形状记忆合金纤维复合材料薄壁梁的主动变形模型

提出具有变形主动驱动作用的SMA纤维混杂复合材料单闭室薄壁截面梁的力-位移本构关系模型。基于变分渐进法导出具有SMA主动纤维的复合材料薄壁空心梁的二维截面刚度系数以及截面内力（矩）与位移（转角）关系方程,含SMA纤维层合板材料性能由混合率进行预测。基于Tanaka的SMA应力应变关系以及Lin的线性相变动力模型,导出了SMA诱发的轴力、扭矩与弯矩的数学表达式。由本文建立的具有拉伸-扭转-弯曲静变形耦合的一般公式出发,讨论周向均匀刚度配置以及周向反对称刚度配置特殊情形,并给出了简化的本构方程。在不考虑SMA纤维含量和温度变化的情况下,本文的模型可以退化为普通纤维复合材料单闭室薄壁截面梁的已有结果。通过数值计算揭示了SMA对弯曲-扭转静变形特性的作用规律,分析了SMA纤维含量与初始应变、驱动温度和复合材料铺层角的影响。     

旋转SMA纤维混杂复合材料薄壁梁的自由振动

研究具有SMA主动纤维的旋转复合材料单闭室薄壁截面梁的耦合自由振动问题.基于Hamilton原理并结合SMA纤维复合材料薄壁梁的二维截面内力(矩)与位移(转角)关系方程,导出旋转单闭室截面薄壁复合材料梁的1D耦合自由振动分析模型.该模型还考虑薄壁梁调矩角和预锥角的作用.采用Galerkin法求解振动模型,获得梁耦合振动...     

复合材料单闭室薄壁梁弯曲与扭转分析

本文主要讨论复合材料单闭室薄壁梁的弯曲与扭转，重点研究横向剪切和限制翘曲的影响。在复合材料薄壁梁弯曲与扭转经典分析理论的基础上，建立了一种能够考虑横向剪切和限制翘曲影响的复合材料单闭室薄壁梁弯曲与扭转分析方法。     

考虑约束扭转的薄壁梁单元刚度矩阵

推导了薄壁空间梁单元刚度矩阵 ,考虑了双向弯曲及截面约束扭转对杆件轴向变形的影响 ;计算了截面的翘曲变形 ,以及二次剪应力对翘曲变形的影响 ,可适用于任意截面 (包括开口、闭口和混合剖面 )的薄壁杆件。计算结果表明 ,考虑约束扭转的薄壁梁单元刚度矩阵有相当好的精确度 ,可以用于薄壁杆件的静动力分析。     

Further discussion on the effect of shear deformation on structure displacement in structural mechanics

剪切变形对位移的影响程度,不仅取决于高跨比,截面形式对其影响也较大. 通过实例讨论了工程中广泛采用的三种形式截面：一般截面、薄壁型截面、复合材料截面. 分析表明：（1） 相较于一般截面形式,薄壁型截面梁中剪切变形对位移的影响较大,尤其是短而高的薄壁梁,剪切变形引起的位移更不能忽略. （2） 复合材料截面梁,剪切变形引起的位移受截面材料弹性模量比、不同材料截面高度比影响较大：截面材料弹性模量比越大,加强材料越厚,剪切变形对位移的影响越大. 这会导致复合材料截面,即使是细长的梁,剪切变形引起的位移有时也不能忽略.     

对结构力学中“剪切变形对位移的影响”的进一步探讨

剪切变形对位移的影响程度,不仅取决于高跨比,截面形式对其影响也较大.通过实例讨论了工程中广泛采用的三种形式截面:一般截面、薄壁型截面、复合材料截面.分析表明:(1)相较于一般截面形式,薄壁型截面梁中剪切变形对位移的影响较大,尤其是短而高的薄壁梁,剪切变形引起的位移更不能忽略.(2)复合材料截面梁,剪切变形引起的位移受截面材料弹性模量比、不同材料截面高度比影响较大:截面材料弹性模量比越大,加强材料越厚,剪切变形对位移的影响越大.这会导致复合材料截面,即使是细长的梁,剪切变形引起的位移有时也不能忽略.     

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Newm ark-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.     

薄壁杆系结构的梁元分析模型

本文导出了用于薄壁杆系结构弹性分析的薄壁梁元分析模型，在空间梁元分析模型^[3]的基础上，采用了一种改进的位移模式，考察了薄壁杆件可能发生的拉压，剪切，弯曲，扭转和翘曲等各变形形式以及它们的耦合效应，得出了相应的单元形函数，同时从工程应变的定义出发，采用Taylor级数展开的方法，建立了单元的五阶近似正交变表达式，并建立了相应的薄壁单元刚度方程，从而得出了局部坐标系下单元刚度矩阵的显式，根据本文所导出的薄壁梁元分析模型，编制了相应的结构计算程序，通过算例验证了本文所推导的单元刚度矩阵，同时通过与传统空间梁元计算模型计算结果的比较，阐述了截面翘曲对薄壁杆系结构的影响。     

