复合材料层合板的弯曲与振动

本文应用应力杂交有限元方法分析了复合材料层合板的弯曲与振动.在本文中,首先根据修正的余能变分原理,构造了一个适合于复合材料层合板特点的矩形应力杂交板弯曲单元.在单元内,分层假设应力参数,在单元的边界上,根据YNS理论的假设确定边界位移场.这样使得构造出来的单元不仅能够考虑横向剪切变形的影响和局部扭曲效应,而且具有较少的自由度数.其次,用此单元求解了层合板的弯曲与振动问题,并将计算结果与精确解进行了比较,比较表明二者非常接近.这说明了在计算方面本文单元具有较高的精确度.     

对称复合材料层合板弯曲的三维数值分析

本文采用三维各向异性有限单元模拟纯弯曲载荷下的复合材料层合板，给出了应力、应变沿厚度方向的变化规律。分析结果表明，在斜交对称铺层层合板的中心区域（远离加载端和自由边的区域），板的层间粘接界面附近，有根强的应力集中现象，可称之为层间效应。层间界面处力学性质的突变导致了层间应力的产生，并使层合板处于三向应力状态。三维数值模型给出的应变分布不同于基于Ｋｉｒｃｈｈｏｆｆ－Ｌｏｖｅ直法线假设的经典层合板理论给出的应变分布。     

复合材料对称层合板单向拉伸与面内剪切下的三维应力分析

本文给出了单向拉伸与面向剪切载荷下复合材料对称层合板中心区域的应力和应变沿板厚的数值计算分布规律。计算结果表明，在斜交对称辅层的层合板中心区域层间界面附近存在着层间边界层效应。层间界面处纤维走向的突变导致局部的三维应力状态和很强的应力集中。     

空心柱形杆的弹性扭转问题

本文证明了对具有任意形状截面的空心柱形杆的弹性扭转问题,当杆的内孔以一定的方式收缩为一点时,杆的应力在L_2空间中强收敛于相应实心杆的应力,从而证明了对柱形杆的弹性扭转问题不存在孔边应力集中现象。     

用界面单元法分析复合材料界面力学性能

本文利用界面单元的固有特性，将其用来模拟复合材料中纤维与基体之间的界面特征，计算了一个沿Ｘ轴方向纤维周期排列的单尾板，在横向载荷作用下的应力分布问题．给出了三相（纤维、基体和界面）特性各种配比时应力分布等高线图以及通过界面时径向应力σｒ的变化情况，反映了界面特性对应力分布的影响．     

带裂纹方形截面杆扭转问题的自然边界元与有限元耦合法

根据基于区域分解的自然边界元与有限元的耦合法,研究了带裂纹的方形截面杆的扭转问题,编制了耦合法计算程序,计算了几种尺寸截面的抗扭刚度、截面各点的应力及裂纹的应力强度因子,并绘出了裂纹尖端的应力分布图.计算中,还探索了松弛因子对迭代收敛速度的影响.从实践上证实了自然边界元与有限元的耦合法所具有的优点.     

以Kirchhoff薄板理论解狭长矩形截面杆的约束扭转

本文以Kirchhoff的薄板理论,解狭长矩形截面杆的约束扭转.这扭转问题,相当于在自由端作用扭矩的悬臂矩形板的弯曲.得到的结果,不仅证实了Timoshenko教授以能量法所得的扭转角,并且也给出应力的值.     

