A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates

A refined trigonometric shear deformation theory (RTSDT) taking into account transverse shear deformation effects is presented for the thermoelastic bending analysis of functionally graded sandwich plates. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, the displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The sandwich with homogeneous facesheet and FGM core is considered. Material properties of the present FGM core are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The influences played by the transverse shear deformation, thermal load, plate aspect ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal–ceramic plates are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded plates.     

复合材料层板小挠度理论的改进

改进了复合材料层板高阶剪切变形理论。改进后的理论与一阶剪切变形理论同样只有5个独立变量,但考虑了横向剪切应变沿板厚呈二次曲线变化及满足了层间剪应力的连续性。该理论比简单高阶理论计算的位移和应力更为精确,且逼近三维弹性解。     

反对称正交铺层层板的热稳定

1.导言 复合材料结构在外载作用下力学响应由于温度的变化,层板的稳定问题的研究才刚开始涉及。热失稳问题在层板结构的应用中可能会产生,比如当宇航器在外层空间飞行时,由于受到太阳的幅射,温度改变而使层板失稳。国外有不少学者已开始这方面的研究,然而大都还限于经典理论范畴。本文提供的层板临界失稳温度控制方程是在Kirchhoff假设基础上考虑横向剪切变形影响后得来的,对于反对称正交铺设层板,可以找到解析解,并将结果与对称正交层板、经典理论结果作了比较,本文的结论对层板热稳定设计有一定     

夹层板大挠度问题的力学表征与数值模拟

随着材料制备工艺的发展和成型加工技术的日趋完善,夹层板在现代航空领域结构设计中获得了广泛应用,以获得理想的重量及其它功能性指标,工程分析时往往利用薄板理论进行近似分析,这忽略了夹层板的良好的抗弯特性,给分析结果带来较大误差.在薄板大挠度问题及夹层板相关理论的基础上,提出分段叠加法分析大挠度夹层板的变形机理,并利用有限元进行了数值模拟,结合某型飞机蜂窝轮舱壁板静力试验验证了夹层板大挠度变形机理的合理性,证明了叠加法的有效性.     

一种含分层复合材料层合板高阶理论及有限元模型

本文提出了一种新的复合材料县合板高阶弯曲位移模式。此模式考虑了横向剪切的影响,得到一种新的厚板有限元模型。对于含有分层的单元,通过改变其单元内横向剪切应力的分布,达到改变单元刚度的目的。因此,此模型适用于任何厚度的或含有分层的复合材料层合板。     

层叠纤维增强板的振动问题

 本文用任意正交铺层的简支矩形板自由振动问题的精确解,通过计算研究了经典层板和考虑剪切的层板振动理论的适用范围;还研究了在经典层板横向振动理论中板平面内两个方向惯性力的影响问题,结论是可以忽略这种影响。     

复合材料叠层板壳有限元的渐近解

 本文针对复合材料叠层板壳结构建立了一个分层计算的有限元模型,此模型的特点是以参考面的位移和各层横向剪应变作为独立的自变量,导出了叠层板壳的有限元模式,这是和原有分层模型的本质区别,从而具有以下优点:(1)刚度矩阵具有良好特性,可采用渐近法求解,大大提高了计算效率,克服了分层模型中的最大困难;(2)完全避免了较薄的板壳在有限元计算中常发生的“剪切自锁”现象;(3)较精确地考虑了各层的剪切效应,无须再引入剪切修正系数。还采用此模型较好地解决了任意铺层的叠层板弯曲、叠层板脱层屈曲和承受任意载荷的轴对称叠层壳的弯曲等问题,证明了此模型的优点和可靠性。此模型还极易推广应用于叠层板壳的动力、稳定和层间应力等问题。     

An advanced five-unknown higher-order theory for free vibration of composite and sandwich plates