DNA纳米管的扭转刚度模型

刚度是衡量材料弹性变形难易程度的一个定量表征参数,与DNA纳米管静动力学特性及其结构生物功能密切相关．本文致力于研究DNA纳米管的扭转刚度．首先,在六角形均匀封装条件下,考虑到单个DNA杆件弯扭组合问题的静不定特点,我们利用平衡方程、变形协调方程和弹性本构方程,合理预测了DNA纳米管扭转实验中单个DNA杆件的弯扭组合变形,由此给出了DNA纳米管扭转刚度预测的解析模型．最后的结果表明：随着DNA杆数的增加,DNA纳米管的弯曲刚度显著增加,而其扭转刚度却几乎不变,合理解释了扭转实验中发现的现象．有关结论为DNA折叠结构的设计和应用提供了参考．     

非线性薄壁复合曲梁广义变分原理之研究

应用拉氏乘子法建立了两端边界均为完全约束的复合材料自然弯曲闭口薄壁细长梁大位移变形弹性理论的非完全广义变分原理的泛函￣［１，２］，其中考虑了对叠层复合材料变得敏感的横向剪切变形以及和扭转有关的翘曲变形的影响，分析中还包括了拉压、弯曲和扭转的相互耦合。由泛函驻值条件可以导出所给问题的平衡方程及全部边界条件。上述方法还可以方便地推广到其它各种非完全约束边界的情况。此外，广义变分原理建立也有助于扩大有限元法和其它近似方法在薄壁复合曲梁中的应用。     

SMA纤维混杂层合梁的材料阻尼

研究一类由形状记忆合金（SMA）和普通纤维混杂而成的层合梁的阻尼特性,基于最大应变能理论提出SAM混杂层合梁的等效材料阻尼预测的数学模型,其中,单层材料的弹性性能和阻尼性能分别采用多胞模型及其阻尼细观力学分析模型确定,利用正交各向异性层合梁的铁木辛柯理论分析梁的变形,通过数值算例分析了SMA含量,纤维铺设角对梁的等效阻尼比的影响。     

Modeling for piezoelectric-shape memory alloy composites

A new concept of a piezoelectric ceramic/shape memory alloy (SMA) composite is proposed with aim of using this as a new actuator material with fast actuation speed and large strain. To prove the new concept, a new model is constructed based on Eshelby formulation where linear piezoelectric constitutive equations and bi-linear superelastic equations of SMA are used. The predictions of the strain induced by applied stress and electric field are made for two simple designs of piezo–SMA composites, 1-D series and 1-D parallel laminated composites. The proposed model indicated that 1-D parallel laminate provides the highest strain induced under bias stress and applied electric field among other composite geometries.     

Micro–macro analysis of shape memory alloy composites

The aim of the paper is to develop a micro–macro approach for the analysis of the mechanical behavior of composites obtained embedding long fibers of Shape Memory Alloys (SMA) into an elastic matrix. In order to determine the overall constitutive response of the SMA composites, two homogenization techniques are proposed: one is based on the self-consistent method while the other on the analysis of a periodic composite. The overall response of the SMA composites is strongly influenced by the pseudo-elastic and shape memory effects occurring in the SMA material. In particular, it is assumed that the phase transformations in the SMA are governed by the wire temperature and by the average stress tensor acting in the fiber. A possible prestrain of the fibers is taken into account in the model.Numerical applications are developed in order to analyze the thermo-mechanical behavior of the SMA composite. The results obtained by the proposed procedures are compared with the ones determined through a micromechanical analysis of a periodic composite performed using suitable finite elements.Then, in order to study the macromechanical response of structural elements made of SMA composites, a three-dimensional finite element is developed implementing at each Gauss point the overall constitutive laws of the SMA composite obtained by the proposed homogenization procedures. Some numerical applications are developed in order to assess the efficiency of the proposed micro–macro model.     

SMA长纤维铝基复合材料的热力学性能

从作者建立的增量型的SMA本构关系出发 ,借助于细观力学的方法 ,推导出了新的长纤维SMA复合材料的增量型细观本构模型 ;应用此模型分析了该复合材料的在循环热载作用下的力学性能 ,尤其是计算了复合材料在不同条件下残余应力的变化 ,这对智能复合材料的设计提供了很大帮助。     

Force-displacement characteristics of simply supported beam laminated with shape memory alloys

As a preliminary step in the nonlinear design of shape memory alloy(SMA) composite structures,the force-displacement characteristics of the SMA layer are studied.The bilinear hysteretic model is adopted to describe the constitutive relationship of SMA material.Under the assumption that there is no point of SMA layer finishing martensitic phase transformation during the loading and unloading process,the generalized restoring force generated by SMA layer is deduced for the case that the simply supported beam vibrates in its first mode.The generalized force is expressed as piecewise-nonlinear hysteretic function of the beam transverse displacement.Furthermore the energy dissipated by SMA layer during one period is obtained by integration,then its dependencies are discussed on the vibration amplitude and the SMA’s strain(Ms-Strain) value at the beginning of martensitic phase transformation.It is shown that SMA’s energy dissipating capacity is proportional to the stiffness difference of bilinear model and nonlinearly dependent on Ms-Strain.The increasing rate of the dissipating capacity gradually reduces with the amplitude increasing.The condition corresponding to the maximum dissipating capacity is deduced for given value of the vibration amplitude.The obtained results are helpful for designing beams laminated with shape memory alloys.     

Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composites

The effects of the inelastic deformation of the matrix on the overall hysteretic behavior of a unidirectional titanium–nickel shape-memory alloy (TiNi-SMA) fiber composite and on the local pseudoelastic response of the embedded SMA fibers are studied under the isothermal loading and unloading condition. The multiaxial phase transformation of the SMA fibers is predicted using the phenomenological constitutive equations which can describe the two-step deformation due to the rhombohedral and martensitic transformations, and the inelastic behavior of the matrix material using the standard nonlinear viscoplastic model. The average behavior of the SMA composite is evaluated with the micromechanical method of cells. It is observed that the inelastic deformation of the matrix due to prior tension results in a compressive stress in the matrix after unloading of the SMA composite and this residual stress impedes the complete recovery of the pseudoelastic strain of the SMA fibers. This explains that a closed hysteresis behavior of the SMA composite is no longer observed in contrast with the case that an elastic behavior of matrix is assumed. The predicted local stress–strain behavior indicates that the cyclic response of matrix is crucial to the design of the hysteretic performance of the SMA composite under the repeated loading conditions.     

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基于形状记忆合金Brinson一维热力学本构关系和von K\'{a}rm\'{a}n几何非线性薄板理论,研究了径向嵌入SMA丝复合材料加热圆板在横向均布 机械载荷作用下的弯曲响应, 获得了周边不可移简支和夹紧圆板的中心最大挠度与升温之间的关系曲线. 结果表明,形状 记忆合金丝在从马氏体向奥氏体的逆相变过程中所产生的相变回复力对板的弯曲变形具有明 显的调整作用. 通过嵌入SMA纤维丝和施加升温载荷可以主动而有效地调节受机 械载荷作用圆板的弯曲变形.     

Nonlinear finite element analysis of shape memory alloy (SMA) wire reinforced hybrid laminate composite shells

This study introduces a non-linear finite element analysis approach to the procedure of modeling hybrid laminate composite shells with embedded shape memory alloy (SMA) wire subjected to coupled structural and thermal loading. Numerical analyses of SMA wire reinforced composite laminates were carried out by synergizing the non-linear laminate shell element with Brison's model of the SMA constitutive law. To verify the proposed procedure, the present illustrative applications involve rectangular laminated panels clamped along one side. Analysis results were compared with corresponding experimental results from a prior study. Several test cases that depend on the volume fraction of SMA, temperature, and ply angles are presented to illustrate the highly entangled thermo-mechanical behavior of shape memory alloy hybrid composites (SMAHCs). The results of the numerical analysis show the ability of the suggested procedure to compute the thermo-mechanical behavior of a SMAHC in accordance with the SMA's internal phase transformations induced by stress and temperature variation and demonstrate very good agreement with experimental results.     

Micromechanics-based constitutive modeling for unidirectional laminated composites

A micromechanics-based constitutive model is developed to predict the effective mechanical behavior of unidirectional laminated composites. A newly developed Eshelby’s tensor for an infinite circular cylindrical inclusion [Cheng, Z.Q., Batra, R.C., 1999. Exact Eshelby tensor for a dynamic circular cylindrical inclusion. J. Appl. Mech. 66, 563–565] is adopted to model the unidirectional fibers and is incorporated into the micromechanical framework. The progressive loss of strength resulting from the partial fiber debonding and the nucleation of microcracks is incorporated into the constitutive model. To validate the proposed model, the predicted effective stiffness of transversely isotropic composites under far field loading conditions is compared with analytical solutions. The constitutive model incorporating the damage models is then implemented into a finite element code to numerically characterize the elastic behavior of laminated composites. Finally, the present predictions on the stress–strain behavior of laminated composite plate containing an open hole is compared with experimental data to verify the predictive capability of the model.     

SMA本构模型及其应用的研究进展

形状记忆合金(SMA)是一类应用前景广阔的智能材料系统, 其最基本的宏观响应特性是在不同温度和应力条件下的相变超弹性和形状记忆特性.近年来, 形状记忆合金本构模型发展迅速, 其在工程结构振动控制领域中的研究和应用也得到了广泛地关注.与此同时, 许多学者将SMA用于当前迅速发展的智能材料结构,发展了一系列SMA复合材料本构模型, 成为目前SMA的应用研究的热点.本文针对形状记忆合金本构模型的发展状况, 首先回顾了近年来常用的和新发展的SMA本构模型, 并根据其包含的力学特点和基本理论将其进行了比较归类, 分析了各类模型特点和适用范围;其次从微/宏观角度介绍了有广阔应用前景的SMA智能复合材料的本构模型的发展状况;接着简要的综述了几类较为实用的SMA本构模型在实现结构的主/被控制、变形控制及结构裂纹诊断与控制等方面的应用现状.最后对目前本构模型的发展趋势、工程应用问题提出了一些看法和展望.