利用外方内圆模型预测单向连续纤维增强树脂基复合材料的横向弹性模量

为了对连续纤维增强树脂基复合材料的横向弹性模量进行较高精度的解析计算,利用代表性体积单元横截面为正方形基体包裹圆形纤维的外方内圆模型,采用先并联后串联和先串联后并联的两种计算方式进行公式推导,借助于Mathematica软件进行符号积分运算,获得了横向弹性模量的2组解析解,将其中间值作为预测值,给出了预测值的近似公式,并与一组实验数据进行了比较。研究表明,外方内圆模型能较好地反映客观实际,利用Mathematica软件可以解决计算困难的问题;将解析解的中间值作为横向弹性模量的预测值,与一组实验数据比较,显示解析计算的相对误差基本在10%以内;给出的近似公式形式简单,且其曲线能较好地吻合中间值曲线,在纤维体积分数小于75%的范围内,近似公式与中间值公式计算结果之间的最大误差不超过7%。     

考虑界面效应的复合泡沫塑料弹性性能数值仿真预测与试验研究

通过对不同空心陶瓷微珠含量的环氧基复合泡沫塑料进行准静态拉伸实验, 研究了填充微珠的体积分数对复合泡沫塑料弹性模量和泊松比的影响。基于其细观结构特征, 利用三维立方单胞有限元模型模拟了细观应力/应变场; 将内聚力单元引入细观有限元模型, 以此来模拟空心微珠与基体材料之间界面相的力学行为。将有限元预测结果以及两种传统的细观解析法与实验数据对比, 发现基于界面理想粘接假设的有限元模型和传统细观解析法均过高估计了复合泡沫塑料的弹性模量和泊松比; 复合泡沫塑料的弹性性能强烈地依赖于界面相的力学性质, 只有考虑界面效应的细观有限元模型才能给出较为精确的预测, 从而验证了文中细观建模方法的合理性。     

双随机分布细观分析模型与复合材料性能预报

发展了一种细观力学有限元分析方法——拟真实的参数化双随机分布模型, 该模型综合考虑了纤维增强树脂基复合材料的真实微结构特点和纤维单丝综合力学性能测试结果的离散性特征, 模拟了复合材料中纤维排列和强度分布的随机性。借助移动窗口法研究了该参数化双随机分布模型的可靠性, 确定了其代表性体积单元的尺寸。基于能量法原理推导了单向复合材料的弹性模量预测公式, 结合能量法和渐进失效分析方法, 利用该细观力学有限元方法分别预测了单向纤维增强树脂基复合材料T300/5228的弹性模量和强度性能。数值模拟结果和大部分试验结果吻合良好, 表明发展的细观力学有限元方法能够较好地预测复合材料的力学性能。      

考虑界面效应的复合泡沫塑料弹性性能数值仿真预测与试验研究

通过对不同空心陶瓷微珠含量的环氧基复合泡沫塑料进行准静态拉伸实验,研究了填充微珠的体积分数对复合泡沫塑料弹性模量和泊松比的影响.基于其细观结构特征,利用三维立方单胞有限元模型模拟了细观应力/应变场;将内聚力单元引入细观有限元模型,以此来模拟空心微珠与基体材料之间界面相的力学行为.将有限元预测结果以及两种传统的细观解析法与实验数据对比,发现基于界面理想粘接假设的有限元模型和传统细观解析法均过高估计了复合泡沫塑料的弹性模量和泊松比;复合泡沫塑料的弹性性能强烈地依赖于界面相的力学性质,只有考虑界面效应的细观有限元模型才能给出较为精确的预测,从而验证了文中细观建模方法的合理性.     

