复合材料点阵夹芯结构的弯曲、屈曲和振动特性研究
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摘要
点阵夹芯结构是一类具有优异力学性能的新型轻质多功能结构，其在航空、航天、船舶和交通领域具有广阔的应用前景。与传统的金属材料相比，碳纤维增强复合材料具有密度低、强度高、模量大的特性，采用复合材料制备点阵夹芯结构，将使材料和结构的优势相得益彰。由于复合材料点阵夹芯结构具有高孔隙率、周期性有序及各向异性的特点，其在刚度、强度、稳定性和振动特性等方面都体现出新的特征，但目前还缺乏该方面的研究成果。本文采用理论分析、数值模拟和实验测量相结合的方法，对复合材料点阵夹芯结构的三点弯曲、整体屈曲、自由振动及缺陷敏感性问题进行了研究，主要包括以下内容：
首先研究了复合材料点阵夹芯结构在三点弯曲载荷作用下的刚度和强度问题。将离散的点阵芯子等效为连续均匀材料，考虑面板的弯曲和芯子的横向剪切，推导了挠度的表达式。将点阵夹芯结构看作由多跨薄板和一维杆单元构成的复合结构，分析了面板和杆件的应力状态，推导了多种失效模式所对应的临界载荷。在此基础上绘制失效机制图，揭示了失效模式与结构几何尺寸之间的关系。以承载效率最大化为目标，对复合材料点阵夹芯结构进行了优化设计，并与金属点阵夹芯结构和复合材料层合结构进行比较，指出了这种新型轻质结构的优势所在。
其次研究了复合材料点阵夹芯结构在面内压缩载荷作用下的整体屈曲问题。延用Allen提出的“折线”位移模型（该模型假设面板与芯子具有不同的转角，且芯子的转角是结构横向位移的函数），在其基础上考虑了面板的层合属性，采用能量变分方法推导了横向位移的通解表达式，通过边界条件确定通解中的未知系数，计算了多种典型边界条件下夹芯结构的屈曲模态和临界屈曲载荷。本文提出的方法解决了Euler理论和Timoshenko理论在夹芯结构屈曲长度较短的情况下计算误差偏大的问题。
然后对复合材料点阵夹芯结构的振动特性进行了理论和数值研究。Allen模型仅适用于简支边界条件下夹芯结构的自由振动问题研究，为了使研究的问题更加具有普适性，本文对Allen模型加以改进，假设芯子的转角与结构的横向位移是两个独立的函数，求解了多种典型边界条件下夹芯结构固有频率和固有振型的解析解。建立了模拟点阵夹芯结构自由振动特性的有限元模型，并讨论了材料性能和几何参数对复合材料点阵夹芯结构固有频率的影响。
最后通过实验模态分析和数值模拟方法研究了芯体材料的局部损伤对复合材料点阵夹芯结构振动特性的影响。讨论了损伤程度、损伤位置、损伤形式和边界条件对点阵夹芯结构固有频率和固有振型的影响，研究结果表明局部损伤将会降低结构的固有频率，并导致结构的固有振型出现明显的局部变形。该研究为复合材料点阵夹芯结构的工程应用提供了有益的指导。
Lattice sandwich structure, as a novel kind of multifunctional lightweightstructure, has widely potential application in the fields of astronautics, aeronautics,ship-building and transportation. They have been traditionally made of metallicmaterials such as aluminium alloy or304stainless steel. There are many advantagesof carbon fiber reinforced composite materials over traditional metallic materials,such as low density, high strength, and high modulus. Therefore, composite latticesandwich structures have been paid more attention in recent years. Due to somefeatures of composite lattice sandwich structures, such as high porosity, periodicity,and anisotropy, their stiffness, strength, stability and vibration properties will shownew characteristics. However, there is little research in this area. In this dissertation,three-point bending problem, global buckling problem, and free vibration problemof composite lattice truss core sandwich structures are studied by the methods oftheoretical prediction, numerical simulation and experimental measurement. Themain contents are as follows:
The stiffness and strength behaviors of composite lattice truss core sandwichstructure under three-point bending load are investigated firstly. Converted discretelattice truss core to continuum homogenized material, the expression for thedeflection is derived by considering bending of the face sheets and transverseshearing of the core. The stress states within the face sheets and the truss membersare analyzed respectively by taking the lattice truss core sandwich structure as acomposite structure composed of multi-span thin plates and one-dimensional strutelements, and the critical loads for various failure modes are predicted. Collapsemechanism map is constructed on that basis, and the relations between failuremodes and structural geometric dimensions are revealed. Optimized design ofcomposite lattice truss core sandwich structure is carried out with the goal of load-carrying efficiency maximization. The advantage of this new type of lightweightstructure is reported by comparing the performances of composite lattice sandwichstructure, metallic lattice sandwich structure and composite laminates.
