平面编织复合材料层板弹性性能的预测

本文在平面编织纤维增强树脂复合材料的单方向直波纹模型的基础上,分别采用经典层合板理论和有限元应变能等效方法,预测了平面编织复合材料层合板迭层对其弹性性能的影响。根据经典层合板理论,由对平面织物复合材料的单向直纹模型的上、下表面施加不同的约束条件,得出层板弹性常数变化范围。用有限元能量法,则预测出不同铺层数的编织复合材料层板的弹性性能。与实验结果比较,表明纵向模量的预测是可靠的。     

考虑不可伸长和材料内阻的旋转复合材料轴的非线性自由振动分析

建立了考虑材料内阻的旋转复合材料轴的非线性动力学模型,研究材料内阻对旋转轴非线性自由振动的影响。模型包括转动惯量和陀螺效应,但剪切变形不予考虑。基于不可伸长假设,采用曲率和惯性非线性描述复合材料轴的大振幅振动。基于复合材料的黏弹性描述阻尼耗散特性。基于扩展的Hamilton原理,导出旋转复合材料轴的弯-弯耦合非线性振动偏微分方程组。采用Galerkin法将偏微分方程进行离散化,采用多尺度法对常微分方程进行摄动分析,导出非线性自由振动解的分析表达式,针对铺层角、长径比、铺层方式和旋转速度进行数值分析,研究材料内阻对旋转复合材料轴的非线性固有频率的影响。将多尺度法求解的结果与数值积分的结果进行了比较,验证了模型与方法的正确性。     

折线型截面复合材料层合梁弯曲性能预测与分析

基于各向异性复合材料层合板弹性理论,研究空间折线型复合材料层合梁弯曲性能计算方法。首先推导了考虑铺层设计的翼缘板和腹板在局部坐标系下的刚度矩阵和本构关系,然后通过平行移轴原理建立折线型复合材料层合梁的整体抗弯刚度理论计算公式,在此基础上求出结构在竖向荷载作用下的挠度值。有限元与理论值对比表明本文的理论计算公式有较好的精度。此外,还分析了翼缘与腹板水平夹角及纤维纵横向铺层比对层合梁挠度的影响。结果表明:结构的挠度随夹角的增大而减小,且夹角越大理论值与有限元值越接近,而纤维纵横向铺层比的变化对结构挠度影响几乎可以忽略。该弯曲预测方法可用于计算Z型、槽型、工字型等空间折线型截面复合材料层合梁刚度和位移。     

磁致伸缩铺层阻尼板壳结构的振动分析

通过理论分析讨论了含磁致伸缩材料和黏弹性材料铺层的层合板壳结构的频率和损失因子。假设黏弹性层仅发生剪切变形, 对磁致伸缩层应用偏置磁场下的线性本构, 推导得到由磁致伸缩层、黏弹性层、复合材料基本层组成的约束阻尼薄壳结构的运动方程, 并求得结构振动频率和损失因子的解。对板、曲板等算例的计算结果表明, 用磁致伸缩材料作约束层可使层合结构损失因子提高。      

轴向冲击下环向加筋复合材料圆柱壳的非线性动力响应

采用半解析的方法，建立离散加筋圆柱壳模型，基于复合材料多层扁壳大挠度的剪切变形理论，利用Hamilton原理导出环向加筋复合材料圆柱壳的非线性运动控制方程；用Galerkin方法对空间变量进行离散，将位移和载荷展开为双级数，得到有关时间的常微分方程组，最后采用R-Kutta方法数值求解．通过算例，讨论了加筋肋骨几何参数、铺层角度、辅层方式、铺层层数等因素对动力响应的影响。     

复合材料多层板壳在非线性弹性失稳时的本构关系

在研究复合材料的多层、夹层和加筋板壳的非线性弹性和塑性失稳问题时,需要用到失稳前的应力与应变之间和失稳时的应力增量与应变增量之间的非线性关系。复合材料在纤维断裂和基体开裂以前的物理非线性,主要是由基体引起的。本文对非线性弹性和处于主动塑性变形阶段的各向同性基体,采用小弹塑性变形理论,导得了应力与应变之间的各向同性非线性关系和应力增量与应变增量之间的各向异性非线性关系。假定纤维是线性弹性的。用复合材料的复合定律,求得了单向增强纤维复合材料层片的应力与应变之间和应力增量与应变增量之间的非线性关系。     

受热复合材料层合板的非线性热振动——Part Ⅱ : 实验研究

对不同铺层方式和铺设角度的复合材料层合板的热振动进行实验研究, 实验结果给出了一些有益的结论, 并有力证明了作者提出的非线性高阶层合理论和非线性热振动分析有限元算法(Part Ι) [1]的正确性。     

