2015级

2015级 博士毕业论文
论文题目：织物增强树脂基复合材料与结构的力学性能研究及多尺度分析
博士研究生：高冀峰
指导老师：陈务军 教授 陆邵明 教授
摘要
随着航天器结构向大型化和轻量化的方向发展，大型空间可展桁架作为航天器的理想支撑结构，逐渐成为航天领域的研究热点。传统机械式空间可展桁架因质量重、展开过程控制环节多等缺点限制了其发展。由织物增强复合材料制备的空间可展桁架以折叠展开机制简单和力学特性优良等特点，在航天工程中具有广阔的应用前景。
本文面向航天领域的前沿需求，以二维仿形织物增强复合材料薄壁管及其制备的新型空间可展开桁架天线作为研究对象。复合材料管中碳纤维增强织物在提高力学性能的同时，其复杂的微观结构导致材料具有拉伸、压缩、剪切、弯曲各向异性的力学特性，同时受树脂基体的影响，表现出较强的温度相关性，这些复杂的力学特性均增加了材料和结构分析的难度。因此，需要针对二维仿形织物增强复合材料薄壁管的力学行为机理和力学模型等科学问题，综合试验途径、固体力学理论和数值分析方法开展研究，以支撑大型空间可展桁架天线总体工程设计应用。
为研究二维仿形织物增强复合材料薄壁管及桁架的力学行为，选择与复合材料管具有相同树脂基体和增强织物的单层织物增强树脂基复合材料(single-ply weave reinforced polymer composite，SpWRPC)，对SpWRPC进行不同温度下的拉伸、压缩、剪切、弯曲和大转角弯折力学特性试验研究。进一步建立从微观纤维、基体层面，细观纱线、晶胞层面至宏观壳元的多尺度方法计算均匀化材料本构，并应用于复合材料管及桁架的计算分析，通过试验对比验证多尺度方法的有效性。论文主要内容包括：
首先，对SpWRPC材料进行了拉伸、压缩、剪切和弯曲试验研究，分析了SpWRPC材料的力学响应和内在联系，并通过显微照片揭示了织物微结构特征及力学机理。针对超薄SpWRPC材料，改进了常规的压缩和剪切试验工装。另一方面，针对复合材料易发生弯折变形的特点，研制了大转角弯折试验工装以研究其弯曲力学性能，分别通过摄影测量和铝合金试件进行了直接和间接标定，验证了工装的有效性。
其次，结合系统的试验方法，研究了SpWRPC材料各力学特性随温度的变化关系。首先应用动态力学分析试验研究了SpWRPC的玻璃态和橡胶态转化温度，结合温度环境箱进行15℃、20℃、25℃、30℃、35℃、40℃和50℃等温拟静态力学试验。应用Correia经验公式对拉伸、压缩、剪切和弯曲材料模量随温度的变化关系进行了表征。结合显微照片和原位测量，揭示了受力工况下复合材料及增强织物的变形机理，及其对材料力学特性的影响。
进一步针对SpWRPC的薄壳形式，增强织物的空间不均匀分布使其具有各向异性的材料力学特性，建立多尺度方法计算其均匀化ABD刚度矩阵。首先进行编织分析确定破斜纹1/3编织方式最小周期编织单元，结合域分解方法建立计算单胞，推导了与ABD刚度矩阵对应的6个标准周期边界条件(periodical boundary condition, PBC)。进一步研究发现非对称织物增强物会导致中性面偏离中间面，若仍选用中间面计算会产生不准确的耦合矩阵。将PBC施加在单胞的中性面计算出均匀化ABD刚度矩阵，从数值模型得到了与试验相一致的变形现象，详细讨论了标准变形下SpWRPC材料的应变场变化规律，并分析了平纹、破斜纹1/3、斜纹1/3织物增强复合材料特性随编织密度的变化关系。
基于宏观壳元本构，针对二维仿形织物增强复合材料薄壁管，推导了考虑材料正交异性本构的等效梁单元。建立整体笛卡尔坐标系和管壁局部坐标系，基于ABD刚度矩阵建立物理方程，依据Kirchhoff假设建立几何方程。采用Lagrange和Hermite形函数描述变形，推导了2节点12自由度等效梁单元的刚度矩阵。通过静力计算对比了壳元构件与梁元构件的拉伸、剪切和弯曲刚度，等效梁单元表现出了较好的计算精度和效率。
最后，分别在12℃、20℃、28℃环境下，研究了二维仿形织物增强复合材料薄壁管在悬臂状态和自由状态的自振频率和振动模态，基于前文提出的多尺度方法，分别建立壳元模型和梁元模型进行对比分析。进一步，结合空间可展开桁架天线的微重力模态试验，基于壳元、梁元模型分别建立单节和五节桁架数值模型，对比试验与模拟结果，验证了多尺度方法的有效性。
本文从微观织物结构和基体层面揭示了SpWRPC材料各向异性力学产生原因及其内在关系，发现了荷载作用下复合材料及增强织物的变形机理，建立了计算均匀化材料特性的多尺度方法并验证了其有效性，为二维仿形织物增强复合材料薄壁管及桁架的工程应用提供了基础性探索和计算方法支撑。
 
关键词：多尺度分析；单层织物增强树脂基复合材料；ABD刚度矩阵；二维仿形织物增强复合材料薄壁管；复合材料梁单元；复合材料空间可展桁架
 
Mechanical Behavior and Multi-scale Analysis of Weave Reinforced Polymer Composite and Structure
 