Accurate prediction of dynamic characteristics is quite critical to understand the strength of layered structures. Nevertheless, the existing five-unknown higher-order theories encounter difficulties to forecast accurately the dynamic response of sandwich structures. Therefore, a new five-unknown higher-order theory is developed for free vibration analysis of composite and sandwich plates, which possesses the same degree of freedom as those of other five-unknown higher-order theories. The developed model can meet beforehand interlaminar continuity conditions and the free-surface conditions of transverse shear stresses. To assess capability of the proposed model, analytical solution for such composite structures with simply-supported conditions has been presented by employing Hamilton’s principle, which is utilized for analysis of mechanical behaviors of composite and sandwich plates. Compared with the three-dimensional (3D) elasticity solutions, 3D finite element results and the results obtained from the chosen five-unknown higher-order models, the proposed model can yield accurately natural frequencies of composite and sandwich plates. Even for the thick plates, the higher-order frequencies calculated from the proposed model are in good agreement with the 3D finite element results. By studying effect of the thickness/length ratios on natural frequencies, it is found that the proposed model is adaptable to predicting natural frequencies of the sandwich plates with the thickness/length ratios between 1/4 and 1/100. In addition, some factors influencing accuracy of five-unknown higher-order models have been investigated in detail. Finally, by means of numerical analysis and discussion, some conclusions have been drawn as well, which can serve as a reference for other investigators.     

考虑横法向热应变的Reddy型功能梯度梁理论

Reddy型高阶理论已被广泛用于功能梯度材料(FGM)结构分析,然而此理论忽略了横法向应变,难于准确分析功能梯度梁的热力行为。为提高Reddy理论分析热力响应的精度,提出了一种考虑横法向热应变的三参数Reddy型高阶功能梯度梁理论。此模型考虑了横法向热应变,但不增加额外位移变量。应用构建的模型分析了功能梯度梁的热力响应,并研究了不同体积分数对面内应力和位移的影响。数值结果表明,所提出的模型能准确分析功能梯度梁的热力响应,而忽略横法向应变的模型计算结果精度较低。     

一种特殊梯度分布的功能梯度矩形板弯曲问题解析解

研究了一种特殊梯度分布功能梯度材料矩形板弯曲问题。假设材料的弹性模量在板厚度方向上呈幂函数分布,泊松比为常数,引入PLEVAKO解,利用分离变量法,导出四边简支功能梯度材料矩形板弯曲问题的解析解。通过算例分析了材料组分变化时,功能梯度板应力和位移的变化规律。结果显示不同梯度分布板结构中的应力、位移的变化规律是不同的,有时甚至差别很大。该方法为发展针对功能梯度材料特点的数值算法和简化理论提供依据。     

基于有限元方法的复合材料层合板自由振动分析

利用有限元分析方法分别研究了正交各向异性、对称角和反对称角铺设的正方形复合材料层合板的线性和非线性自由振动问题.结合一阶剪切变形理论推导出层合板自由振动的有限元方程,构造了三维有限元模型,并对其基频进行计算.数值结果与其他的文献的结果对照表明,用有限元方法求得的基频与用各阶剪切变形理论求得的结果非常接近,但对于厚板结果与经典Kirchhoff的结果有一些差距,对于其他理记是一致的.     

编织玻璃纤维与碳纤维铺层功能梯度板吸能特性研究

为探讨由SW100/5228A玻璃纤维编织（GFRP）层板与CCF-1/5228A碳纤维复合材料（CFRP）层板以不同比例组成的功能梯度板的吸能性能,用重量80g直径23mm的弹丸对六种比例组成的功能梯度板进行了速度约70m/s的弹道试验。对弹击后的试样进行了损伤分析和剩余强度试验,通过C扫描发现,大面积损伤往往发生在...     

复合材料层合板弯曲振动高阶理论及有限元模型

本文提出了一种新的复合材料层合板高阶弯曲位移模式,此位移模式既考虑横向剪切的影响,又考虑了法向正应力的分布,进而建立的相当于三维弹性理论解的二维有限元模型,具有精度高、计算量并不大的优点。     

Impact of aperture on dynamic response of sandwich plates with aluminium face-sheets and PMI core based on an alternative finite element formulation and experiments

Apertures generally exist in the sandwich structures attributing to mechanical connection and lightweight, which might induce failure of such structures. Thus, it is required to realize the impact of aperture on mechanical behaviors of sandwich structures. If transverse shear deformations are unable to be described accurately, the reasonable prediction of dynamic behaviors of the form-core sandwich plates with apertures will meet severe challenges due to a large difference of transverse shear mo...     

