层合梁横向冲击的动力学效应

研究了十字叠层复合材料梁横向冲击响应的动力学效应，根据冲击实验曲线及动态有限元方法计算了惯性效应和应力波效应对位移和应力响应的影响。     

非均质混杂叠层梁的分层剪切理论

本文研究了正交各向异性混杂叠层梁的应力与变形计算.叠层梁是由几层弹性性质明显不同的非均质子层梁组成.对每一子层梁应用剪切理论,并假设相邻子层梁的交界面是理想连接.文中导出了关于子层梁剪切转角ψ_i的二阶常微分方程组.求解微分方程组可得到叠层梁应力与位移关于剪切转角的ψ_i解析表达式.叠层梁组分材料中任一点应力可按有效模量理论和整体——局部方法[3]求得.     

叠层板型燃料堆芯元件模型的流固耦合振动

叠层板状结构是新型核反应堆设计中所采用的一种堆芯元件，具有结构合理、比功率高和传热性能好等显著特点。提出了单梁与多梁对接的力学模型，以干模态振型函数序列作为试函数对复模态振型方程进行变分求解，研究了叠层板状元件在湿模态下的固有频率与振型，发现叠层板状结构的流致振动具有复模态特性，文中初步找到一些规律性的结果，为设计和安全分析提供一些有用的方法和数据。     

连续配筋混凝土路面动荷响应分析

将连续配筋混凝土路面视为粘弹性地基上正交各向异性板,运用三角级数和积分变换方法,对路面受局部冲击荷载作用时的动力响应做了分析,得到了路面的挠度、内力和应力的解析解,进行了数值计算分析,并和不考虑地基粘性时的静力、动力响应做了比较。最后,讨论了荷载冲击周期及地基粘性对动态响应的影响。     

Hamilton体系中Timoshenko梁冲击问题的描述和求解

针对T im oshenko梁的冲击问题,在H am ilton体系中通过直接求解H am ilton矩阵的本征值问题并利用共轭辛正交关系,给出了以位移和应力表示的全状态向量解的一般表达式。根据边界条件给出了频率方程和广义模态函数向量。从H am ilton正则方程出发证明了广义模态函数向量的正交性,并给出了动响应及数值结果。从文中可以看出在H am ilton体系中结构弹性动力学问题的描述和求解的一般方法。通过比较本文结果与已有结果可以看出本文方法的正确性和可行性。     

砖砌体双向受力单元非线性分析模式

本文借鉴了前人的试验研究,在假定砌体单元为材料主方向的正交各向异性体的基础上,建立了应力增量和应变增量关系式。并应用正交各向异性体弹性常数转换方法,推导出在应力主方向的切线刚度阵,并由此建立了砖砌体双向受力单元非线性分析模型,应用于墙梁结构计算,与试验结果比较吻合。     

基于响应的梁损伤识别

采用扭转弹簧模拟悬臂梁的损伤，导出了损伤梁位移模态和转角模态的近似公式，获得了损伤梁在单点激励下，零初始条件的位移和转角响应。发现损伤梁的转角响应在损伤处发生阶跃变化，而损伤梁的转角响应对位置的一阶偏导数在损伤处有脉冲两数型突变的特点，从而提出了基于损伤梁转角响应的损伤判据函数。通过对损伤梁和损伤桁架结构的数值模拟，表明提出的判据函数不仅可以利用简谐激励下的响应识别梁的损伤，电可以利用冲击激励下的响应识别桁架的损伤。实验结果表明利用所提出的判据函数，可以同时判别损伤的位置和损伤的程度。     

正交各向异性薄板振动响应的波函数法

提出了适用于正交各向异性薄板弯曲振动响应预测的波函数法,基于Kirchhoff正交各向异性薄板振动控制方程,推导了体现各主轴物理量且精确满足其控制方程的复合结构波函数。通过傅里叶变换,在波数域对响应函数进行角积分,得到处于外部激励下的无限正交各向异性板振动响应。结合正交各向异性薄板的物理边界,运用加权余量法求得各正交各向异性结构波函数的系数,得到薄板的弯曲振动响应。建立矩形正交各向异性板的波函数响应模型,通过双级数解法验证了方法的正确性,与有限元法的对比结果说明,波函数法对正交各向异性薄板在中频范围的振动响应预测有着更高的计算效率。     