With the development of the spacecraft structure towards large-scale and lightweight, the large space deployable trusses have gradually become an ideal support platform for spacecraft structures. Conventional mechanical space trusses limit the development of deployable structures due to the weight and multi-process control links. The spatial deployable truss structure made by weave reinforced polymer composite has the advantages of simple deformation mechanism and high mechanical properties, exhibiting great potential application in aerospace engineering.
In this paper, a 2-D imitation forming weave reinforced composite thin-walled pipe and its new space deployable truss antenna are taken as the research object. The addition of a carbon fiber fabric increases the strength and stiffness, while the microstructure makes the composite pipe with anisotropic material properties. Under different temperature conditions, the mechanics properties of composite pipe show strong temperature dependence. To support the design and application of large-scale space deployable truss antenna, it is necessary to study the mechanical behavior and mechanical model of the 2-D imitation forming weave reinforced composite thin-walled pipe by means of comprehensive experimental approach, solid mechanics theory and numerical analysis method.
In order to study the mechanical behavior of 2-D imitation forming weave reinforced composite thin-walled pipe and trusses, the plane composite material with the same polymer and reinforced fabric is first studied. This paper studies the tensile, compression, shear, bending and large-angle bending tests of single-ply weave reinforced polymer composite (SpWRPC) under different temperature environments. A multi-scale method from the microscopic fiber and matrix level, mesoscopic yarn and unit level, to macro shell and beam element level, is designed to advance the analysis capability. The main concerns of this thesis include:
Firstly, the anisotropic material properties of SpWRPC are measured by tensile, compression, shear, bending and large-angle bending tests. The mechanical response and internal relationship of SpWRPC are analyzed. The micro-structure characteristics and mechanical mechanism of the fabric are revealed through the observation of micro-experiments. The conventional compression and shear test equipment are improved. The SpWRPC undergoes large-angle bending during the deformation process. The tooling for large-angle bending test is developed. The validity of the tooling was verified by direct and indirect calibration of photogrammetry and aluminum alloy specimens, respectively.
Secondly, the DMA test is applied to determine the glass transition temperature and the rubber transition temperature. Within the temperature environment chamber, the isothermal quasi-static experiments are performed under the complete temperature range of 15 °C, 20 °C, 25 °C, 30 °C, 35 °C, 40 °C and 50 °C. Correia’s empirical formula is used to characterize the mechanical behaviour of materials as an explicit function of temperature. The deformation mechanism of composites and reinforced fabrics under loading conditions and their effects on the mechanical properties of materials are revealed by combining micro fiber photographs and in situ measurements.
Furthermore, the uniform ABD stiffness matrix is applied to describe the shell stiffness of SpWRPC. Firstly, the geometry of the broken twill 1/3 weave method is analyzed, and ten minimum RUCs are found within the fabric form. The domain decomposition method is used to establish the RVE. Further, the six periodic boundary conditions corresponding to the ABD stiffness matrix are derived in detail. It is found that asymmetric fabric reinforcement causes the neutral plane to deviate from the middle plane. Inaccurate coupling effect will arouse if the intermediate plane is still selected to calculate. The uniform ABD stiffness matrix of SpWRPC is obtained by applying PBC to the neutral plane of RVE. The reasonable deformation and strain distribution of the unit cell are obtained. The multi-scale method is further used to predict the stiffness and modulus of SpWRPC with the forms of reinforced fabrics plain, broken twill 1/3, and twill 1/3.
The space beam elements equivalent to the 2-D imitation forming weave reinforced composite thin-walled pipe is deduced to facilitate modelling and to improve computational efficiency. To consider the orthotropic material properties in the pipe wall, the global Cartesian coordinate system along with the local orthogonal coordinate system on the pipe wall is established to describe the deformation of the beam. The physical equations of the beam are obtained based on the ABD stiffness matrix, and the geometric equation is established according to the Kirchhoff hypothesis. The constitutive equations of thin-walled tubes are obtained by merging the physical equations and geometric equations. The Lagrange shape function is used to describe the longitudinal deformation and torsional deformation, and the Hermite shape function is used to describe the bending deformation. The stiffness matrix of the 2-node 12-degree-of-freedom beam element is derived in detail. The tensile, shear and bending stiffness are compared with shell element model. The equivalent beam element shows good calculation accuracy and efficiency.
Afterwards, the effect of temperature on the vibration characteristics of 2-D imitation forming weave reinforced composite thin-walled pipe is studied. The dynamic mechanical responses of the composite pipe in cantilever and suspension states are measured at 12 °C, 20 °C, and 28 °C, respectively. The numerical model with the shell element and the beam element is compared to the experiment results at 20 °C. The excellent coincidence of the modal shapes and neutral frequencies between the numerical the test results are obtained. The modal shape and the frequencies of truss with a single unit and five units are tested under the microgravity environment. The equivalent FE models are respectively established based on the shell elements and beam elements. The numerical analysis results and test results are discussed in detail.
This thesis reveals the reasons of anisotropic mechanics of SpWRPC material and its intrinsic relationship from the micro fabric structure and matrix level. It finds the deformation mechanism of composite material and reinforced fabric under load. A multi-scale method is established to calculate the properties of uniform material. This thesis provides a basic exploration and calculation method for the engineering application of the 2-D imitation forming weave reinforced composite thin-walled pipe and truss structures.
 
Key words: Multi-scale analysis; Single-ply weave reinforced polymer composite; ABD stiffness matrix; 2-D imitation forming weave reinforced composite thin-walled pipe; Composite beam element; Deployable composite truss structure