Secondly, the global buckling problem of composite lattice truss coresandwich structure under in-plane compressive load is investigated. On the basis ofAllen's displacement model (which assumes that the face sheets and the core havedifferent rotation angles, and the rotation angle of the core is a function of thetransverse displacement of the sandwich structure), considering a sandwichstructure with laminated face sheets, the expression of general solution for transverse displacement is derived using the energy-variational method, theunknown coefficients in the general solution are determined by the correspondingboundary conditions, and the buckling modes as well as critical buckling loadsunder various typical boundary conditions are calculated. The errors of both Eulertheory and Timoshenko theory increase with the shortening of the buckling lengthof the sandwich structure, while the present method overcomes this problem.
Then, the free vibration problem of composite lattice truss core sandwichstructure is studied by theoretical and numerical methods. An improved zig-zagmodel, which is suitable for free vibration problem of sandwich structure not onlyunder simply-supported boundary conditions, but also under other boundaryconditions, is constructed on the basis of Allen's model, and the natural frequenciesand corresponding vibration modes of sandwich structure under various boundaryconditions are calculated. Besides, a finite element model is set up to simulate thefree vibration characteristics of lattice truss core sandwich structure, and the effectsof material properties and geometric parameters on the natural frequencies of latticetruss core sandwich structure are also discussed.
Finally, the effects of local damage of the core on the vibration characteristicsof composite lattice truss core sandwich structure are studied by experimentalmodal analysis and numerical simulation method, and the effects of damage extents,damage locations, damage forms, and boundary conditions on the naturalfrequencies and natural vibration modes of lattice truss core sandwich structures areinvestigated. It is found that local damage will decrease the natural frequencies andresult in obvious local deformations appearing in the natural vibration modes. Thepresent study provides useful guidance for engineering application of compositelattice truss core sandwich structure.
首先研究了复合材料点阵夹芯结构在三点弯曲载荷作用下的刚度和强度问题。将离散的点阵芯子等效为连续均匀材料，考虑面板的弯曲和芯子的横向剪切，推导了挠度的表达式。将点阵夹芯结构看作由多跨薄板和一维杆单元构成的复合结构，分析了面板和杆件的应力状态，推导了多种失效模式所对应的临界载荷。在此基础上绘制失效机制图，揭示了失效模式与结构几何尺寸之间的关系。以承载效率最大化为目标，对复合材料点阵夹芯结构进行了优化设计，并与金属点阵夹芯结构和复合材料层合结构进行比较，指出了这种新型轻质结构的优势所在。
其次研究了复合材料点阵夹芯结构在面内压缩载荷作用下的整体屈曲问题。延用Allen提出的“折线”位移模型（该模型假设面板与芯子具有不同的转角，且芯子的转角是结构横向位移的函数），在其基础上考虑了面板的层合属性，采用能量变分方法推导了横向位移的通解表达式，通过边界条件确定通解中的未知系数，计算了多种典型边界条件下夹芯结构的屈曲模态和临界屈曲载荷。本文提出的方法解决了Euler理论和Timoshenko理论在夹芯结构屈曲长度较短的情况下计算误差偏大的问题。
然后对复合材料点阵夹芯结构的振动特性进行了理论和数值研究。Allen模型仅适用于简支边界条件下夹芯结构的自由振动问题研究，为了使研究的问题更加具有普适性，本文对Allen模型加以改进，假设芯子的转角与结构的横向位移是两个独立的函数，求解了多种典型边界条件下夹芯结构固有频率和固有振型的解析解。建立了模拟点阵夹芯结构自由振动特性的有限元模型，并讨论了材料性能和几何参数对复合材料点阵夹芯结构固有频率的影响。
最后通过实验模态分析和数值模拟方法研究了芯体材料的局部损伤对复合材料点阵夹芯结构振动特性的影响。讨论了损伤程度、损伤位置、损伤形式和边界条件对点阵夹芯结构固有频率和固有振型的影响，研究结果表明局部损伤将会降低结构的固有频率，并导致结构的固有振型出现明显的局部变形。该研究为复合材料点阵夹芯结构的工程应用提供了有益的指导。
Lattice sandwich structure, as a novel kind of multifunctional lightweightstructure, has widely potential application in the fields of astronautics, aeronautics,ship-building and transportation. They have been traditionally made of metallicmaterials such as aluminium alloy or304stainless steel. There are many advantagesof carbon fiber reinforced composite materials over traditional metallic materials,such as low density, high strength, and high modulus. Therefore, composite latticesandwich structures have been paid more attention in recent years. Due to somefeatures of composite lattice sandwich structures, such as high porosity, periodicity,and anisotropy, their stiffness, strength, stability and vibration properties will shownew characteristics. However, there is little research in this area. In this dissertation,three-point bending problem, global buckling problem, and free vibration problemof composite lattice truss core sandwich structures are studied by the methods oftheoretical prediction, numerical simulation and experimental measurement. Themain contents are as follows:
