation of the displacements and stresses throughout the thickness of a corrugated thick plate depending on the corrugation amplitude and spatial frequency is analyzed. The results are compared to the exact solution for a flat plate