复合材料定向管热弹动力响应特性研究

为研究复合材料定向管热弹性问题,采用求解轴对称流动Euler方程组的正格式方法对管内火箭燃气射流场进行数值模拟,得到了管内流场热力载荷。运用非线性有限元方法,建立了复合材料定向管非线性热弹性有限元模型,将定向管模态计算结果与模态试验结果作比较,验证了有限元模型的有效性,计算了复合材料定向管分别在火箭燃气动压载荷、非定常温度场和耦合状态下的动力学响应。结果表明:由非定常温度场热冲击引起的定向管内壁面热应力响应呈现脉冲形状,轴向应力对复合材料定向管定位部间管段的应力响应影响较径向应力和周向应力明显,热冲击引起的热应力在复合材料定向管的热弹性应力响应中占主导作用。     

叠层板在两项简谐激励作用下的组合共振分析

研究了在四边简支的边界条件下,正交各向异性矩形叠层板在两项横向简谐激励作用下的非线性组合共振及其稳定性问题。在给出了正交各向异性叠层板的振动微分方程的基础上,利用伽辽金法导出了相应的无量纲化达芬型非线性强迫振动方程。应用多尺度法对组合共振问题进行求解,得到了系统在稳态运动下的幅频响应方程。基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件。通过数值算例,对几种复合材料薄板的共振特性进行了分析,分别给出了不同条件下系统运动的响应图、幅频图和动相平面图,讨论了不同参数对系统非线性动力学行为的影响。     

The influence of transverse shear on the static flexure and Charpy impact response of hybrid composite materials

Classical laminated anisotropic plate theory, extended to include the effects of transverse shear, is applied to the three-point beam bending problem, to determine the deflections under load, hence flexural modulus, and also the energy absorbed by the beam to the point of peak load, i.e. to first failure. A standard unnotched Charpy impact specimen configuration, constructed of a multi-lamina hybrid composite material, is analysed. Transverse shear is shown to have a significant influence on the response. The analytical results are compared with experimental data, for both impact and static loadings. A definite loading rate dependence is observed.     

基于新修正偶应力理论的Mindlin层合板自由振动分析

该文基于各向异性修正偶应力理论建立一个Mindlin层合板（跨厚比10~20的中厚板）自由振动模型。该理论偶应力曲率张量不对称,但偶应力弯矩对称。利用Hamilton原理推导振动微分方程和边界条件。新模型可退化为修正偶应力层合薄板振动模型和经典Mindlin层合板振动模型。以正交铺设简支方板为例计算了偶应力模型的自振频率,分析偶应力Mindlin层合板的自由振动尺度效应。算例表明,该文建立的新修正偶应力层合板模型能够用于分析细观尺度下Mindlin层合板的自由振动及尺度效应。     

含孔复合材料层合板孔边的应力集中

针对含孔有限宽复合材料层合板的应力集中问题,提出一种计算孔边应力分布及应力集中因子的方法：先利用经典层板理论,将复合材料层合板化归为各向异性板;再将各向异性板等效转换为一偏轴拉伸的单向纤维层板;最后利用含孔偏轴单向板的孔边应力计算公式来分析一般铺层层合板孔边应力集中情况。根据所推导的计算公式,分析讨论了板宽/孔径比、铺层比例、铺层方式、材料性能参数等因素对孔边应力集中的影响。     

A model of composite laminated Reddy beam based on a modified couple-stress theory

In this paper, a new anisotropic constitutive relation based on a modified couple-stress theory is defined for composite laminated Reddy beam. The theory contains only one material length-scale parameter in each ply of the composite laminated beam. The example of a cross-ply simply supported beam subjected to transverse load q₀sin(πx/L) is presented. Numerical results show that the proposed beam model can capture the scale effect of the microstructure. The proposed model can be reduced to several models of the modified couple-stress theory by adopting the assumptions in Timoshenko beam, Bernoulli–Euler beam and material isotropy. It can be seen that the deflections and stresses obtained by the proposed beam model are smaller than those based on Timoshenko and Bernoulli–Euler beam assumptions.     