论文题目：平面张力膜动力学等效方法与振动特性分析及试验研究
博士研究生：张祎贝
指导老师：陈务军 教授 付功义 教授
摘要
平面张力薄膜结构具有重量轻、面质比高、折叠容易、展开可靠等优点，在航天器结构中有广泛的应用。目前已研制出数十米级的平面张力薄膜结构，并在向公里级的方向发展。这种大尺寸结构的振动特性对空气阻力效应十分敏感，其在地面大气环境中的自振频率将明显低于真空环境下的值。因此，为了得到与太空中真空环境一致的振动特性，在地面振动试验中必须消除空气阻力效应的影响。
为了消除空气阻力效应对结构振动特性的影响，本文提出网格膜等效试验方法。当网格膜的镂空率较高时，其振动过程对周边空气的扰动较小，因此对空气阻力效应不敏感。为了验证上述方案的科学性和可行性，需要深入研究两种结构的动力学特性以及对空气阻力效应的敏感程度。因此，本文首先从理论方面改进了平面张力膜结构的动力学方程，提出了矩形张力膜与网格膜结构的动力学等效准则，并完成了地面大气环境和低真空环境下的对比验证试验。
首先，基于冯·卡门大变形理论建立了平面张力膜结构的非线性动力学方程，通过一阶和二阶精度的泰勒级数展开方法引入大转角项，并建立了自振频率求解方法。同时，对比了理论计算与数值模拟得到的结构大变形振动频率。算例结果表明，按照改进方程计算得到的振动频率与数值模拟差异较小，最大偏差低于16%，且基本不随振幅的增加而增大；若不考虑大转角项，该偏差会随着振幅的增加而逐渐增大，最高可达39%。
其次，分别建立了矩形膜与网格膜的考虑大变形的动力学方程，并进行质量归一化处理，随后按照对应线性、非线性刚度项相等，建立了两种结构的动力学等效准则，可使得两种结构在初始变形为一阶振型时的大变形自振频率基本一致，以及前几阶小变形自振频率基本一致。然后通过数值模拟进行验证，在相同的初始振幅下，矩形膜与网格膜在初始变形为一阶振型时的大变形自振频率基本一致，以及小变形振动下前三阶频率基本一致。
第三，设计研制了一套新型低真空双向张拉平面膜结构模态试验系统，主要包括低真空环境模拟分系统、平面膜结构双向张拉分系统与振动测量分系统。由于试验空间有限，振动测量分系统只配备了4个激光位移计。针对这一情况，提出将FFT（Fast Fourier Transformation）法和SSI（Stochastic Subspace Identification）法结合使用，当观测点数目较少时仍能进行有效的模态识别。
第四，设计制作了平面张力膜和等效网格膜，分别进行了地面大气环境和低真空环境下的振动试验，结果表明：矩形膜在地面大气环境和低真空环境下的振动频率差异极大，低真空环境下振动频率大约是地面大气环境下的3倍；网格膜在地面大气环境和低真空环境下的振动频率则基本一致。同时，按照等效准则设计的矩形膜与网格膜，在小变形振动试验中，测得矩形膜低真空环境下的前3阶频率与地面大气环境下网格膜的结果基本一致；在大变形振动试验中，两种结构的动态响应也基本相同，说明地面大气环境下的网格膜可以作为矩形膜的等效结构进行振动试验，模拟与矩形膜在真空环境下基本一致的动力学特性。
第五，研究了不均匀应力场、空气阻力效应与膜内微气泡膨胀对矩形膜结构模态的影响。通过频率表达式推导、数值模拟与试验，发现当矩形膜的侧边由于斜拉而导致应力场不均匀时，其对结构振动频率的影响很小，但相应振型有差异。同时，通过试验研究了空气阻力效应对双向张拉矩形膜结构振动频率的影响，给出了一个基于附加质量法的经验公式，针对具体结构标定两个参量后，可估计该矩形膜在不同气压和张拉状态下的前3阶振动频率。此外，通过试验发现对于含有微气泡的单向张拉薄膜，当微气泡由于内外压差增大而膨胀时，膜内张力会随之增大。进一步试验发现，这种张力变化能力与试件长度无关，与试件宽度成正比。说明在宏观尺度，这种结构变化基本是一个等应变过程，因此对结构应力场均匀性的影响较小，但对应力场的数值有明显影响。当环境气压降低后，需要重新测定膜内的应力场，再计算结构频率。
最后，对本文的研究成果进行了总结，并指出了今后的研究方向。
 
关键词：平面张力膜；矩形膜结构；网格膜结构；大变形；动力学等效准则；低真空振动试验；模态识别方法；不均匀应力场；空气阻力效应；微气泡
 
DYNAMIC EQUIVALENT METHODOLOGY AND VIBRATION CHARACTERISTIC ANALYSIS FOR PRE-STRESSED PLANAR MEMBRANES: THEORETICAL MODEL AND EXPERIMENTAL VERIFICATION
ABSTRACT
Pre-stressed planar membrane structures are widely utilized in aerospace structures, due to the advantages of light weight, high ratio of area to mass, excellent folding and unfolding capabilities. At present, the size of these structures has reached ten-meter level, and may reach kilometer level in future. The vibration characteristics of these extremely large structures are apparently sensitive to the air damping effect, thus their natural frequency in ground atmospheric environment can be significantly lower than that in vacuum. Therefore, the air damping effect must be eliminated in the ground vibration test to obtain the same vibration characteristics of planar membranes in outer space vacuum environment.
To eliminate the air damping effect, a grid membrane composed of cross-strips is firstly proposed as the alternative structure of rectangular membranes in ground vibration tests. The perturbance to the surrounding air should be small when the hollow ratio of the grid membrane is high enough, thus the grid membrane can be insensitive to the air damping effect. To verify the above scheme, the dynamic characteristics and air damping effect sensitivities of rectangular membranes and grid membranes should be analyzed comprehensively. In this paper, the dynamic equation considering large deformation was firstly improved for planar membrane structures, then the dynamic equivalent criterion of the two structures was proposed subsequently. Finally, a series of experiments in ground atmospheric and low vacuum environments were carried out to further investigate the dynamic performance.
Firstly, the nonlinear dynamic equation of pre-stressed planar membrane structures is deduced based on the Von Karman large deformation theory, and large rotation is taken into account through the Taylor series expansion considering the first or second order series. Meanwhile, the vibration frequencies of rectangular membranes under large vibration amplitudes are compared with the theoretical calculation and numerical simulation. The theoretical result is similar to the numerical simulation when considering the large rotation item. The maximum deviation is less 16%, and is basically stable while the vibration amplitude becomes large. On the contrary, this deviation reaches nearly 39% when not considering the large rotation item. In addition, this deviation increases with the vibration amplitude becoming large.
Secondly, the mass-normalized dynamic equations of rectangular membranes and grid membranes are formulated, then the dynamic equivalent criterion is established by assuming the corresponding linear and nonlinear stiffness items equal. According to this criterion, the frequencies of the two structures under large deformation vibration can be basically same, when the initial displacement of the membrane is set as the first vibration mode. Meanwhile, the first three frequencies of the two structures under small deformation vibration can be identical. The numerical simulation results show that, when the two structures are of the same initial vibration amplitude, the deviation of the frequencies under large deformation vibration is basically same.
Thirdly, an innovative low-vacuum-level biaxial tensioned rectangular membrane modal testing system is developed, which includes three subsystems to realize low-vacuum-simulation-environment, biaxial tensile assembly and vibration measurement, respectively. Due to compartment limited space, the number of the equipped laser displacement sensors is only four, which may result in difficulty for modal identification. Therefore, the Fast Fourier Transformation (FFT) method and Stochastic Subspace Identification (SSI) method are combined for utilization. This method is verified effective to identify the first three vibration frequencies of biaxial tensioned rectangular membranes.
Fourthly, the proposed dynamic equations and equivalent criterion are verified on the basis of a series of tests conducted in both ground atmospheric and low vacuum environments. The results show that the vibration frequency of rectangular membrane in low vacuum is about three times of that in ground atmospheric environment. In contrast, the vibration frequency of the grid membrane in ground atmospheric environment is basically the same as that in low vacuum. Meanwhile, in the small deformation vibration test, the first three frequencies of the rectangular membrane in low vacuum are basically the same as those of the grid membrane in ground atmospheric environment. In the large deformation vibration test, the vibration characteristics of the two structures also exhibit a fine consistency. Consequently, grid membrane can be utilized in the ground vibration test as the alternative structure for rectangular tensile membranes to eliminate the air damping effect.
Fifthly, the influence of non-uniform stress field, air damping effect and micro-bubble expansion on vibration characteristics of rectangular membranes are investigated with the testing system. According to the derivation of frequency formula, numerical and experimental analyses, the uneven stress field from the non-uniform tension is found to have little effect on the membrane frequency, but the relevant vibration modes could be different. Meanwhile, an empirical formula on the basis of the added-mass method is proposed to describe the air damping effect on biaxial tensioned rectangular membranes. This formula needs to calibrate two parameters based on the testing results of a specific rectangular membrane, then can be utilized to predict the first three frequencies of this membrane under different air pressures and tensile states. In addition, if the membrane contains micro bubbles, the micro bubbles would expand mainly out of plane while the internal and external pressure difference increases, resulting in an in-plane contraction and the tension varies accordingly. This tension variation ability is independent on the specimen gauge length and proportional to the specimen gauge width. Therefore, this structural deformation could be assumed as equal-strain, thus could not largely affect the uniformity of the stress field. However, the value of the stress field could be obviously influenced. Therefore, it is necessary to re-measure the stress field before calculating structural frequencies when the ambient pressure decreases.
The research findings are summarized in the final chapter, and future research topics are presented.
 
