Analytical solutions to edge effect of composite laminates based on symplectic dual system

In the symplectic space composed of the original variables, displacements, and their dual variables, stresses, the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper. In contrast to the traditional technique using only one kind of variables, the symplectic dual variables include displacement components as well as stress components. Therefore, the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously. After being introduced into the symplectic dual system, the uniform schemes, such as the separation of variables and symplectic eigenfunction expansion method, can be implemented conveniently to analyze composite laminate problems. An analytical solution for the free edge effect of composite laminates is obtained, showing the effectiveness of the symplectic dual method in analyzing composite laminates.     

基于树脂层强度预测分层萌生载荷

轴向拉伸下的层合板在自由边缘附近存在奇异应力场,容易产生分层萌生进而导致结构破坏.而大多数基于材料力学方法的分层萌生研究对强度参数的确定有较强的主观性,缺乏合理解释.本文通过在层间插入一定厚度的树脂层,将分层萌生视为层间树脂层在三维应力状态下的强度破坏,根据有明确试验标准的树脂强度和Mohr判据判断是否发生分层萌生.采...     

基于对偶变量变分原理的完整约束系统保辛算法

基于对偶变量变分原理,选择积分区间两端位移为独立变量,构造了求解完整约束哈密顿动力系统的高阶保辛算法。首先,利用拉格朗日多项式对作用量中的位移、动量及拉格朗日乘子进行近似;然后,对作用量中不包含约束的积分项采用Gauss积分近似,对作用量中包含约束的积分项采用Lobatto积分近似,从而得到近似作用量;最后,在此近似作用量的基础上,利用对偶变量变分原理,将求解完整约束哈密顿动力系统问题转化为一组非线性方程组的求解。算法具有保辛性和高阶收敛性,能够在位移的插值点处高精度地满足完整约束。算法的收敛阶数及数值性质通过数值算例验证。     

基于对偶变量变分原理和两端位移独立变量的保辛方法

将广义位移和动量同时用拉格朗日多项式近似,并选择积分区间两端位移为独立变量,然后基于对偶变量变分原理导出了哈密顿系统的离散正则变换和对应的数值积分保辛算法。当位移和动量的拉格朗日多项式近似阶数满足一定条件时,可以自然导出保辛算法的不动点格式。通过数值算例分析了位移和动量采用不同阶次插值所需最少Gauss积分点个数,并讨论了位移插值阶数、动量插值阶数以及Gauss积分点个数对保辛算法精度的影响,说明了上述不动点格式恰好是一种最优格式。     

Parameters of the Edge Effect as a Function of the Mechanical Characteristics of a Composite with an Interfacial Crack

The paper studies the dependence of edge effects in a laminated composite of regular structure with a periodic system of symmetric interfacial cracks on the mechanical characteristics of the composite components. Loading the composite induces constant strain in the reinforcement direction. The problem is solved in exact formulation using the linear elastic equations for piecewise-homogeneous media and a criterion for quantitative evaluation of edge effects. An approximate solution of the problem is found by the mesh approach. A difference scheme for the mixed problem under consideration is derived. The edge-effect zones for normal stresses are constructed. The maximum values of the normal stress concentration factors are determined     

Influence of Young's Moduli of a Laminated Composite with a Periodic System of Cracks on Edge Effects

A problem on edge effects in a laminated composite with a periodic system of symmetric contact cracks is studied. Loading of the composite induces constant deformation in the reinforcement direction beyond the edge effect. The problem is solved in an exact formulation under the linear theory of elasticity for piecewise-homogeneous media. An approximate solution is found by the mesh approach using the concept of a base scheme. For stresses _ij , the shape and size of the edge effect zone are studied depending on the ratio of Young's moduli of the composite components, which varies over a wide range     

The distributions of the interlaminar stress in a laminated shell with free end boundary

This paper studies the free edge effect yielded by interlaminar stress in a laminated cylindrical shell made up of fiber reinforced layer [0°], [90°] and the isotropic material layer under axisymmetric thermal load or radial pressure. Both ends of the shell are in free boundary condition. The exact solution of the problem can be obtained by using the three-dimensional theory of elasticity. For illustration, the numerical laminar stresses in a double-layer laminated shell under thermal load or radial pressure are calculated.     

