一维准晶功能梯度层合圆柱壳热电弹性精确解

两种或多种不同性质材料组成的层状结构可以满足工业发展的需求. 然而, 材料属性在接触面的突变问题, 容易导致层间界面处产生应力集中、裂纹以及分层等问题. 功能梯度材料利用连续变化的组分梯度来代替突变界面, 可以消除界面处的物理性能突变, 提高结构的粘结强度. 本文以一维准晶功能梯度层合圆柱壳为研究对象, 利用类Stroh公式和传递矩阵方法, 建立了材料参数沿径向呈现幂函数变化的层合圆柱壳模型, 获得了简支边界条件对应的一维准晶功能梯度层合圆柱壳的热电弹性精确解. 数值算例中讨论了层合圆柱壳内外表面承受温度载荷时, 功能梯度指数因子对温度场、电场、声子场和相位子场的影响, 尤其是对层合圆柱壳内外表面的影响. 结果表明, 指数因子改变了材料参数的空间分布情况, 进而对温度场、电场、声子场和相位子场都有影响; 增加功能梯度指数因子, 可减小温度载荷引起的内表面变形, 进而提升结构强度. 本文得到的结果可以为功能梯度准晶层合圆柱壳的设计和制造提供可靠的理论依据.      

EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS 1)

两种或多种不同性质材料组成的层状结构可以满足工业发展的需求. 然而, 材料属性在接触面的突变问题, 容易导致层间界面处产生应力集中、裂纹以及分层等问题. 功能梯度材料利用连续变化的组分梯度来代替突变界面, 可以消除界面处的物理性能突变, 提高结构的粘结强度. 本文以一维准晶功能梯度层合圆柱壳为研究对象, 利用类Stroh公式和传递矩阵方法, 建立了材料参数沿径向呈现幂函数变化的层合圆柱壳模型, 获得了简支边界条件对应的一维准晶功能梯度层合圆柱壳的热电弹性精确解. 数值算例中讨论了层合圆柱壳内外表面承受温度载荷时, 功能梯度指数因子对温度场、电场、声子场和相位子场的影响, 尤其是对层合圆柱壳内外表面的影响. 结果表明, 指数因子改变了材料参数的空间分布情况, 进而对温度场、电场、声子场和相位子场都有影响; 增加功能梯度指数因子, 可减小温度载荷引起的内表面变形, 进而提升结构强度. 本文得到的结果可以为功能梯度准晶层合圆柱壳的设计和制造提供可靠的理论依据.     

含有压电层的各向同性圆柱壳结构的双稳态特性分析

分析了上下表面含有压电层材料的各向同性壳体结构的双稳态特性.通过分析壳体结构内力与中面应变和柱壳曲率增量之间的关系,建立了含有压电材料的各向同性弹性柱壳的力学模型,推导给出了结构系统的弹性应变能的数学表达式.根据最小势能原理推导出实现圆柱壳双稳态的条件方程.结果表明,柱壳双稳态特性与结构系统初始曲率及电场作用形式有关.当满足一定条件时,柱壳具有双稳态,其对应于第二个平衡状态,即柱壳的第二个(卷曲)稳定状态.同时,建立了含有压电材料各向同性壳体结构的有限元模型,对其卷曲过程进行了数值模拟,获得了结构系统稳态卷曲半径和应力分布.理论与数值模拟结果的比较验证了理论模型的正确性.     

双层壳的双稳态力学特性理论分析和数值模拟

双稳态结构一般均由复合材料制作而成,然而复合材料有其固有的缺陷,即采用正对称铺层的层合板在弯曲过程中会产生扭转变形,而采用反对称铺层的层合板容易受到温度影响.对于各向同性材料结构,在变形过程中既没有拉弯耦合效应也没有弯扭耦合效应.本文据此建立了存在预应力的各向同性材料圆柱壳的双稳态力学模型,给出了其变形过程中的弯曲应变能和拉伸应变能的表达式.结果表明,预应力柱壳总应变能有两个极小值,故柱壳存在两个稳定状态,通过计算得到了结构卷曲半径的大小.同时,对双层壳的双稳态过程进行了有限元数值模拟.数值结果与理论模型解吻合很好.     