含非均匀界面相纤维增强复合材料热传导性能预测的递推公式

研究了含非均匀界面相纤维增强复合材料的宏观等效传热性能。将热导率沿径向连续变化的界面相离散为多个热导率均匀的同心圆柱层,采用广义自洽法和复变函数理论,推导了复合材料宏观等效热导率的解析递推公式,并由递推公式给出了均匀界面相和理想零厚度界面的封闭公式。理想零厚度界面复合材料的热导率与已有理论结果一致。理想零厚度界面和非均匀界面相模型的计算结果与实验数据比较表明,当纤维体积分数较小时,2种模型的预测结果与实验数据吻合均较好,当体积分数较大时,与实验数据相比,非均匀界面相模型的精度大大高于理想零厚度界面模型的精度。本文中给出的递推公式亦可用于计算多涂层纤维增强复合材料的热导率。     

单层平面索网结构非线性频率简化计算方法研究

单层平面索网玻璃幕墙结构是广泛应用于大型公共建筑中的一种新型结构形式,由于其挠度较大,结构具有较高的几何非线性,其动力特点不同于传统的线性结构。采用连续化薄膜理论建立了单索幕墙的非线性振动方程,并采用谐波平衡法求解了结构非线性频率的解析表达式,为校核解析公式的正确性,将其计算结果同精确的有限元非线性时程方法的计算结果进行了比较,吻合很好,该解析公式具有相当高的精度。同时指出结构位移为3/2结构振幅位置处的刚度即为单索幕墙结构的等效线性刚度,采用该等效线性刚度即可得到上述非线性频率的解析表达式。此外得到的结构非线性振动方程和非线性频率为结构在动力荷载下响应的求解提供了基础。     

法向接触刚度对装配体振动模态影响的研究

在对装配体进行模态分析时,装配体接触面间的法向接触刚度对计算结果具有很大影响,但在实际中由于处理困难却往往被省略。基于有限元建模方法分析了装配体接触面法向接触刚度对装配体振动模态的影响。首先,根据接触力学理论推导了法向接触刚度与接触表面粗糙度和接触应力之间的关系;然后,探讨了通过改变层单元弹性模量来模拟法向接触刚度的有限元建模方法;最后,通过算例分析了考虑与不考虑接触刚度时振动模态的差异。研究结果表明,考虑法向接触刚度的有限元等效模型计算结果与解析解非常接近,不考虑接触刚度的整体模型计算结果与解析解异较大,一般超过了10%以上,且频率越低差异越大,另外振型也有明显差异。本文建立的有限元建模方法可用于研究法向接触刚度对装配体振动模态的影响。     

采用波叠加法技术求解加肋板的辐射声功率

波叠加原理提供了计算加肋板辐射声功率的方法。首先对结构的动力方程进行Fourier变换或者单元体积速度匹配,获得结构离散单元的体积速度。然后根据结构与介质的交界面相容性条件,建立虚拟声源强度与单元体积速度的代数方程。进而求解虚拟声源的强度,获得计算结构辐射声功率的两种方法。以求解加肋简支矩形板的声功率为例,其结果与解析法获得的结果进行了对比,表明这两种方法都同样具有较高的计算精度。相对于利用Fourier变换的方法,采用单元体积速度匹配原则的方法不需要计算结构的振动模态耦合矩阵,计算简单直接,而且行之有效。     

基于广义模态截断扩增方法的结构频响拓扑变量灵敏度分析

基于结构拓扑优化设计中的变密度法,采用伴随法推导结构在简谐激励下的频响振幅对单元设计变量的解析灵敏度列式。针对灵敏度数值求解中传统模态位移法引发的低精度问题,通过引入计算成本较低的广义模态截断扩增方法提升灵敏度的计算精度。数值算例将该文方法与全局有限差分法和其他灵敏度计算方法进行了比较。结果证明了该文方法在不同的激励频率及有限元网格密度下高效求解高精度灵敏度的有效性。     