KEY WORDS: Pre-stressed Planar Membrane, Rectangular Membrane, Grid Membrane, Large Deformation, Dynamic Equivalent Criterion, Low Vacuum Vibration Test, Modal Identification Method, Non-uniform Stress Field, Air Damping Effect, Micro Bubble
 
 
 
论文题目：织物增强形状记忆聚合物复合材料力学行为及本构模型研究
博士研究生：樊鹏玄
指导老师：陈务军 教授
摘要
织物增强形状记忆聚合物复合材料（Fabric Reinforced Shape Memory Polymer Composites, FRSMPCs）具备智能化、高强度、抗分层和大变形等优势，近年在空间可展结构领域成为研究重点。由于大变形、渐进损伤、时温相关性等强非线性，基于形状记忆的折叠和展开过程的力学模型准确建立及其力学行为特征急需深入研究，为FRSMPCs空间可展结构提供理论基础。针对形状记忆聚合物基体和织物增强形状记忆复合材料的本构模型和力学行为，论文主要开展了如下研究：
对基体材料环氧基形状记忆聚合物（Epoxy Shape Memory Polymer, ESMP）进行黏弹性力学性能试验，揭示了材料的黏弹性随温度变化规律和大应变率相关规律。将Neo-Hookean超弹-黏弹性模型中的黏弹性参数设置为温度的连续函数建立准确描述不同温度下ESMP应力松弛过程的本构方程。研究了ESMP在不同应变水平下自由恢复和约束恢复的形状记忆性能，基于热-黏弹性理论，运用Arrhenius方程向超弹-黏弹性本构方程中引入玻璃化转变效应，建立了ESMP的形状记忆本构方程并通过解析计算揭示了黏弹性形状记忆效应的机理。
对单层碳纤维织物增强的FRSMPCs进行动、静力学测试，揭示了材料在不同状态下的刚度和强度特性。基于多尺度有限元方法和ABAQUS二次开发平台编写了均匀化计算程序，实现对FRSMPCs在不同状态下等效刚度的准确预测。采用主应力判定准则建立了拉压异性本构方程，对三点弯曲试验进行了准确的数值模拟，表征了材料的拉压异性特征。
针对弯折试件的渐进损伤问题，运用宏-细观协同多尺度分析（Marco-micro Collaborative Nonlinear Multiscale Analysis, MCNMA）方法，在细观尺度上建立准确考虑FRSMPCs损伤演化的代表性体积元（Representative Volume Element, RVE）模型，对薄板弯折试验实现了准确的模拟预测。针对复合材料构件的渐进损伤问题，为降低MCNMA方法高昂的计算成本，基于连续损伤力学理论向FRSMPCs的刚度矩阵引入损伤内变量描述刚度退化效应，建立了各向异性连续损伤本构方程，准确模拟预测了弯折试件和薄壁圆管结构压扁折叠的渐进损伤过程。
对薄板弯曲试件和薄壁圆管结构的“力-变形-温度”三维演化形状记忆过程进行试验研究，发现材料损伤对形状记忆过程中反弹力的大小有显著影响。以FRSMPCs的连续损伤本构方程为基础，引入随温度变化的存储应变和材料刚度矩阵，建立了考虑损伤的形状记忆本构方程。准确地模拟了薄板弯曲和薄壁圆管结构折叠的形状记忆过程，验证了该本构方程在复杂应力状态和结构问题中的正确性，同时对薄壁长管结构的双重折叠形状记忆过程进行模拟验证了该本构方程在复杂结构中的适用性。
 
关键词：织物增强形状记忆聚合物复合材料；环氧基形状记忆聚合物；黏弹性特征；形状记忆本构方程；等效刚度预测；拉压异性；宏-细观协同非线性多尺度分析；连续损伤本构方程
 