缺口复合材料层合板疲劳性能的试验研究

对带各种缺口的复合材料层合板的疲劳性能进行了研究.设计了不同类型的缺口试件,分别进行静态和疲劳试验.试验数据表明,缺口对复合材料的静强度和静刚度的影响不大,缺口试样的疲劳寿命还高于无缺口试样,与金属材料相比,复合材料对缺口不敏感.采用条状试样获得的力学性能不能代表复合材料的真实性能,实验表明自由边的缺口对结构提高疲劳寿命是有利的.文中还对疲劳过程中复合材料的刚度变化进行了研究,对文中所研究的层合板,刚度的变化可分为三个阶段,通过剩余刚度可以预测复合材料的疲劳寿命.     

复合材料圆筒自由边效应的有限元分析

本文分析复合材料圆筒在内压作用下的自由边效应,讨论圆筒的叠层顺序对自由边应力的影响,预报最易发生边界脱层的界面．有限元分析结果表明：层间剪切破坏是该结构发生边界失效的主要原因,不同的叠层顺序可较大地影响自由边层间剪切应力,而大变形情况下线性有限元分析结果与非线性有限元数据相差较大,几何非线性的影响不容忽视．     

Energy release rate analysis of delamination in laminates

Delamination growth caused by local buckling of delaminated laminate under compression may lead the structure to failure. In this paper, a two-dimensional model of delaminated laminates was studied using a combination of post-buckling theory and fracture mechanics. The delaminated laminate under compression is first analysed by the first-order deformable plate thoery. Then, the energy release rateG at every point along the delamination front is derived by means of a variation problem with a moving boundary. Finally, the near-surface elliptical delamination is also discussed. There is a large variation of energy release rateG along the delamination front, the direction in which delamination growth may occur depends upon the delamination aspect ratio, the state of applied load and the orientation of plies.Supported by the Chinese Science Foundation of Aeronautics     

Gradient model in the problem of stress-concentration around a circular hole in two-component stochastic composites

The gradient model of stochastically inhomogeneous media is used to study the stress concentration around a circular hole in a two-component elastic composite. The study is based on a general solution of the system of equilibrium equations expressed in terms of harmonic functions and functions that satisfy the Helmholtz equation. This solution is used to solve problems for an infinite plane with a circular hole under uniform and uniaxial tension. The results obtained are compared with the solutions found using the theory of effective moduli, which is simpler __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 41–53, December 2007.     

Deformation of Cross-Ply Composite Laminates with Cracked Ceramic Matrix

The deformation of cross-ply ceramic-matrix composite laminates under biaxial loading is studied theoretically. Experimentally, microscopic damage evolution in cross-ply ceramic-matrix composite laminates has not been well characterized yet, mainly due to the difficulties involved in testing of anisotropic plates under biaxial loading. It is assumed that the initial damage mechanism observed in ceramic-matrix composite laminates is the formation of tunneling macrocracks both in the 90°- and 0°-plies. The paper addresses the stiffness-deterioration behavior of cross-ply ceramic-matrix laminates with transverse and longitudinal macrocracks. The analysis is based on the equivalent-constraint model of a damaged laminate. Numerical results for SiC/CAS cross-ply laminates of various lay-ups are presented and discussed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 37–46, January 2005.     