黏弹性层合悬臂薄壁圆柱壳的模态特性研究

基于薄壳理论和黏弹性理论, 得出了黏弹性层合悬臂薄壁圆柱壳模态特性的半解析解. 根据乐甫薄壳理论, 建立了基层和黏弹性阻尼层薄壁圆柱壳的一阶状态微分方程, 结合黏弹性阻尼层的变形协调关系和层间作用力关系, 利用传递矩阵法得出了整体结构的传递矩阵, 采用高精度的精细积分法得出了固有频率、模态损耗因子和三维模态振型, 最后通过有限元法进行了比较, 通过算例验证了传递矩阵法对黏弹性层合薄壁圆柱壳模态特性研究的有效性.     

黏弹性层合圆柱壳的蠕变分岔屈曲

采用Boltzmann积分型本构关系描述铺设单层的黏弹性力学行为,基于DMV扁壳假定和Kármán- Donnell几何非线性关系,研究了对称铺设黏弹性层合圆柱壳的前屈曲变形特征和分岔蠕变屈曲．对玻璃纤维/环氧树脂基复合材料层合圆柱壳的分析结果表明,在前屈曲阶段,挠曲变形和环向薄膜力随时间的变化趋势主要取决于圆柱壳的铺设方式,可以呈现完全相反的变化特征；层合短圆柱壳两端的边界条件对其蠕变分岔屈曲行为有决定性的影响,径厚比的增加将使分岔形式的延迟失稳现象更加明显．     

宏纤维压电层合壳结构非线性屈曲分析

以纤维压电MFC （Micro-Fiber Composite）层合圆柱壳为例,研究了其在准静态屈曲下的非线性振动响应。基于Reissner-Mindlin一阶剪切变形假设,采用大转角几何全非线性理论,建立了带有纤维角度的MFC层合壳结构的非线性屈曲与振动分析模型。采用全拉格朗日方程（Total Lagrange Formulation）对非线性模型进行线性化处理,并结合Riks-Wempner弦长控制迭代法进行准静态求解,然后在每个解点进行自由振动分析。通过与文献数据对比验证了所建模型的准确性。并用该计算模型对MFC-d31层合圆柱壳进行屈曲及自由振动分析,研究了几何参数（曲率、厚度、纤维角度和不同外加电压）对频率的影响。结果表明,厚度、曲率和纤维增强角度对结构的临界载荷有显著的影响,且结构的临界载荷随着上述参数的增大而增大;电场强度可对不同纤维角度壳体的自振频率进行调节,能够提高结构的临界载荷;纤维角度越大,电压对结构自振频率调节的效果越明显。     

轴向运动层合圆柱壳体的振动特性

研究了轴向运动层合圆柱壳体的振动特性．基于Donnell壳体理论,建立了轴向运动层合圆柱壳体的横向振动方程,使用Galerkin方法求解该振动方程,得到其固有频率,通过与有限元结果对比说明方法的有效性．分析了轴向速度、纤维方向角、长径比和厚径比对壳体振动特性的影响．研究表明：当纤维方向角为 (15?/-15?)s时,轴向运动柱壳前3阶固有频率达到最大值．     

一种特殊梯度分布的功能梯度圆柱壳的二维分析

功能梯度材料是一种新型材料,其结构分析已成为当今力学研究的热点。本文对一种特殊梯度分布的功能梯度材料圆柱壳进行了二维精确分析。从弹性力学平面应变问题的基本方程出发,引入应力函数,导出功能梯度材料圆柱壳受静载作用下的控制微分方程。假设材料的杨氏模量沿半径方向呈幂函数分布,泊松比为常数,利用分离变量法,导出了简支边界情况下功能梯度圆柱壳的精确解。通过算例分析了不同梯度变化时,功能梯度圆柱壳内的应力和位移变化规律。计算结果表明不同梯度分布的圆柱壳结构中的应力、位移沿厚度方向的变化规律是不同的,有时甚至差别很大。因此对于材料性质梯度变化的功能梯度材料圆柱壳,必须针对其自身特点,建立相应的理论分析模型。     

黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论，研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法，由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程，根 据Laplace逆变换的极值定理，获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式，通过数值算例重点分析了临界载荷随铺设角的变化特征，两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系，得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

复合材料层合板壳非线性力学的研究进展

复合材料层合板壳是由多种组分材料组合而成.与单一材料的板壳结构相比,它无明确的材料主方向,各层间材料间断和不连续,具有明显的几何非线性和材料非线性等新的特点.其失效模式也远比单一材料的情况复杂,具有如基体开裂、脱胶、分层、分层裂纹偏转、多分层以及分层传播等多种模式.各国学者基于不同的考虑,提出了多种方法研究复合材料层合板壳的失效.首先,在简要介绍了层合板壳线性力学基本理论的基础上,重点回顾了层合板壳结构非线性力学几种基本理论发展的过程,主要阐述了经典大挠度非线性理论、一阶剪切变形理论、高阶剪切变形理论、锯齿理论、广义分层理论的理论体系及基本公式,并对几种理论之间的联系和差异进行了总结;其次,介绍了当前层合结构非线性领域的研究进展,综述了典型复合材料板壳结构的失效机理及优化设计、复合材料板壳结构在复杂环境下的破坏机理、复合材料板壳结构的物理非线性、含脱层纤维增强复合材料板壳结构的破坏机理等各研究热点的最新研究成果;最后,对该领域未来的研究方向进行了展望.     

Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment

Influences of large deformation (geometrical non-linear) and rotary inertia on wave propagation in a long, piezoelectric cylindrically laminated shell in thermal environment is presented in this paper. Nonlinear dynamic governing equations of piezoelectric cylindrically laminated shells are derived by means of Hamilton’s principle. The wave propagation modes are obtained by solving an eigenvalue problem. Numerical examples show that the characteristics of wave propagation in piezoelectric cylindrically laminated shells are relates to the large deformation, rotary inertia and thermal environment of the piezoelectric cylindrically laminated shells. The effect of large deformation, rotary inertia and thermal load on wave propagation in the piezoelectric cylindrically laminated shells is discussed by comparing with the result from the small deformation (geometrical linear shell theory). This method may be used to investigate wave propagation in various laminated material, layers numbers and thickness of piezoelectric cylindrically laminated shells under large deformation. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.     

Torsional postbuckling characteristics of functionally graded graphene enhanced laminated truncated conical shell with temperature dependent material properties

Buckling and postbuckling characteristics of laminated graphene-enhanced composite (GEC) truncated conical shells exposed to torsion under temperature conditions using finite element method (FEM) simulation are presented in this study. In the thickness direction, the GEC layers of the conical shell are ordered in a piece-wise arrangement of functionally graded (FG) distribution, with each layer containing a variable volume fraction for graphene reinforcement. To calculate the properties of temperature-dependent material of GEC layers, the extended Halpin-Tsai micromechanical framework is used. The FEM model is verified via comparing the current results obtained with the theoretical estimates for homogeneous, laminated cylindrical, and conical shells, the FEM model is validated. The computational results show that a piece-wise FG graphene volume fraction distribution can improve the torque of critical buckling and torsional postbuckling strength. Also, the geometric parameters have a critical impact on the stability of the conical shell. However, a temperature rise can reduce the crucial torsional buckling torque as well as the GEC laminated truncated conical shell's postbuckling strength.     

Analytical solution for axisymmetric problem of thick laminated closed cantilever shells in hamilton system

By giving up any assumptions about displacement models and stress distribution, the mixed state Hamilton equation for the axisymmetric problem of the thick laminated closed cantilever cylindrical shells is established. An identical analytical solution is obtained for the thin, moderately thick and thick laminated closed cantilever cylindrical shells. All equations of elasticity can be satisfied, and all elastic constants can be taken into account. This work is supported by the National Natural Science Foundation of China.     