直角平面内圆孔对稳态SH波的散射

利用复变函数方法和多极坐标移动技术，研究了直角平面内圆孔在直边分布有反平面稳态载荷时的sH波散射问题．首先构造出直角平面内不含有圆孔时满足边界应力条件的Green函数解；其次提出直角平面内存在圆孔时满足边界应力自由条件的散射波解，并利用叠加原理写出问题的位移总波场．借助于多极坐标移动技术和圆孔边界处应力自由条件，列出求解散射波解中未知系数的无穷代数方程组，在满足计算精度的前提下，通过有限项截断进行求解．作为算例，具体讨论了圆孔边界处的环向动应力随不同波数、圆孔位置及载荷分布位置和分布范围大小的变化情况，算例结果说明了算法的有效实用性．     

波形钢腹板箱梁的约束扭转剪应力分析

基于周边不变形理论,结合闭口薄壁杆件约束扭转的计算分析,研究了波形钢腹板箱梁在约束扭转时混凝土悬臂板上扭转剪应力的分布,并进行了计算.通过对悬臂板在约束扭转中剪力流计算公式的推导,进一步阐述了其自由扭转剪应力及翘曲扭转剪应力的分布,指出了相关文献在这部分计算中存在的问题.通过一个简支波形钢腹板组合箱梁算例,将该文方法计算结果与ANSYS有限元计算结果进行比较.结果表明:在波形钢腹板箱梁截面中,主要由波形钢腹板承受扭转剪应力,其次是混凝土底板,底板剪应力最大值发生在底板中心处,其数值近似等于腹板剪应力的一半,而混凝土顶板和悬臂部分的扭转剪应力很小;该文计算的扭转剪应力结果在总体上符合有限元得到的扭转剪应力分布规律,在悬臂自由端为0,随着离开悬臂自由端距离的增大,扭转剪应力逐渐增大并达到峰值.     

平面弹性裂纹分析的一种有效边界元方法

提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法．该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界．算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的．此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析．这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响．     

The dynamic behaviour of piezoelectric laminated bars

A theory of laminated electroelastic bars with layers arranged symmetrically about the middle plane of the bar is constructed. Particular attention is given to the influence of the electrical conditions on the faces of the piezoelectric layers on the equations of the theory of bars. Formulae are obtained which, after solving the problem of a laminated bar, enable one to transfer from one-dimensional required quantities to three-dimensional required quantities. As an example, the vibrations of a three-layer electroelastic bar are considered, the displacements, stresses and electrical quantities are calculated, and the dependence of the electromechanical coupling coefficient on the frequency of the vibrations and the thicknesses of the elastic and piezoelectric layers is investigated.     

Deformation of laminated anisotropic bars in the three-dimensional statement 1. Transverse-longitudinal bending and edge compatibility condition

By using the methods of asymptotic splitting, the 3D problem on the transverse-longitudinal bending of elastic anisotropic laminated bars under the action of longitudinal and transverse loads is split into a number of plane boundary-value problems, whose solution allows one to construct asymptotic approximations for all components of the displacement vector and the strain tensor at each point in the bars. A system of ordinary differential equations of transverse-longitudinal bending is obtained for laminated bars with arbitrary anisotropy of its layers. A condition for the edge compatibility of materials in laminated orthotropic bars is deduced. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 379-410, May-June, 2009.     

Free-edge stress analysis of general composite laminates under extension, torsion and bending

In this study, based on the reduced form of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates subjects to extension, torsion, and bending. The constant parameters being in the displacement field, which describe the global deformation of a laminate, are appropriately calculated by using the improved first-order shear deformation theory. Reddy’s layerwise theory is subsequently employed for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. Various numerical results are developed for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates near the free edges. Finally the effects of end conditions of laminates and geometric parameters on the boundary-layer stress are studied.     

Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory

The free vibration of laminated composite plates on elastic foundations is examined by using a refined hyperbolic shear deformation theory. This theory is based on the assumption that the transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies the conditions of zero shear stresses at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In the analysis, the foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second foundation parameter is zero. The equation of motion for simply supported thick laminated rectangular plates resting on an elastic foundation is obtained through the use of Hamilton’s principle. The numerical results found in the present analysis for free the vibration of cross-ply laminated plates on elastic foundations are presented and compared with those available in the literature. The theory proposed is not only accurate, but also efficient in predicting the natural frequencies of laminated composite plates.     