层合板冲击损伤的PD率效应本构模型分析

从近场动力学(简称PD)理论的PMB材料模型出发,结合Kelvin-Voigt粘弹性固体模型,建立PD率效应本构模型。采用LAMMPS软件模拟了环氧树脂板、纤维增强复合材料单向层板和多向铺层层合板受冲击的情况。通过分析各板的冲击损伤,探索纤维对板的增强作用。同时,分析了不同冲击速度下层合板上下表面的损伤程度,初步探讨了从低速碰撞到高速冲击过程中复合材料层合板的破坏机理及规律。     

Analytical formulation of stresses in curved composite beams

Summary This paper outlines an analytical method for computing normal and shear stresses generated in a curved laminated beam under bending loads. Each cross section is assumed to be symmetrical and loads are applied in the plane of symmetry. We build a statically admissible stress field in order to plot normal and shear stress distributions. Received 5 March 1997; accepted for publication 18 September 1997     

材料非线性对复合材料层合板热自由边界效应的影响

本文用准三维有限元法研究了材料非线性对复合材料层合板热自山边界效应的影响,给出了修正型Hahn-Tsai非线性应力-应变关系的三维形式。由本文非线性分析方法得到的层间应力与以往由线性分析方法得到的层间应力做了比较,结果表明:材料非线性能显著降低层间剪应力的集中程度,但对层间正应力影响不太明显。     

一种预测层合板层间剪应力的新后处理方法

层合板是航空航天领域典型的承力构件,过大的层间应力是导致其分层失效的主要原因.准确的层间应力预测往往依赖于三维平衡方程后处理方法(TPM).然而,该方法需要计算面内应力的一阶导,使得基于C0型板理论构造的线性单元无法使用TPM计算横向剪应力.本文在三维平衡方程后处理方法的基础上,提出了一种新后处理方法(NPM).新后处理方法通过虚功等效法消除了三维平衡方程后处理方法中产生的位移参数的高阶导.基于提出的新后处理方法和C0型板理论,仅需使用线性单元就可以预测层合板的横向剪应力.为了验证所提方法的有效性,本文基于修正锯齿理论(RZT)和所提方法构造了一种C0连续的三节点三角形线性板单元.数值算例表明,所提方法和三维平衡方程后处理方法具有相同的计算精度,提出的板单元能够准确高效地预测层合板的横向剪应力.此外,所提方法便于结合现有的有限元商用软件使用,基于商用软件中板壳单元获得的节点位移,使用新后处理方法极易获得准确的层间剪应力.     

On the description of anisotropic damage in composite laminates

A general anisotropic damage theory of cracked laminates is formulated here. The deformation of composite laminates is composed of matrix elastic strains, pseudo-elastic damage strains due to cracking and permanent damage strains due to interlaminar slip. The surface of damage initiation is constructed according to the concept of linear elastic fracture mechanics for the virgin material. After the initial damage, a pesudo-elastic damage can be used to describe the damage behaviour if interlaminar slip is negligible. Damage evolution, load induced anisotropy and interlaminar intralaminar interaction for composite laminates are examined; the latter can perturb the normality structure of damage strain rate. Explicit expressions are given for pseudo-elastic (or secant) moduli of the damaging composite laminates, under a non-interacting assumption imposed on the cracks between different families.     

缝纫复合材料层合板面内弹性模量分析

基于对缝纫孔附近局部细观结构的分析,提出了一种预测缝纫复合材料层合板面内力学性能的理论模型．从分析缝孔单胞的纤维弯曲几何特征入手,最终得到单向板及层合板的弹性常数．通过有限元分析研究了缝纫参数对复合材料层合板面内等效模量的影响．研究结果表明,缝纫造成单向板及层合板面内材料性质的不均匀,随着缝纫密度和缝纫线直径的增加,层合板的等效模量逐渐降低．     

接合残余应力在界面端的应力奇异性

接合残余应力对异种接合材料强度的影响很大，正确地分析接合残余应力在界面端附近的分布及其奇异特性，是研究异材强度评价方法的关键问题之一，本文利用弹性学中的Ｇｏｕｒｓａｔ公式和有关微分方程解的理论，求得了平面近似下的界面端附近的残余应力场及其应力奇异性，与单纯的外力作用时的情况不同，残余应力在界面端有可能出现对数型的应力奇异性，并且不能仅用Ｄｕｎｄｅｒｓ的异材参数来描述。