On the vibration of laminated nonhomogeneous orthotropic shells

In this paper, an analytical procedure is given to study the free vibration of the laminated homogeneous and non-homogeneous orthotropic conical shells with freely supported edges. The basic relations, the modified Donnell type motion and compatibility equations have been derived for laminated orthotropic truncated conical shells with variable Young’s moduli and densities in the thickness direction of the layers. By applying the Galerkin method, to the basic equations, the expressions for the dimensionless frequency parameter of the laminated homogeneous and non-homogeneous orthotropic truncated conical shells are obtained. The appropriate formulas for the single-layer and laminated complete conical and cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the influences of the non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the dimensionless frequency parameter are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.     

Nonlinear Theory of Dynamic Stability for Laminated Composite Cylindrical Shells

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The vibration and buckling of laminated non-homogeneous orthotropic conical shells subjected to external pressure

In this paper, the free vibration and buckling of laminated homogeneous and non-homogeneous orthotropic truncated conical shells under lateral and hydrostatic pressures are studied. At first, the basic relations, the modified Donnell type dynamic stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells, the Young's moduli and density of which vary piecewise continuously in the thickness direction. Applying superposition and Galerkin methods to the foregoing equations, the buckling pressures and dimensionless frequency parameter of laminated homogeneous and non-homogeneous orthotropic conical shells are obtained. The appropriate formulas for single-layer and laminated cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the effects of the number and ordering of layers, the variations of conical shell characteristics, together and separately variations of the Young's moduli and densities of the materials of layers on the critical lateral and hydrostatic pressures, and frequency parameter are found for different mode numbers. The results are compared with other works.     

Developing a Compressive Failure Theory for Nanocomposites

The paper addresses a compressive-failure theory for polymer-matrix nanocomposites in the case where failure onset is due to microbuckling. Two approaches based on the three-dimensional linearized theory of stability of deformable bodies are applied to laminated and fibrous nanocomposites. According to the first approach (continuum compressive-failure theory), nanocomposites are modeled by a homogeneous anisotropic medium with effective constants, including microstructural parameters. The second approach uses the piecewise-homogeneous model, three-dimensional relations for fibers (CNT) and matrix, and continuity conditions at the fiber-matrix interface. The compressive-failure theory is used to solve specific problems for laminated and fibrous nanocomposites. Some approximate failure theories based on the one- and two-dimensional applied theories of stability of rods, plates, and shells are analyzed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 3–37, March 2005.     

爆炸冲击下复合材料层合扁球壳的动力屈曲

研究计及横向剪切的复合材料层合扁球壳在爆炸冲击载荷作用下的非线性轴对称动力屈曲问题。通过在复合材料层合扁球壳非线性稳定性的基本方程中增加横向转动惯量项并引入R.H.Cole理论的爆炸冲击力,得到爆炸冲击下复合材料层合扁球壳的动力控制方程,应用Galerkin方法得到用顶点挠度表达的爆炸冲击动力响应方程,并采用Runge-Kutta方法进行数值求解,采用Budiansky-Roth准则确定冲击屈曲的临界载荷,讨论了壳体几何尺寸对复合材料层合扁球壳冲击屈曲的影响;数值算例表明,此方法是可行的。     

复合材料旋转壳自由振动分析的新方法

提出了一种半解析区域分解法来分析任意边界条件的复合材料层合旋转壳自由振动. 沿壳体旋转轴线将壳体分解为一些自由的层合壳段, 视位移边界界面为一种特殊的分区界面;采用分区广义变分和最小二乘加权残值法将壳体所有分区界面上的位移协调方程引入到壳体的能量泛函中, 使层合壳的振动分析问题归结为无约束泛函变分问题. 层合壳段位移变量采用Fourier 级数和Chebyshev 多项式展开. 以不同边界条件的层合圆柱壳、圆锥壳及球壳为例, 采用区域分解法分析了其自由振动, 并将计算结果与其他文献值进行了对比. 算例表明, 该方法具有高效率、高精度和收敛性好等优点.