非线性变形对大范围平面运动梁动力学特性的影响

根据柔性梁的几何非线性变形理论,从连续介质的力学原理出发,针对大范围运动的平面柔性梁,考虑了弯曲的非线性因素对横向变形的影响,得到了较为精确的变形模式。利用Lagrange方程建立了非线性变形模式下的动力学方程。仿真算例说明横向变形的非线性因素会对柔性梁的变形位移产生影响。     

基于二次摄动法的SMA层合梁非线性自由振动分析

为对SMA(形状记忆合金)层合梁的非线性自由振动进行分析,使用Brison一维本构模型描述SMA的力学特性,基于不同剪切函数和Von Karman大变形理论,建立梁质点位移与应变之间的关系,使用Hamilton变分原理,获得在弹性地基上两端简支SMA层合梁的动力学方程并进行无量纲处理。使用二次摄动法获得SMA层合梁的非线性自由振动方程。研究不同SMA体积分数、预应变、SMA铺设角度、温度变化对非线性振动的影响。     

基于Total-Lagrange法SMA管接头的有限元分析

基于非线性连续介质力学的有限变形理论和Total-Lagrange增量方法,考虑到形状记忆合金材料(SMA)的强物理非线性,推导了适用于有限元计算的虚功方程和增量型本构方程,并相应编制了考虑物理非线性和有限变形的增量有限元程序,特别讨论了计算中应注意的问题和处理方法。最后采用该方法模拟SMA管接头的工作过程,研究了影响接触应力、扩孔载荷、加热温度等的几个因素。     

热-机载荷下形状记忆合金梁的力学模型及其求解

在现有的形状记忆合金(Shape memory alloy,SMA)简化模型的基础上,结合温度与相变临界应力的关系,从应变角度出发,提出一种形式简单、物理意义更加明确且能反应SMA在热-机载荷下力学行为的分段线性模型。基于Bernoulli-Euler梁理论,利用SMA分段线性模型,建立SMA梁非线性弯曲过程中弯矩与曲率关系的力学模型。结合SMA梁力学模型,设计一套简便易行的求解流程,分别对纯弯曲和受均布载荷的简支梁进行数值求解,分析梁截面上应力分布、弯矩与挠度关系、记忆因子的变化等。结果显示建立的SMA分段线性模型能有效描述热-机载荷下SMA的力学行为,可建立简单有效的SMA结构的力学模型,更便于工程应用和理论分析。     

形状记忆合金驱动梁的变形分析及试验研究

将预拉伸的形状记忆合金 (Shapememoryalloy ,简称SMA)薄片作为驱动器 ,粘贴在构件表面。加热SMA ,当其发生相变时 ,会产生很大的恢复力 ,驱动构件发生变形。建立了粘有SMA薄条应变驱动器的简化机翼—梁的力学模型 ,分析了单边粘贴SMA梁的压弯复合变形 ,给出了其应变分布及弯曲变形的解析表达式。同时通过试验对理论结果进行了验证。     

计及非线性变形的空间自由旋转梁有限元模型

根据柔性梁的几何非线性变形理论,针对大范围运动的空间柔性梁,在考虑了弯曲和扭转的非线性因素对3个变形方向的影响的基础上,利用有限元方法进行离散,得到了较为精确的变形模式。利用Lagrange方程建立了非线性变形模式下的动力学方程,该方程包含了较为完全的刚度矩阵和各种耦合项。对一带有扭转弹簧的中心体-空间柔性梁结构进行仿真计算,说明变形耦合在横向变形中的作用不可忽视。     

NiTi形状记忆合金弹簧电热驱动特性

测定了 Ni Ti形状记忆合金弹簧在电热作用下的动态回复变形速度和电阻的特性曲线。结果表明 ,电流是影响 SMA弹簧电热驱动性能的主要因素 ,通过选择合适的电流可控制 SMA弹簧的回复变形过程。     

计及非线性变形的刚-柔耦合动力学建模

考虑变形产生的几何非线性效应对运动柔性梁的影响，在柔性梁的纵向、横向变形位移中均考虑横向弯曲以及轴向伸缩的耦合作用，从非线性应变-变形位移的原理出发，说明增加耦合变最后，剪应变为零，由此得出的变形模式更符合工程实际和简化需要。并采用有限元离散，通过Lagrange方程导出系统的动力学方程。最后对一带有中心体的柔性梁，在大范围运动为自由和大范围运动为已知两种情况下进行仿真计算，结果表明，在结构有初始变形的情况下，仅在纵向变形中计及变形二次耦合量的一次动力学模型，与考虑完全几何非线性变形的文中模型具有一定的差异。     