FABRIC REINFORCED SHAPE MEMORY POLYMER COMPOSITES
ABSTRACT
Fabric Reinforced Shape Memory Polymer Composites (FRSMPCs) have recently drawn considerable attentions in the area of space deployable structures due to their elegant performances in intelligence, material strength, delamination resistance and large deformation. Due to the strong nonlinearity caused by the large deformation, the progressive damage and the time-temperature correlation, mechanical behaviors and constitutive models of FRSMPCs need to be comprehensively investigated to provide theoretical basis for space deployable structures. Focusing on the mechanical behaviors and constitutive modeling of FRSMPCs, the main work and corresponding conclusions are thus as follows:
Experiments on the viscoelastic behaviors of the pure matrix Epoxy Shape Memory Polymer (ESMP) are carried out to reveal the temperature influence on the viscoelastic properties and the rate-dependence in large strain regime. A constitutive equation is established to precisely describe the stress relaxation process of ESMP considering temperature influence based on Neo-Hookean hyper-viscoelastic model, where the material parameters are assumed to be functions of the temperature. Shape memory properties of ESMP are experimentally investigated in both free recovery and constrained recovery modes. A shape memory constitutive equation are derived based on the thermo-viscoelasticity, where the glass transition effect is introduced into the hyper-viscoelastic constitutive equation by Arrhenius equation. Based on which, the viscoelastic mechanism of shape memory process are addressed by analytical calculations.
A series of dynamic and static experiments are carried out to investigate the stiffness and strength of FRSMPCs in different states. User subroutines of multiscale homogenization are developed in the ABAQUS environment to predict the equivalent stiffness matrix of FRSMPCs. Highly agreements are reached between the predictions and experimental results. A tension-compression asymptotic constitutive equation is established using the principle stress to judge the tension/compression state, based on which, the bending experiment of FRSMPCs is precisely simulated and the tension-compression asymptotic of FRSMPCs is characterized.
For the progressive damage problem in bending components, a Marco-micro Collaborative Nonlinear Multiscale Analysis (MCNMA) method is utilized to simulate the bending process of FRSMPCs, where the Representative Volume Element (RVE) model that can accurately depict the damage evolution of FRSMPCs is established in the micro scale. For the progressive damage problem in composites structures, in order to reduce the high computational cost in the MCNMA method, a progressive damage constitutive equation of FRSMPCs is proposed based on the Continuum Damage Mechanics (CDM) by introducing the internal damage variables into the stiffness matrix. Bending experiments of FRSMPCs plates and folding experiments of thin-walled tubes are accurately simulated by the constitutive equation.
The 3D evolution of force-deformation-temperature are investigated through the shape memory experiments of bending components and folding tubes, where the damages can significantly influence the value of rebound force. A shape memory constitutive equation of FRSMPCs is established based on the progressive damage constitutive equation, where the stiffness matrix and storage strain are verified with the temperature. Commendable simulation results are obtained by using the constitutive equation to calculating the shape memory experiments of bending component and thin-walled tube. Simultaneously, the dual folding shape memory process of thin-walled long tube structure is also simulated to verify the availability of the constitutive equations in complicated structure problems.
 
KEY WORDS: Fabric Reinforced Shape Memory Polymer Composites, Epoxy Shape Memory Polymer, Viscoelastic Properties, Shape Memory Constitutive Equation, Equivalent Stiffness Matrix Predictions; Tension-compression Asymmetry, Marco-micro Collaborative Nonlinear Multiscale Analysis, Continuum Damage Constitutive Equation


2015 硕士毕业论文
论文题目：共轭互承式结构的有限元结构分析：编织木拱桥的参数化分析
研究生：Madalitso Njobvu
指导老师：陈务军 教授
学科专业：结构工程
摘要
互承结构是由比结构跨度短的刚性梁相互支撑而形成，中国古代的木桁架拱（俗称彩虹桥）从技术上来说，是一种互承结构。
互承结构在古建筑和结构工程中具有广泛的应用价值，因此有必要根据现代结构分析方法和技术要求，掌握互承结构的力学行为，从而理解互承结构本质并推动该结构形式的发展。有限元分析被广泛应用于各种结构分析，但互承结构复杂的几何形状和连接方式导致建模过程消耗大量的劳动成本。
幸运的是，互承结构在很大程度上表现出规则性和重复性，因此可以开发一种快捷的方法来建立模型。本研究的目的是提供通过Python代码实现在有限元软件中高效建模，并将模型参数化的方法，为下一步力学性能分析做准备。
由于二维的互承框架结构较为简单，分析二维计算模型有助于形成对互承结构载荷路径的直观理解。Popovic、Kohlhammer等人在研究互承框架结构的原理后，将互承结构分为三个系统：单杆、基本体系、组合体。二维计算模型的研究能够应用于彩虹桥的结构分析。
八个世纪以来，彩虹桥已经成为中国拱桥文化遗产的重要部分。在没有数值方法、材料力学性能和计算机辅助等高级经验模式的情况下，彩虹桥充分体现了传统工程技术的能力。通过不断试验的错误总结和建筑师的经验，彩虹桥随后产生了一种称为廊桥的变体。本文对虹桥与廊桥的几何构型和施工过程做了简单的比较。
本文使用定制的Python代码建立参数模型，并利用有限元软件ABAQUS对某古代木拱桥进行了有限元分析。拱桥的跨度，高度和宽度被设置为几何参数，并导出不同的模型。用户通过修改Python代码中的几何参数改变跨度、高度和宽度来快速构建模型。
模型中考虑的其它参数包括三个载荷情况。实体单元C3D8和梁单元B12、B13组成的三维实体模型来执行分析。为了验证结果，固体单元模型和梁单元模型的结果与以前的研究中的实验数据进行了比较。
利用梁单元B31和B21分别在三维和二维空间中建立模型。所有节点都被认为是铰接，边界条件为固定在地面上且所有自由度都受到约束。根据木材的实验数据中得到物理力学性能，采用线弹性模型假设，并在ABAQUS中用Python代码模拟正交各向异性材料性质，来精确地模拟木材机械性能。
快速和高效地建立模型能够使研究能够寻求更关切的问题，如具有不同几何参数的模态分析。本文以静态分析为出发点，分析预测了改变参数后的结果，与前人研究的初步结论相吻合。
关键词：彩虹桥; 结构分析; 互承结构; 互承单元; 空间结构; 参数分析; 木建筑史.
 