A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation

Based on a modified couple stress theory, a model for composite laminated beam with first order shear deformation is developed. The characteristics of the theory are the use of rotation–displacement as dependent variable and the use of only one constant to describe the material’s micro-structural characteristics. The present model of beam can be viewed as a simplified couple stress theory in engineering mechanics. An example as a cross-ply simply supported beam subjected to cylindrical bending loads of f_w = q₀ sin (πx/L) is adopted and explicit expression of analysis solution is obtained. Numerical results show that the present beam model can capture the scale effects of microstructure, and the deflections and stresses of the present model of couple stress beam are smaller than that by the classical beam mode. Additionally, the present model can be reduced to the classical composite laminated Timoshenko beam model, Isotropic Timoshenko beam model of couple stress theory, classical isotropic Timoshenko beam, composite laminated Bernoulli–Euler beam model of couple stress theory and isotropic Bernoulli–Euler beam of couple stress theory.     

Efficient laminated composite beam element subjected to variable axial force for coupled stability analysis

A numerically efficient laminated composite beam element subjected to a variable axial force is presented for a coupled stability analysis. The analytical technique is used to present the thin-walled laminated composite beam theory considering the transverse shear and the restrained warping-induced shear deformation based on an orthogonal Cartesian coordinate system. The elastic strain energy and the potential energy due to the variable axial force are introduced. The equilibrium equations are derived from the energy principle, and explicit expressions for the displacement parameters are presented using the power series expansions of displacement components. Finally, the member stiffness matrix is determined using the force–displacement relations. In order to verify accuracy and efficiency of the beam element developed in this study, numerical results are presented and compared with results from other researchers and the finite beam element results, and the detailed finite shell element analysis results using ABAQUS; especially, the influence of variable axial forces, the fiber orientation, and boundary conditions on the buckling behavior of the laminated composite beams is parametrically investigated.     

修正偶应力理论层合薄板稳定性模型及尺度效应

该文将各向同性修正偶应力理论推广到各向异性,提出各向异性的细观尺度的复合材料层合板的本构方程,基于虚功原理建立了各向异性修正偶应力理论并用于建立复合材料层合薄板偶应力理论稳定性模型。该理论的偶应力部分的转角不是独立变量(称为C1理论),对于各单层引入纤维和基体材料的不同的两个材料细观参数,建立了适用于层合板/夹层板的偶应力理论模型。该理论的应变不对称,但是,用于各向同性材料与修正偶应力理论等价。为了便于工程应用,忽略基体材料的细观长度参数,建立了各单层只含一个材料细观参数的偶应力层合薄板理论稳定性模型。算例表明建立的偶应力层合板模型能用于分析层合板稳定性的尺度效应。     

A theory of one-dimensional fracture

A completely analytical theory is developed for the mixed mode partition of one-dimensional fracture in laminated composite beams and plates. Two sets of orthogonal pure modes are determined first. It is found that they are distinct from each other in Euler beam or plate theory and coincide at the Wang-Harvey set in Timoshenko beam or plate theory. After the Wang-Harvey set is proved to form a unique complete orthogonal pure mode basis within the contexts of both Euler and Timoshenko beam or plate theories, it is used to partition a mixed mode. Stealthy interactions are found between the Wang-Harvey pure mode I modes and mode II modes in Euler beam or plate theory, which alter the partitions of a mixed mode. The finite element method is developed to validate the analytical theories.     

热载荷下轴对称回转复合材料层合壳体的边界效应

本文采用有限单元法研究轴对称回转复合材料层合壳体在热荷载作用下壳体内的温度场和热应力场的分布, 并以算例讨论了温度场的分布、铺层次序、壳厚对层合壳体热应力(包括层间应力)的影响。      

Damage Constitutive Equations and its Application to Fiber Reinforced Composites under Transverse Impact

Two continuous field variables, called as continuity tensor and damage variable tensor, are used to describe the anisotropic responses of an elastic-brittle material under transverse impact load. Based on the continuum damage mechanics, anisotropic damage constitutive equations in both full and incremental forms are proposed here. The expressions of effective elastic module tensor, damage variable tensor and damage propagation force tensor are further derived, and the methods for determining the tensors are explained in detail. An example of strain and damage response of a fiber reinforced composite laminated plate under transverse impact load is employed to demonstrate the application of this theory. In the example, the damage variable coupled with geometric large deformation of laminated plate is also considered. The calculating results illustrate the influence of damage on strain field in the impacted laminated plate.