功能梯度形状记忆合金纳米梁力学性能研究

功能梯度形状记忆合金(Functionally Graded Shape Memory Alloys, FG-SMA)兼具功能梯度材料和形状记忆合金的双重特性,故在航空航天、生物医疗、微机电系统(Micro Electro Mechanical System, MEMS)中得到了广泛的应用。当微结构尺度达到纳米尺度,表面效应对微结构力学性能的影响是十分显著的。为了探究表面效应对功能梯度形状记忆合金纳米梁力学性能的影响规律,基于梁弯曲理论及Gurtin-Murdoch表面弹性理论,考虑拉压不对称、温度对FG-SMA纳米梁的影响,建立了考虑表面效应的FG-SMA纳米梁相变力学模型。分析了梯度指数、载荷、温度及拉压不对称系数对FG-SMA纳米梁力学性能的影响规律。研究表明,弯矩、梯度指数对截面响应影响显著,而温度和拉压不对称系数对其影响较小;忽略表面效应的影响会低估FG-SMA纳米梁的抗弯性;在弯矩达到一定程度后,表面效应对FG-SMA纳米梁中性轴偏移趋势影响不大。研究结果对FG-SMA纳米梁在微机电领域的设计及应用提供了一定的基础与依据。     

含形状记忆合金(SMA)层柔性梁的振动频响特性

主要研究具有形状记忆合金（shape memory alloy,SMA）层的梁结构的动力响应特性，重点分析了应力诱发马氏体相变的影响。首先采用SMA超弹性分段线性的应力－应变模型表示SMA的超弹性本构特征；其次借助有关粘弹性材料结构动力学分析的复模量方法，推出简谐激励作用下SMA层的面内变形和应力之间的关系，提出具有SMA表层的简支梁横向稳态频率响应求解的数学模型。SMA超弹性非线性的影响使得结构产生复杂的动力学特征，如存在多值稳态解、跳跃性、周期3响应等。上述现象的发生与激振力幅值、温度的变化密切相关。     

基于有限段方法的SMA扭转驱动器柔性机构动力分析

柔性机构的动力学分析是柔性机构学研究的重要课题,柔性部件的变形对系统的安全性和可靠性有直接的影响。针对SMA柔性扭转驱动器的梁式柔性构件的特点,应用有限段的方法建立了其离散分析模型。充分利用ADAMS软件在多体系统动力学分析上的优势,应用ADAMS宏命令建立了SMA柔性扭转驱动器的有限段离散模型,将柔性机构的动力学问题转化为多刚体动力学问题,从而实现对柔性机构动态特性的分析。     

Finite Element Method on Shape Memory Alloy Structure and Its Applications

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy(SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software.This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation.Two scalars,named by phase-transition modulus and equivalent stiffness,are defined to make it easy to establish and implement the finite element method for a SMA structure.An incremental constitutive equation is developed to formulate the relationship of stress,strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness.A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus,stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition.A finite element equation is established to express the incremental relationship of nodal displacement,external force and temperature change in a finite element discrete structure of SMA.The incremental constitutive equation,phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure.Two SMA structures,which undergo large and uneven deformation,are numerically simulated by the supposed finite element method.Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation,and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.     

基于ANSYS的三闭式SMA混杂复合材料箱型薄壁梁的模态分析

采用有限元分析软件ANSYS对SMA混杂复合材料箱型薄壁梁进行了模态分析。首先建立了SMA混杂复合材料箱型薄壁梁的有限元模型，运用ANSYS软件中的Material Designer模块建立SMA/石墨/环氧树脂复合材料模型并获得其材料参数，通过ANSYS复合材料ACP模块对复合材料箱型薄壁梁进行铺层，然后对SMA混杂复合材料箱型薄壁梁进行模态计算，讨论了配置方式、铺层角度、宽高比、单层SMA体积含量、SMA安装位置对固有频率的影响。     

Modeling and free vibration behavior of rotating composite thin-walled closed-section beams with SMA fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy(SMA) fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton’s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin’s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.     