二维平纹机织复合材料弹性性能预测的域分解方法

为了预测二维平纹机织复合材料的弹性性能, 提出了基于有限元重合网格法的域分解方法。域分解方法与传统代表体元法的有限元建模不同, 前者不再建立精细的纤维与基体模型, 而是分别建立二维平纹机织复合材料单胞的整体域与纤维域, 整体域是真实基体体积与纤维体积的叠加, 两区域网格独立剖分, 互不影响。采用MSC. Nastran中的多节点约束在纤维节点与基体节点之间建立位移协调来模拟纤维和基体单元的位移函数关系, 实现了纤维域和基体域的耦合计算。研究表明, 域分解方法大大简化了机织复合材料细观力学建模的复杂性, 降低了建模时间, 采用域分解方法预测的二维平纹机织复合材料弹性常数与试验值吻合较好, 充分说明了该预测模型与方法的正确性。研究了不同纤维体积分数下, 域分解方法预测二维平纹机织复合材料的弹性常数的变化趋势, 结果表明, 随纤维体积分数增加, 模量呈上升趋势, 泊松比呈降低趋势。     

Base force element method based on the complementary energy principle for the damage analysis of recycled aggregate concrete

The finite element method (FEM) is an effective approach for exploring the failure mechanism of heterogeneous materials. According to the complementary energy principle, the use of FEM might suffer from several difficulties in terms of keeping the elements and their boundaries balanced, as well as finding interpolation functions. In this study, we introduced an efficient approach to researching the failure mechanism of the material, named base force element method (BFEM), according to complementary energy principle. Specifically, the element compliance matrix of an arbitrary quadrilateral element with four mid-edge nodes was expressed based on the complementary energy principle. Then, the node displacement was obtained by the governing equation using the Lagrange multiplier method. In addition, both the compliance matrix and the node displacement were represented as explicit expressions without the use of Gaussian integration. A numerical model of the recycled aggregate concrete (RAC) was established according to the Monte Carlo method. A comparative sample of the digital image model was also established using digital image technology. The influences of substituting recycled aggregate and the relative mechanical properties of adhered mortar to those of new mortar on the failure mechanism of RAC were studied. The simulation results indicated that the BFEM is an effective approach to researching the damage mechanism of heterogeneous materials.     

Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli

Two real-domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency are investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher-order and higher floating-point precision numerical approximation, the latter being novel in this context. A general formula for higher-order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating-point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher-order approximations in standard double precision and increased quadruple precision. It is found that, as the order of the approximation increases, the elasticity moduli tend toward the analytical solution. Using higher floating-point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli. Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.     

Finite element characterization of the size-dependent mechanical behaviour in nanosystems

Mechanical behaviour analysis plays an important role in the design of micro/nano-electromechanical system (MEMS/NEMS) devices for reliability. In this paper, the size-dependent mechanical properties of nanostructures are numerically studied with the finite element method (FEM) by developing a kind of surface element to take into account the surface elastic effect. This method is then applied to the investigation of the interaction between two pressurized nanovoids and the effective moduli of two-dimensional nanoporous material. The numerical results indicate that surface elasticity can significantly alter the nature of interaction forms and the effective moduli by inducing a strong size dependence in conventional results.     

Base force element method (BFEM) on potential energy principle for elasticity problems

Using the concept of base forces, the problem of the explicit tensor expression of the element stiffness matrix for a new finite element method (FEM)??the base force element method (BFEM) was studied. The mathematic model of the BFEM on potential energy principle was established by using an explicit expression. A code for the BFEM was developed using MATLAB computer language. The approach was used to solve several problems of elasticity theory, and various shape elements were compared and analyzed. The numerical results are consistent with those of the theoretical solutions, and the applicability of this approach is verified.     

The boundary finite element method for predicting directions of cracks emerging from notches at bimaterial junctions

The analysis of a bimaterial medium with various notch opening angles has been carried out using boundary finite element method (BFEM) under arbitrary loading conditions. Introduced as novel method for stress concentration problems at geometrical discontinuities, cracks, bimaterial notches etc., the BFEM has been proved as numerically highly efficient. This has become more and more important because wedge type construction creates stress concentrations which may lead to crack initiation in many practical situations where multi-layered composite material is used, e.g. within aerospace, ship or automobile structures. So, the computational prediction of potential directions for crack initiation is essential for the knowledge of weak regions. All the analysis results are based on the hypothesis of Erdogan and Sih and have been verified by the well established finite element method. Results for potential crack initiation angles of both homogeneous and bimaterial media are presented with multiple examples of different wedge angles and different loading combinations.     