Optimization of a Composite Plate Buckling under Thermal Action with Account of Reliability

Optimization of the structure of a laminated anisotropic composite plate subjected to thermal action is considered. The thermoelastic properties of the laminated composite are determined from the known stochastic properties of the components and the given values of the variable structural parameters, using the method of orientational averaging. The properties to be optimized - the critical load and thermal stresses - depend on two variable parameters, the stochastic properties of the composite and the temperature. In the space of the properties being optimized, the domain of admissible solutions and the parameters of the property scatter ellipses at the characteristic points of the project are found. For the compromise optimum project obtained, the reliability is determined with account of the correlation between the critical and thermal stresses. Reduced requirements to the critical loads and thermal stresses lead to an increase in the reliability of the project.     

Multiobjective Optimization of a Composite Cylindrical Shell with an Elastic Core with Account of Reliability

Multiobjective optimization of the structure and geometry of a laminated anisotropic composite shell with an elastic core under thermal action is considered. The thermoelastic properties of the laminated composite are determined from the known properties of the monolayer and the given values of the variable structural and geometric parameters. The properties to be optimized - the critical load and thermal stresses - depend on two variable parameters, the stochastic properties of the composite, and the temperature. In the space of the properties being optimized, the domain of allowable solutions and the property scatter ellipses for the optimum compromise project are found. The reliability of the project is determined with regard for the correlation between the critical and thermal stresses.     

复合材料层合板的三维非线性分析

本文提出了一种研究复合材料层合板壳三维问题的解析方法．该方法采用摄动方法和变分原理来满足三维弹性理论基本微分方程及限制条件，分析了受横向载荷作用的复合材料各向异性单层圆板及层合圆板的三维非线性问题．得到了高精确度的摄动级数解答．大量结果表明横向剪应力和横向正应力在层合板的三维非线性分析中是很重要的．     

正交异性悬臂柱壳轴对称问题的弱形式解

导出层合柱壳轴对称问题的平衡方程和边界条件的弱形式,提供了方程和边界条件放在一起的算子形式,建立了悬臂柱壳轴对称问题的热应力混合方程,给出了正交异性层合悬臂柱壳在热荷载和机械荷载作用下的弱形式解。本文提出的方法弱化了求解方程和边界条件,化解了问题,具有一般性并便于推广。     

Modeling of Structures in the Mechanics of Composites

One possible general statement of a quasi-static problem in the mechanics of composites is considered. It is assumed that a composite is characterized not only by the heterogeneity of a regular structure, but also by the presence of imperfections, impurities, cracks, and the roughness of surfaces, which are partly taken into account by introducing appropriate couple stresses. Two statements, in displacements and in stresses, are considered together with the statement of the same problems in the case where the constitutive relations are linear integral operators. The boundary-value problem remains nonlinear due to the nonlinearity of a scattering function which enters into the heat equation. The theory of effective moduli for a nonpolar medium is discussed in more detail. The equilibrium equations for a homogeneous medium with reduced characteristics and the equation of heat inflow, introduced in nonlinear (in an explicit form) and linear variants, are examined. For a simple laminated composite, all effective mechanical and thermophysical characteristics are found in an explicit form. The effective material functions for a transversely isotropic medium are constructed on the basis of a unique dimensionless relaxation kernel with the use of several Il'ushin kernels. Based on the known solution of the boundary-value problem for the reduced medium, the stress and strain concentration tensors, at any point of a simple laminated composite, are also constructed in an explicit form. In this case, the changes in the structure are taken into account.     

Two new hyperbolic shear displacement models for orthotropic laminated composite plates

Two hyperbolic displacement models, HPSDT1 and HPSDT2, are developed for a bending analysis of orthotropic laminated composite plates. These models take into account the parabolic distribution of transverse shear stresses and satisfy the condition of zero shear stresses on the top and bottom surfaces of the plates. The accuracy of the analysis presented is demonstrated by comparing the results with solutions derived from other higher-order models and with data found in the literature. It is established that the HPSDT1 model is more accurate than some theories of laminates developed previously, and therefore the analysis can be expanded to laminated composite shells.