湿热环境下复合材料层板的几何非线性分析

根据Reddy的高阶剪切变形理论,在应力应变本构关系中考虑湿热环境的影响,用虚位移原理推导出以位移形式表达的复合材料层板的几何非线性控制方程及相应的边界条件。选定的边界条件为弹性转动约束。选择不同的弹性转动系数,可以得到介于简支到固支之间的不同边界条件。假设材料的物性参数不随湿热环境而变化。用Galerkin方法求解控制方程。数值结果所用的边界条件为四边固支。最后讨论了温度和湿度、长厚比、长宽比和铺层数等各种参数变化的影响。计算和分析的结果均表明温度的升高对层合板的弯曲产生非常不利的影响;而加湿对层合板的弯曲影响是非常有限的。在其它几何条件不变的情况下,增加铺层数,不仅能降低挠度,也能明显地降低弯矩或弯曲应力。     

三维复合材料层合板渐进损伤非线性分析模型

为有效反映复合材料层合板层间相互作用和材料损伤非线性,建立了中等尺度的三维复合材料层合板渐进损伤分析模型。非线性渐进损伤分析过程包括应力求解、材料损伤失效判据及材料性能退化方案3个方面。讨论了损伤材料性能退化方案,引入与材料损伤模式相对应的损伤变量表征材料点的损伤状态,材料的刚度矩阵按损伤变量退化。基于该模型可成功预测复合材料层合板损伤起始、扩展直至最终失效的整个过程和极限强度。经文献试验数据验证,12种不同铺层顺序层合板的计算强度与试验数据均吻合较好,表明该模型在复合材料层合板极限强度预测上的有效性。     

各向异性复合材料开孔板拉伸强度预测及模型验证

基于有限断裂力学方法建立了一种预测多向复合材料开孔板拉伸强度的通用和半经验模型。该模型同时采用基于应力形式的失效准则和基于能量形式的失效准则预测失效。模型仅需铺层弹性常数、无缺口层合板的强度以及0°铺层的断裂韧性等参数。基于线弹性断裂力学建立了多向复合材料层合板的断裂韧性与0°铺层断裂韧性之间的关系, 进而预测了任意铺层复合材料开孔板发生纤维主导拉伸失效时的强度。将模型预测结果与开孔板拉伸强度的试验数据进行了对比验证, 预测误差最大为9.7%, 与点应力和平均应力等方法的对比表明, 该模型的预测精度高于传统的特征长度方法。      

A precise measurement of some nonlinear effects and its application to the evaluation of nonlinear elastic constants of quartz and GaPO4

This paper deals with a precise measurement of amplitude frequency and intermodulation effects, and its application to the evaluation of nonlinear elastic constants of quartz and gallium orthophosphate (GaPO/sub 4/). An evaluation is based on the methods used previously concerning determination of the higher-order material constants in the quartz. Using a measurement of the intermodulation products and measurement of drive level dependence of resonant frequency of quartz resonators, we have determined some effective elastic constants of fourth order. The computer-based method of solution of the set of equations gives an access to obtain a number of effective nonlinear stiffnesses of fourth order. The measurements and computer solutions are performed on different Y-cuts resonators, both for quartz and gallium orthophosphate resonators, vibrating in fundamental thickness shear mode. The experimental results are discussed.     

Nonlinear Elastic Properties of Superconducting Antiperovskites MNNi3 (M =Zn,Cd, Mg,Al, Ga,and In) from First Principles

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi ₃ (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs.     

Elastic Constants of Synthetic Single Crystal Corundum at Room Temperature

The six elastic constants (and six elastic compliances) of corundum were determined in the kilocycle per second frequency range by an accurate resonance method. The results were checked in the megacycle per second range with a less accurate, pulse velocity method. The elastic moduli for polycrystalline alumina calculated from the single crystal compliances determined by the resonance method are in good agreement with experimental values obtained on high density polycrystalline alumina. The variation of Young’s modulus and of the shear modulus with orientation was calculated from the compliances and the results are shown graphically. The results of the present work do not agree well with previous work on single crystal sapphire. The specification of orientation and the theory used to calculate the elastic constants are given in detail to support the contention that the results of the present work are correct.     