FINITE ELEMENT STRUCTURAL ANALYSIS OF RECIPROCAL STRUCTURE: PARAMETRIC ANALYSIS OF WOVEN TIMBER ARCH BRIDGE OF SONG DYNASTY
 
Abstract
Reciprocal structures are constituted of mutually supporting rigid beams that are short concerning the span of the whole structure. China’s ancient woven timber arch bridge popularly referred to as Rainbow Bridge is technically a reciprocal structure.
Reciprocal structures are efficient and widely used in ancient architectural and structural engineering endeavors. To understand and promote reciprocal structures, it is indispensable to grasp its structural behavior based on modern structural analysis method and technical requirement. Finite element analysis is extensively used for any kind of structure. Due to high complex geometry and connections, building the model comes at a high labor cost.
Fortunately, reciprocal structures exhibit regular and repetitive form to a large extent, an efficient way to build model could be developed. This research aims to provide a way to write a Python code implemented in FEM software that can efficiently build the model (or models) and can be easily parameterized and made ready for further investigation.
Reciprocal frame structures best understood when analyzed in two-dimensional computational models. The models help build the intuitive understanding of load paths in a reciprocal structure. The principle of reciprocal frames as explored by Popovic, Kohlhammer and others help break down the structure into three systems when analyzing the structural behavior of reciprocal structures namely: single bar, basic and component systems. This understanding from a two-dimensional computational model can be applied in the structural analysis of the Rainbow Bridge.
Over eight centuries, the Rainbow Bridge has been part of China’s heritage of arch bridges. It boasts of engineering competence even at a time when numerical methods, material mechanics and computer-aided advanced modes of empirical inquiry such as FEM where not available nor understood. By trial under error and heavy reliance on the experience of master builders, the Rainbow Bridge has spawned a variation called the Lounge Bridge. A simple comparison between the Rainbow Bridge and the Lounge bridge has been made concerning their geometric configuration and construction history.
A finite element analysis on an ancient timber arch bridge is performed using the FEM software ABAQUS. A parametric model has been established using customized python code. This python code aids the user to quickly build the model by varying the span, height, and width. The span, height, and width are set in as geometric parameters resulting in different models.
Other parameters considered in the model include three load cases, A 3D solid model made up of the solid element C3D8, and two models built using beam elements B12 and B13 to perform the analysis. To validate the results, the solid element model and the beam element models have their respective results compared to experimental data carried out in previous research.
The beam models are created in 3D and 2D space using the B31 and B21 finite elements respectively. All joints are considered as pin joints, and boundary condition is fixed to the ground, all degrees of freedom are constrained. A linear elastic behavior is assumed, and orthotropic material properties were modeled in the python code implemented in ABAQUS to simulate as accurate as possible wood mechanical properties. The physical-mechanical properties are taken from experimental data of wood products.
The ability to be able to build models quickly and efficiently allows the research to pursue more pertinent issues such as Modal Analysis with varying geometric parameters. Static analysis has been performed in this dissertation as a starting point and results predicted after the parametric analysis is done fit the preliminary conclusions previously made in past research.
Keywords: Rainbow Bridge; Structural Analysis; Structural Reciprocity; Mutually Supported Elements; Spatial Structures; Parametric Analysis; Timber Construction History.
 
论文题目：环氧形状记忆聚合物的热力学试验及相变本构研究
研究生：王丽君
指导老师：陈务军 教授
学科专业：结构工程
摘要
作为智能材料（Smart Materials）域新型代表之一的形状记忆聚合物（Shape Memory Polymers, SMPs)，不仅驱动方式多样，而且因其具有非常强的变形能力，低密度、高回复以及易于加工成型等优点，近年来成为研究人员研究的热点之一。同时，形状记忆聚合物因具有不同于其他聚合物材料的独特形状记忆特性，在航空航天医药电子等领域有非常广泛的应用前景。因此，对形状记忆聚合物材料的研究将有希望极大推动智能结构在各个领域的发展。基于该类材料的应用前景与经济效益，本文主要针对以环氧基（Epoxy）为代表的形状记忆聚合物的力学行为进行了比较系统的试验研究工作，同时对该类材料的本构模型进行了分析与研究。具体内容如下：
首先，本文针对环氧基形状记忆聚合物开展了较为系统的形状记忆性能试验。（1）对SMP进行了拉伸、弯曲、扭转三种变形条件下的形状记忆回复试验，测定了不同变形条件下表征材料记忆性能的形状记忆固定率和回复率；（2）进行了了拉伸变形条件下不同预应变的自由回复、约束回复试验，得到了材料在自由回复过程的回复应变随温度的变化规律，约束回复过程回复应力随温度的变化规律；（3）通过恒定荷载的升温加载试验，研究了载荷对形状记忆聚合物相变温度的影响，为该类材料本构模型的建立提供了试验基础。
其次，针对环氧基形状记忆聚合物的热力学性能的研究试验包括。（1）通过动态热机械分析试验，得到了该环氧基形状记忆聚合物的相变温度，以及该材料储能模量、损耗模量以及损耗模量正切值随温度的变化规律；（2）用电子万能试验机，进行了环氧基形状记忆聚合物的不同温度下的应变率试验、蠕变试验以及松弛试验，研究了不同温度下环氧基形状记忆聚合物的热力学特性。
接着，本文基于相变理论合理的解释了形状记忆聚合物在热力学循环过程中的形状记忆性能；同时，揭示了材料内部玻璃相与橡胶相的体积分数随温度变化的规律。在所建立的新型相变模型基础上，本文提出了以经典粘弹性理论为基础的本构模型：该模型既可以描述相变过程中玻璃相与橡胶相体积分数变化，也能表征形状记忆聚合物粘弹性、形状记忆特性。在新型相变模型中，形状记忆聚合物材料整体应变被分为：玻璃相机械应变，橡胶相机械应变，储存应变及热膨胀应变。其中，储存应变在形状固定及升温回复阶段随温度的变化规律是本文重点讨论的部分。基于此，本文分别给出了典型热力学循环过程中各阶段材料的应力-应变关系。通过粘弹性理论和橡胶自由能理论分别给出了玻璃相和橡胶相的应力应变关系式。
最后，基于上述形状记忆聚合物的新型相变本构理论，本文模拟分析了形状记忆聚合物在热循环形状记忆过程、以及恒定荷载作用下的应变响应。通过与试验结果的对比，验证了新型相变模型的准确性，同时分析了因未考虑温度变化速率带来的局限性。
关键词：形状记忆聚合物，形状记忆性能，热力学性能，玻璃态体积分数，相变本构理论，储存应变
 