Deformation by moving interfaces from single crystal experiments to the modeling of industrial SMA

Microstructure-based micromechanics models have to be developed in order to successively predict complex thermomechanical behaviors of shape-memory alloys (SMA). However, a proper implementation of the deformation mechanism—motion of internal interfaces in solid state—into the micromechanics models of SMA polycrystals is very important. In this work, experimental characteristics of the deformation mechanism surveyed from literature data obtained from uniaxial loadings of SMA single crystals are summarized. Original results of thermomechanical tension/compression loading experiments on CuAlNi and CuAlZnMn single crystals and CuAlZnMn polycrystals are also reported. Oriented single crystals may transform into different martensitic phases under various orientations of the uniaxial loading axes and sense of the applied stress. This phenomenon is called martensite formation anisotropy and possible consequences for thermomechanical behaviors of CuAlZnMn polycrystals are suggested.     

含SMA约束层的复合材料矩形板的阻尼能力分析

研究由形状记忆合(shape memory alloy，简写为SMA)SMA约束层、SMA纤维混杂叠层材料构成的复合材料矩形板的阻尼性能。采用多胞模型和细观力学阻尼分析方法，分别预测叠层复合材料单层的弹性性能和阻尼性能，在叠层材料中计入横向剪切变形的影响。在导出矩形板的应变能和耗散能的基础上，根据最大应变能理论建立板的模态阻尼比的数学表达式。数值结果表明，文中提出的含有SMA约束层的SMA纤维叠层复合材料的集成阻尼设计方法，是一种有效的阻尼增强方案。     

SMA柔性扭转驱动器的结构设计与优化研究

设计了一种基于柔性结构的SMA扭转驱动器,通过加热SMA丝收缩带动柔性结构变形从而实现驱动器的扭转输出。柔性结构在SMA丝拉力作用下的变形情况对驱动器的转角输出有很大的影响,为获得最大的输出转角,需对柔性结构的形状和SMA丝的作用点位置进行优化设计。采用三次B样条曲线描述柔性结构的形状,通过有限元法分析柔性结构的变形,并应用遗传算法进行柔性结构的形状优化和SMA丝作用点位置优化。实际算例表明,利用优化方法可快速有效地获得使SMA柔性扭转驱动器输出转角最大的柔性结构形状与SMA丝作用点位置。     

FRP 层压复合梁结构屈曲变形在线监测方法

为了实现梁结构屈曲变形在线监控,提出了一种FRP层合梁屈曲变形重构方法。首先,依据高阶剪切变形理论,提出了一种复合梁结构变形场描述方法,并基于冯卡门应变梯度理论,推导出了中性轴应变表述方式。然后,利用最小二乘变分法建立了位移重构模型。其中,利用四次B-样条基函数构造了屈曲变形位移插值函数,推导了理论中性轴应变计算公式。并基于少量应变测量,提出了非线性项应变解耦方法,建立了测量应变与实测中性轴应变转换关系。最后,为了验证所提方法的精确性,以25层碳纤维复合梁为样件,搭建固定-简支梁试验平台,对其进行数值计算和试验论证。结果表明,建立的屈曲变形重构模型在不同轴向载荷作用时,位移场重构误差均小于8%。     

Residual deformation of active structures with SMA actuators

In this paper, a three species thermomechanical constitutive model for Shape Memory Alloy (SMA) actuators, based on previous work by Boyd and Lagoudas (Proceedings of the 4th International Symposium on Plasticity and its Current Applications, Baltimore, MD, 19–23 July, 1993) is developed. The three species that contribute to the specific free energy of SMA are: self-accommodated martensite, detwinned martensite and austenite. The total martensitic volume fraction is decomposed into two parts: self-accommodated and detwinned martensite. The dissipation potentials, utilized for the evolution of the volume fractions of the two parts of martensite, are explicity given for 1-D. The concept of critical stress associated with detwinning of self-accommodated martensite, is introduced to incorporate the observed phenomenon during cooling of SMA actuators. The constitutive model described above is well suited for applications in active structures, because the maximum amount of the detwinned martensitic volume fraction is related to the current stress and temperature of the SMA actuator. This maximum amount of volume fraction can be reached during cooling in a constrained structural environment and is determined by the evolution of the internal variables. A prototype structural example, which is a flexible cantilever beam with an externally attached SMA actuator, is used to demonstrate the capability to predict the residual deformation and stress upon cooling.