The stiffness and strength behaviors of composite lattice truss core sandwichstructure under three-point bending load are investigated firstly. Converted discretelattice truss core to continuum homogenized material, the expression for thedeflection is derived by considering bending of the face sheets and transverseshearing of the core. The stress states within the face sheets and the truss membersare analyzed respectively by taking the lattice truss core sandwich structure as acomposite structure composed of multi-span thin plates and one-dimensional strutelements, and the critical loads for various failure modes are predicted. Collapsemechanism map is constructed on that basis, and the relations between failuremodes and structural geometric dimensions are revealed. Optimized design ofcomposite lattice truss core sandwich structure is carried out with the goal of load-carrying efficiency maximization. The advantage of this new type of lightweightstructure is reported by comparing the performances of composite lattice sandwichstructure, metallic lattice sandwich structure and composite laminates.
Secondly, the global buckling problem of composite lattice truss coresandwich structure under in-plane compressive load is investigated. On the basis ofAllen's displacement model (which assumes that the face sheets and the core havedifferent rotation angles, and the rotation angle of the core is a function of thetransverse displacement of the sandwich structure), considering a sandwichstructure with laminated face sheets, the expression of general solution for transverse displacement is derived using the energy-variational method, theunknown coefficients in the general solution are determined by the correspondingboundary conditions, and the buckling modes as well as critical buckling loadsunder various typical boundary conditions are calculated. The errors of both Eulertheory and Timoshenko theory increase with the shortening of the buckling lengthof the sandwich structure, while the present method overcomes this problem.
Then, the free vibration problem of composite lattice truss core sandwichstructure is studied by theoretical and numerical methods. An improved zig-zagmodel, which is suitable for free vibration problem of sandwich structure not onlyunder simply-supported boundary conditions, but also under other boundaryconditions, is constructed on the basis of Allen's model, and the natural frequenciesand corresponding vibration modes of sandwich structure under various boundaryconditions are calculated. Besides, a finite element model is set up to simulate thefree vibration characteristics of lattice truss core sandwich structure, and the effectsof material properties and geometric parameters on the natural frequencies of latticetruss core sandwich structure are also discussed.
Finally, the effects of local damage of the core on the vibration characteristicsof composite lattice truss core sandwich structure are studied by experimentalmodal analysis and numerical simulation method, and the effects of damage extents,damage locations, damage forms, and boundary conditions on the naturalfrequencies and natural vibration modes of lattice truss core sandwich structures areinvestigated. It is found that local damage will decrease the natural frequencies andresult in obvious local deformations appearing in the natural vibration modes. Thepresent study provides useful guidance for engineering application of compositelattice truss core sandwich structure.
引文
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