THE THERMOMECHANICAL TESTS AND PHASE TRANSITION CONSTITUTION MODEL OF EPOXY SHAPE MEMORY POLYMER
Abstract
Shape Memory Polymers (SMPs), a new type of smart materials, have become the focus of attention of researchers in recent years because of their various driving modes, strong deformation ability, low density, high recovery and easy processing. At the same time, shape memory polymers have very strong development prospects in many fields (such as aerospace) for their unique shape memory characteristics. Therefore, the research on shape memory polymer materials will greatly promote the development of intelligent structures in various fields.
 Based on the application prospects and economic benefits of this kind of materials, the mechanical behaviors and constitution model of shape memory polymers represented by epoxy were studied systematically in this thesis. The details are as follows:
Firstly, the shape memory properties of epoxy-based shape memory polymers were testsed systematically. (1) The shape memory recovery of SMP under tensile, bending and torsion conditions was testsed. The shape memory fixation rate and recovery rate of SMP under different deformation conditions were measured; (2) In this thesis, the free and constrained recovery processes of different prestrain under tensile deformation are further developed. The variation of the recovery strain with temperature and the recovery stress with temperature during constrained recovery are obtained; (3) In order to study the effect of stress on the critical temperature of shape memory polymer, three groups of temperature-increasing loading testss under constant load were carried out, which provided the experimental basis for the constitutive model of material.
Secondly, the research about the thermodynamic properties of epoxy based shape memory polymers has been carried out. (1) The phase transition temperature of the epoxy-based shape memory polymer was measured by dynamic thermomechanical analyzer, and relationship of the tangent value, the storage modulus, and loss modulus of the material varied with temperature was measured too. (2) The strain rate tests, creep tests and relaxation tests of epoxy-based shape memory polymer at different temperatures were carried out by using electronic universal testsing machine. The thermodynamic properties of epoxy-based shape memory polymer at different temperatures were studied.
Then, based on the new phase transition model proposed by predecessors, the shape memory properties of shape memory polymers during thermodynamic cycling are described in depth, and the variation of volume fraction of glass and rubbery phases with temperature is explained accurately. On the basis of the new phase transition model, a constitutive model based on the classical viscoelastic theory and free energy theory is proposed. The model can not only describe the volume fraction of glass and rubbery phases during phase transition, but also characterize the viscoelastic and shape memory properties of shape memory polymers.
 In the new phase transition model, the shape memory polymer material includes glass phase mechanical strain, rubbery phase mechanical strain, storage strain and thermal expansion strain. Among them, the variation of storage strain with temperature in the stage of shape fixing and temperature recovery is the key points discussed in this thesis. Based on the viscoelastic theory and the rubbery free energy theory, the stress-strain relationship of materials in different stages of typical thermodynamic cycling process is given.
Finally, based on the new phase transition constitutive theory, the thermal cycling shape memory process and the strain response of SMP under constant load are simulated and analyzed. The rationality and accuracy of the new phase transition model are verified by comparison with the experimental results.
KEY WORDS: shape memory polymers, shape memory effect, thermo-mechanical property volume fraction of glass phase, phase transition model, Storage strain

论文题目：PV-ETFE气枕系统在多物理场作用下的性能分析
研 究 生：阴悦
指导老师：陈务军 教授
学科专业：结构工程
 
中文摘要:
    乙烯-四氟乙烯（Ethylene-tetrafluoroethylene, ETFE）膜材作为一种新型的建筑材料，具有轻质、耐冲击、透光率高、化学性质稳定、自洁性较好等特点，广泛应用于大跨度建筑中。柔性太阳能电池（Photovoltaics，PV）具有较好的柔韧性和高温适应性，将ETFE气枕和PV结合为光伏膜结构一体化（Building Integrated with Photovoltaics, BIPV）建筑，利用PV将太阳能转化成电能和热能，可充分利用两者优势，有效降低膜结构建筑能耗。由于PV-ETFE气枕性能具有复杂的长期性、时变性、动态性，对其各项性能参数进行全面测量较为困难因此有必要建立合理的数值分析模型，全面分析气枕的综合性能并揭示更为深刻的问题。此外，PV在吸收外界光照辐射后表面温度急剧升高，其电性能必定会受到一定影响；而ETFE薄膜具有较高的温度敏感性，其力学性能也会随温度变化产生一定响应，故有必要从材料层面入手，研究PV-ETFE复合材料的光电-热-力性能。
     首先，以三层PV-ETFE气枕夏季性能试验为依据，概述了该气枕系统的光电光热性能及结构性能。基于实际试验环境与气枕性能分析结果，从日照辐射与PV-ETFE气枕的温度场、结构场及气枕内流场出发，分别建立各物理场作用分析模型及热-流耦合分析模型。 然后，在COMSOL Multiphysics多物理场分析软件中建立三维光热-流-结构多场耦合分析模型，研究了上海地区夏季9:00~17:00时段内三层PV-ETFE气枕在多物理场作用下的膜面力学性能、温度场及内部流场分布的动态变化规律，并与PV-ETFE气枕夏季性能试验结果进行对比，验证了数值模型的合理性与准确性，可推广用于PV-ETFE气枕的设计施工与性能优化分析。
     最后，研究了柔性薄膜有机太阳能电池（Organic photovoltaics，OPV）与ETFE薄膜的材料层压方法及其对光电-热-力性能的影响。在日照辐射强度为1000 W/m2的光照条件下，分别对不同形式的柔性OPV-ETFE复合材料进行单轴拉伸试验，得到了应力-应变曲线、温度及电压变化曲线，并分析了光电-热-力性能之间的相互作用现象与规律。基于试验实测情况建立柔性OPV-ETFE复合材料光热-力性能数值分析模型，分析OPV-ETFE材料在多物理场作用下的光热-力性能，可为柔性OPV-ETFE气枕系统的深入研究奠定一定基础。
     关键词：PV-ETFE气枕系统；光伏建筑一体化；光热-流-结构性能；柔性有机薄膜太阳能电池；光电-热-力性能
    PERFORMANCE ANALYSIS OF PV-ETFE CUSHION SYSTEM UNDER MULTIPHYSICAL CONDITIONS
                   ABSTRACT
     As a new type of building material, ETFE (Ethylene-tetrafluoroethylene) membrane has many advantages such as light weight, impact resistance, high light transmittance, stable chemical property and good self-cleaning property. It is widely used in large-span buildings. The flexible photovoltaics (PV) has good flexibility and high temperature adaptability. If the ETFE cushion and the PV are combined into a building integrated photovoltaic (BIPV) building, the solar photovoltaic can easily converted solar irradiation into photoelectricity and heat for the cushion which can effectively reduce building energy consumption. Because the performance of PV-ETFE cushion has complex long-term, time-varying and dynamic characteristics, it is difficult to measure its performance parameters comprehensively, so it is necessary to establish a reasonable numerical analysis model, analyze the comprehensive performance of the cushion system and reveal more profound problems. In addition, PV absorbs external light radiation and then the surface temperature rises sharply, its photoelectrical properties will certainly be affected. Besides, ETFE film has property of high temperature sensitivity and its mechanical properties will also have a certain response with temperature changes. Therefore, it is necessary to study the electro-thermo-mechanical properties of PV-ETFE composite from the aspect of material.
     First of all, based on the performance test of the three-layer PV-ETFE cushion in summer, the photoelectric-thermal-structural performance of the cushion system was summarized. Based on the analysis results of actual test environment and the cushion performance, we set up the multiphysical model and the thermos-fluid coupling model respectively with respect to irradiance, the temperature field, structural field and inner liquid field of PV-ETFE cushion.
     Then, multiphysical coupling model was established in COMSOL Multiphysics. Membrane mechanical properties, thermal field and internal fluid field distribution of the three-layer PV-ETFE cushion were obtained. After that the results between the experiment and numerial simulation were compared to verify the rationality and accuracy of the numerical model. All the results in this chapter could serve as a reference in the process of design and construction for PV-ETFE cushion.
     Finally, the material composite method of flexible thin film solar cells and ETFE films was studied. Uniaxial tensile tests of different forms of flexible OPV-ETFE composites were carried out under the illumination condition of 1000 W/m2irradiation. The stress-strain curves, temperature and voltage variation curves were obtained and the interaction between photoelectric-thermal-mechanical properties is analyzed. The fifth chapter built a numerical analysis model of flexible OPV-ETFE composite to study its photothermal-mechanical properties and then analyzed of coupling properties of OPV-ETFE materials in multi-physical field. This study can serve as a foundation research for the flexible OPV-ETFE air cushion system.
     Key words: PV-ETFE cushion system; building integrated with photovoltaics; photo-thermo-fluid-structure performance; flexible organic photovoltaics; photoelectric-thermal-mechanical performance.