基于双轴拉伸试验的飞艇蒙皮材料非线性分析

飞艇蒙皮为多功能层压织物材料,力学行为呈现复杂的非线性,合理表征其非线性的力学模型对飞艇结构设计与分析至关重要。本文对飞艇蒙皮材料试件进行了7个应力比双轴拉伸试验,基于正交异性材料模型,采用应变残差平方和最小方法计算弹性常数,建立线性力学模型;根据试验数据建立应力弹性常数响应面,建立以应力为变量的完整三次式非线性力学模型。并根据此力学模型建立飞艇蒙皮材料有限元分析模型,通过数值模拟七种应力比下的双轴拉伸试验,分析结果的应力分布和分缝位移与试验现象一致。将分析得到的应力-应变曲线与试验结果进行对比,两者能很好的吻合,表明非线性力学模型及分析方法适用于飞艇结构分析。     

On the nonlinear viscoelastic behaviour of nylon fiber

Nonlinear time-dependent stress relaxation was determined experimentally in nylon fiber in the small strain domain. This process is accounted for on the basis of a quasi-linear viscoelastic theory. A nonlinear modified constitutive equation for the viscoelastic medium is deduced. In processing the experimental data it turned out to be necessary to keep the nonlinear terms up to cubic in the constitutive equation for nylon fiber. The elastic and rheological constants in the constitutive equation for nylon fiber are evaluated.     

The band gap of 1D viscoelastic phononic crystal

The band gap of one dimensional (1D) phononic crystal with viscoelastic host material is studied in this paper. The standard solid model is used to simulate the viscoelastic behavior of the host material and the fillers embedded in the host material are still assumed elastic material. The band gap problem in 1D phononic crystal leads to an eigenvalue problem by using the plane wave expansion method and the Bloch–Floquet wave theory in a periodic structure. An iterative algorithm is designed to obtain the band gap structure due to the dependence of elastic constants on frequency for the viscoelastic host material. A numerical example is given for steel/epoxy phononic crystal. The band gap of 1D phononic crystal is evaluated for different viscoelastic constants, namely, relaxation time, initial and final state elastic modulus. It is found that the viscoelastic constants of host material affect not only the location but also the width of band gaps.     

Material characterization of laminated composite materials using a three-point-bending technique

A three-point-bending technique is presented for identifying the elastic constants of laminated composite materials. In the proposed technique, three strains in the axial, lateral, and 45° directions on the bottom surface at the mid-span of a symmetric angle-ply beam subjected to three-point-bending testing are measured for elastic constants identification. The narrow beam theory together with the trial elastic constants is used to predict the theoretical strains of the beam. The theoretical and experimental strains of the beams are then used in a stochastic optimization method to identify the elastic constants of the beam. The accuracy and applications of the proposed technique are demonstrated by means of a number of examples on the elastic constants identification of graphite/epoxy (Gr/ep) or glass/epoxy (Gl/ep) laminated composite materials. The effects of specimen aspect ratio and thickness on the accuracy of the proposed method are investigated.     

用浸液超声法测量单向复合材料的弹性常数

本文系统的给出了用浸液超声法测量单向纤维增强复合材料五个独立的弹性常数的理论和实验方法,并对不同体积分数的两种不同表面处理的单向高强玻璃纤维增强复合材料(GRP)进行了测量研究。结果表明界面质量对GRP的弹性常数在实验的误差范围内看不出影响。实验数据和Halpin-T sai方程预示值相当一致。和实验值对照,外推得到的高强玻璃纤维的弹性常数和工程常数是相当准确的。      

纤维增强复合材料动态性能参数的识别方法

构造了一种纤维增强复合材料等效动态性能本构模型。根据经典层板理论分别推导出了显含弹性常数和显含阻尼系数的纤维增强复合材料层板的刚度矩阵和等效阻尼矩阵。利用模态试验方法, 得出了弹性常数、等效阻尼系数与层板振动模态之间的显式关系。通过识别本构方程中的等效阻尼系数, 可以方便地推导出任意铺层数和任意铺层角度下层板的等效阻尼矩阵。算例分析表明, 利用此方法识别出的弹性常数和等效阻尼能够满足工程精度要求。      

Ultrasonic Study of Elastic Anisotropy of Material Composite

The anisotropic elastic properties of two Aluminium Matrix Composites (AMC) were characterised using an ultrasonic method. The composite materials, fabricated by squeeze casting included aluminium matrix reinforced by alumina fibre and carbon fibre, respectively. The elastic constants were determined using an optimisation method associated to a classical ultrasonic immersion device. The methodology to recover the elastic constants consists in minimising the square deviation between calculated velocities and the experimental ones, measured under variable incidence from a computer controlled ultrasonic immersion device. The method of optimisation we use in this work is based on Levenberg–Marquard algorithm allowing a better convergence to the physical solution of the inverse problem. The elastic anisotropy of the two materials is discussed and the results are compared to experimental data taken from tensile tests and to values obtained by two models: the rule of mixture and a simplified Eshelby model.