微分求积法与有限元相结合分析带弹性安置质量圆板的横向振动

微分求积法(GDQM)是近年来发展起来的一种结构计算方法,但是目前仍存在很多的局限性。而有限元法是一种成熟的计算方法,但是计算比较繁琐。用GDQM与有限元相结合对中心带有弹性安置质量圆板的轴对称自由振动进行了计算分析,同时发挥GDQM精度高、计算量小、收敛快和有限元法十分灵活的优点,使两种方法得到了有机结合,首次提出了一种结构分析的新思路。计算结果与现有文献的结果作了对比,证明方法具有较高的精度。     

隔离非线性分层壳有限单元法

分层壳单元由于其模型简单,物理意义清晰,被广泛应用于建筑结构的有限元数值模拟中。该文基于隔离非线性有限元法提出了分层壳单元的高效非线性分析模型,将分层壳单元的截面变形（应变和曲率）分解为线弹性变形和非线性变形,以单元中面的高斯积分点作为非线性变形插值结点,建立了非线性变形场,并根据虚功原理,推导了分层壳单元的隔离非线性控制方程,采用Woodbury公式和组合近似法联合求解控制方程。依据时间复杂度理论的统计分析表明:该文建立的方法相较于传统变刚度有限元方法在非线性分析效率方面具有显著优势。并与有限元软件ANSYS的计算结果进行对比,验证了该文方法的准确性。     

Deformation behavior and mechanical properties of braided rectangular pipes

The purpose of this study is to clarify the deformation behavior and the relationship between the braiding angle and mechanical properties for the braided rectangular pipe. Three-point bending test was performed for each specimen. Furthermore, the effect of the solid-core bar on the deformation state of the rectangular pipe was studied by finite element method (FEM). Moreover, the effect of the braiding angle on the deformation behavior in detail was investigated. The bending modulus and the bending strength for each specimen were decreased with an increase in the braiding angle. The local deformations occurred at the compression side under loading nose and decreased with an increase in stiffness properties in circumferential direction. From FEM analysis, using the aluminum solid-core bar was effective to restrain the local deformation. The difference between the bending moduli of experiments and FEM was decreased with an increase in the modulus in transverse direction.     

光滑有限元的声学研究：时域和频域分析

摘　要：在使用有限元进行声场的数值模拟中,存在着两个主要误差,一个是数值方法中常规的插值误差,另外一个是计算声学中所特有的耗散误差(dispersion error),后者则是影响声学模拟仿真置信度的最重要因素。产生耗散误差的本质原因是由于有限元的数值模型刚度“偏硬”造成的。为了控制耗散误差,最重要的是使数值模型更好的反映真实模型。本文采用了一种基于边光滑的有限元方法(ES-FEM)来对声场的时域和频域进行数值模拟研究。该方法只采用对复杂问题域适应性很强的三角形网格,通过引进基于边的广义梯度光滑技术,能够使得有限元系统得到适当的“软化”。关于时域和频域的算例表明了在使用同样网格的情况下,本方法在声学模拟中的精度都要比有限元模型的高。     

The use of boundary strip method (BSM) for evaluation of the transverse mechanical properties of fibrous composites

The boundary strip method (BSM) is applied for evaluation of the transverse mechanical properties of fibrous composites with random and periodical fiber distributions. This special semi numerical method helps find the link between the microscopic behavior of the composite material and its macroscopic response in a rather detailed manner, enabling definition of stress and strain magnitudes at each point of the cross section. Here, specifically statistical model based on the boundary strip method, is used for assessment of the transverse effective moduli of fibrous composites. Random fiber distributions are compared with periodic fiber distributions having square or hexagonal array arrangements. Those are the common models used nowadays and modeled by the finite element or the boundary element. A comparison with the bounds of the polarization extremum principles is conducted too. The influence of the randomly distributed fibers on the transverse effective moduli is investigated and a good correlation is found between the results of the present model and the lower bound of the polarization extremum principles.