金属梯度多孔夹芯板振动特性分析

金属梯度多孔材料芯层的胞孔壁厚度及半径沿芯层厚度方向逐渐变化,使得芯层的材料参数如密度和弹性模量等逐渐变化;采用金属梯度多孔材料代替传统均质多孔芯层会影响夹芯板的振动特性。基于高阶夹芯板理论且考虑梯度多孔芯层密度和弹性模量的耦合影响,建立了复合材料面层-金属梯度多孔夹芯板的振动方程。分析了3种密度的梯度芯层:单向分布、正梯度对称分布和负梯度对称分布对夹芯板固有频率的影响;最后讨论了3种梯度夹芯板在相同三角脉冲载荷作用下的振动响应。计算结果表明梯度芯层密度对称分布的夹芯板固有频率大于单向分布的夹芯板固有频率。     

计及横向剪切效应的环形谐振子理论研究CSCD

经典环形谐振子理论是一种基于忽略横向剪切变形假设建立的环理论,因而无法准确求解高径比较大的环问题。为了克服上述不足,基于Timoshenko理论和哈密顿原理,建立考虑横向剪切效应的环形谐振子新理论,包括广义本构关系、平衡方程和周期性条件等。利用经典的布勃诺夫-伽辽金法,并结合有限元法,获得谐振子在缓慢、匀速转动过程中二阶弯曲角频率和进动系数的理论解。研究表明,横向剪切变形会在一定程度上影响环形结构二阶弯曲角频率和进动系数的计算结果;环形谐振子的进动系数不是恒定的,它会随着高径比h/r的增大而缓慢地减小。     

一种准确预测层合梁结构层间剪应力的新锯齿理论

层合梁是航空航天领域典型的承力构件，而过大的层间剪应力（层间处的横向剪应力）是导致其分层失效的主要原因。针对常见的层数较多的复合材料层合梁以及材料属性差异较大的三明治夹层梁，现有的理论模型仍然无法准确预测其横向剪应力。通过构造一个新的线性分段锯齿函数，提出了一种能够准确预测层合梁结构横向剪应力的新锯齿理论模型。几个典型的数值算例表明，本文提出的新锯齿理论模型在计算层数较多和材料属性差异较大的层合梁时，具有较高的计算精度，能够准确预测层合梁的分层。另外，该模型预先满足横向剪应力层间连续条件，无需三维平衡方程后处理就能够准确预测层合梁的横向剪应力。位移场中未知量个数少，不含横向位移的一阶导，便于C⁰梁单元的构造。     

一种精化的层合梁脱层模型

建立了一种精化的复合材料层合梁脱层模型。脱层梁被分为3个区,各区位移场为厚度坐标的三次函数,能满足层间位移和剪应力的连续条件、脱层界面的脱层条件和脱层边界点的位移连续条件。构造了其有限元模型。算例表明该模型较之基于经典理论和一阶剪切变形理论的脱层模型精度显著提高。     

Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel

In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG) spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the val-idation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.     

轻质量低成本无人机舵面结构优化与验证

复合材料蜂窝夹芯结构因其高比强度、比模量及可设计性而广泛应用于航空飞行器结构。文章提出了 1种轻质量、低成本舵面结构方案——通过增大蜂窝芯密度使其剪切模量提高,进而降低复合材料面板应力水平,减小面板厚度。首先,根据理论选择通过增大蜂窝密度提升蜂窝剪切模量;然后,对结构进行有限元计算与分析,发现蒙皮应力水平随蜂窝芯剪切模量增大而显著降低;最后,设计不同蜂窝芯密度的蜂窝夹芯结构进行试验。试验结果证明,蜂窝芯越致密,其典型力学性能越高,冲击后的剩余强度也越高。