论文题目：仿生飞爬机器人及其柔性驱动
研 究 生：贾林睿
指导老师：陈务军 教授
学科专业：结构工程
 
中文摘要:
    侦察机器人是一种特殊的移动机器人，需要有卓越的机动性能以及优异的隐蔽工作能力。本课题即是面向灾后搜救、建筑检测、军事侦察等需求，研制一种具有陆空两栖运动能力，具备侦察、感知、操作等功能的机器人。
???????? 本文从需求出发，总结比较了空中以及陆地行动方式的优劣，提出了一种结合旋翼以及仿生爬行两种运动模式的飞爬机器人，模仿螳螂的运动姿态，研制机器人样机并进行了仿真验证及试验研究。
根据昆虫腿结构，本文设计了三段式仿生腿，求解了单腿的最大步长、最大越障高度等指标，指导了腿节比例的优化设计。进一步建立了结合控制的机构动力学模型，对机器人在飞行着陆状态下的响应进行了仿真。制造了样机并将试验与仿真结果进行比较，验证了控制算法的有效性以及仿真模型的准确性。
???????? 生物腿部的柔性在足式运动过程中起到重要的作用。据此，本文提出了一种小型串联粘弹性驱动器，并针对该驱动器开发了闭环位置以及力控制算法。为精确识别驱动器的参数，对所用的聚氨酯肌腱建立了五项Mooney-Rivlin超弹模型叠加Prony级数表示的粘弹模型，取得了良好的拟合效果。基于该本构模型，建立了驱动器的仿真模型，结合研制的试验平台，验证了驱动器的实用性及控制算法的有效性。
???????? 侦察机器人工作环境恶劣，需要有较强的防护能力，外骨骼是最佳的选择。在观察三维重建的螳螂腿部关节基础上，本文针对外骨骼形式的仿生腿，提出了一种形态仿生柔性关节，分析了关节设计的限制条件，进行了有限元静力学仿真，最后制造了实物样机，给出了柔性主动关节的形式。该仿生关节具有柔性传导，承载力大，节约空间的优点，并能在过载情况下发生“脱臼”，避免结构件的损伤。
 
关键词：飞爬机器人；串联粘弹性驱动器；粘弹性本构模型；形态仿生关节
 
BIONIC AIR-LAND ROBOT AND ITS FLEXIBLE ACTUATING
ABSTRACT
 
Spy robot is a special kind of mobile robot, which have great demand on excellent motion performance and good secret work ability. This essay is about the development of an air-land spy robot.
Based on the demand, the advantages are compared between different ways of flying and walking, and a robot which combined with rotors and bionic crawling is proposed. By mimicking the posture of mantis, the conceptual design is proposed.
A segmented bionic leg is proposed based on the structure of insect leg. The maximum step size and leg lifting height are calculated to help with the optimization of length ratio of leg segments. A multi-body dynamic simulation model is built and simulates the response of landing process. A prototype is built and the result of experiment and simulation are compared.
The flexibility of animals’ leg plays an important role in ground movement, a series viscoelastic actuator is proposed based on the theory, and closed loop control methods are conducted. In order to accurately identify the parameters of actuator, a viscoelastic constitutive model based on five Mooney-Rivlin super elastic model and viscoelastic model expressed in Prony series is fitted to the tensile response of polyurethane tendons which are used in the actuator. A simulation model based on the model of tendon and an experimental platform of actuator are built. The simulation and the experiment results are compared which proves the practicability of the actuator and the effectiveness of the control method
A spy robot usually has bad working environment and needs to be protected. The exoskeleton is a good choice. Based on the observation of 3D reconstructed model of mantis articulation, a shape bionic flexible joint is proposed. The restrictive conditions are conducted and the stress of skeleton is analyzed by FEM and finally, the prototypes are built and the design of flexible active joint is proposed. The bionic joint has its advantages in flexibility, good bearing capacity and space saving, in addition, it could ‘dislocate’ in the case of overload to protect the structure from mechanical damage.
KEY WORDS: Air-land robot; Series viscoelastic actuator; Viscoelastic constitutive model; Shape bionic joint