考虑横向剪切效应时圆柱型正交各向异性球面扁壳在横向载荷作用下的非线性压屈

本文应用参考文献所介绍的修正迭代法探讨了横向载荷作用下,圆柱型正交各向异性圆底球面扁壳的非线性稳定同题,得出了这一同题的解析解。在求解过程中,本文放弃了经典板壳理论的Kirchhoff假定,从而考虑了横向剪应变对于弯曲变形的影响, 计算结果表明:本文的分析方法和结论是正确的;对于正交各向异性复合材料板壳而言,横向剪切效应是值得注意的。     

正交各向异性扁球壳的非线性振动

本文以正交各向异性扁球壳非线性动力方程为基础,提出以简单多项式作为振型函数,采用Galefkin技术,导出了带有平方项的Duffing型方程。并分别用摄动法和数值积分法求出其解。研究了扁球壳的拱高、正交各向异性系数、边界条件和中心集中质量对系统非线性动力特性的影响,给出了扁球壳由非线性振动硬特性向软特性过渡的临界拱高H_(cr)和对应于最大软特性的最大拱高H_M。     

计入剪切变形的正交各向异性扁壳的基本解

本文采用Ｈｏｒｍａｎｄｅｒ算子法将控制计入剪切变形的正交各向异性扁壳的偏微分方程组转化为含有一个未知函数的高阶偏微分方程，然后，利用平面波分解法将偏微分方程转化为常微分方程来求解。以定积分表示的形式提出了计入剪切变形的正交各向异性扁壳的基本解。     

正交各向异性薄板振动响应的波函数法

提出了适用于正交各向异性薄板弯曲振动响应预测的波函数法,基于Kirchhoff正交各向异性薄板振动控制方程,推导了体现各主轴物理量且精确满足其控制方程的复合结构波函数。通过傅里叶变换,在波数域对响应函数进行角积分,得到处于外部激励下的无限正交各向异性板振动响应。结合正交各向异性薄板的物理边界,运用加权余量法求得各正交各向异性结构波函数的系数,得到薄板的弯曲振动响应。建立矩形正交各向异性板的波函数响应模型,通过双级数解法验证了方法的正确性,与有限元法的对比结果说明,波函数法对正交各向异性薄板在中频范围的振动响应预测有着更高的计算效率。     

不同边界条件下截顶正交各向异性圆锥壳的振动和声辐射研究

采用波传播法和Galerkin法,研究了两端简支和固支边界条件对截顶正交各向异性圆锥壳的固有频率和声辐射的影响,通过与现有文献及数值仿真结果相比较,验证了理论分析的正确性。结果表明,简支和固支边界对正交各向异性圆锥壳固有频率的影响与圆锥壳半顶角的大小和母线与环向方向的弹性模量比的大小相关。当正交各向异性圆锥壳的半顶角较大时,对与不同的弹性模量比,固支圆锥壳的固有频率都大于简支圆锥壳的固有频率;而对于小半顶角的正交各向异性圆锥壳,当弹性模量比较小时,简支圆锥壳在大周向波数处的固有频率略大于固支圆锥壳的固有频率。随着圆锥壳半顶角的增大,两种边界对正交各向异性圆锥壳的声压级的影响也逐渐增大。     

正交各向异性平面问题边界元素法研究

边界元素法是近年来受到国内外广泛重视并得到迅速发展的一种计算方法。本文系统地研究了正交各向异性平面问题边界元素法的有关基本问题,包括基本解,C矩阵、G_ii矩阵和域内应力的表达式等,并在此基础上建立了常值边界元素和线性边界元素的计算公式。所述理论和公式适用于各类边值问题。最后,按本文所述理论和公式计算了含孔正交各向异性板的应力,数值结果与解析解相符甚好。      

扁壳有限条的静力和动力分析

本文用限条法导出了分析二次抛物形扁壳的计算模式。所采用的曲条单元可用于分析在某一方向曲率较大的二次抛物壳体。经过蜕化,它还可计算双曲扁壳、柱壳及析板等结构。用这一摸式在微型机上编制了FORTRAN静力和动力程序,并对各种正、负及零高斯曲率扁壳进行了计算。对双曲马鞍型壳还进行了静力和动力试验,将理论计算值与实验结果进行比较,两者符合较好。将有限条法的计算情况与有限元法进行比较,前者具有计算精度高、省时、省内存等优点,并使许多问题可在微型机上解决。     

解正交各向异性板的虚肋法

本文提出一种求解正交各向异性板的新的计算方法,使之等效为各向同性加肋板。从而解决了采用各向同性板通用程序求解正交各向异性板的计算问题,扩大了微机通用程序的实用范围。     

复合材料夹层板壳一种等效分析方法

本文研究了复合材料夹层板壳的一种等效分析方法,首先由壳体理论导出了夹层板壳的内力和位移表达式,通过与各向异性单层板壳理论的比较,提出了二者等效的条件,从而把夹层板壳问题简化为一个等效各向异性单层板壳问题,这用有限元法很容易求解,并对一个工程实例进行了计算,证实了该方法的有效性。     

复合材料夹层板壳一种等效分析方法

本文研究了复合材料夹层板壳的一种等效分析方法,首先由壳体理论导出了夹层板壳的内力和位移表达式,通过与各向异性单层板壳理论的比较,提出了二者等效的条件,从而把夹层板壳问题简化为一个等效各向异性单层板壳问题,这用有限元法很容易求解,并对一个工程实例进行了计算,证实了该方法的有效性。      

板壳分析与应用

板壳分析是现代固体力学的一个重要分支。这门学科几乎与一切工程设计都有关联,对航天、航空、航海、机械、石化、建筑、水利、动力、仪表、交通等工程设计,尤其具有指导意义。现今,经典的薄板壳线性 理论已较成熟,并在各种工程设计中起着指导作用。然而,在薄板壳非线性领域和厚板壳线性领域,还有许多问题未被解决。章在介绍这门学科发展历史的基础上,概述了作近四十年结合工程实际对波纹板壳、单层板壳、双层金属旋转扁壳、网格扁壳、夹层板壳和复合材料层合板壳等六类薄板壳的非线性弯曲、稳定和振动问题以及厚、薄板壳弯曲问题进行理论探索的情况。     

A 3D shell-like approach using a natural neighbour meshless method: Isotropic and orthotropic thin structures

A three-dimensional shell-like approach for the analysis of composite thin plates and shells using a meshless method, the natural neighbour radial point interpolation method (NNRPIM), is presented. In the NNRPIM the nodal connectivity is enforced using the natural neighbour concept. The node-depending background mesh used in the numerical integration of the NNRPIM interpolation functions is entirely created from the unstructured nodal arrangement. The radial point interpolators are used to construct the NNRPIM interpolation functions, which possesses the delta Kronecker property, used in the Galerkin weak form. The novelty of this work lays on the development of a unique NNRPIM approach when 3D thin structures are considered. This new approach leads to remarkable results and it is extremely suitable to the composite structure problem. In order to demonstrate the effectiveness of the method the 3D shell-like NNRPIM analysis is used to solve several isotropic and orthotropic thin plates and shells problems.     

正交异性扁薄球壳的非线性轴对称振动

给出了一种研究圆柱正交异性扁薄球壳非线性轴对称自由振动的新的时间模态方法。首先,使用变分法导出了决定振动频率的一对代数-微分方程。然后,利用作者提出的改进的修正迭代法求得了渐进解。这使此种壳体的非线性振动的进展获得扩充研究。     

复合材料浅球壳模态分析与结构优化设计

复合材料层合壳体在航空、航天、工程结构中得到了广泛应用.结合复合材料层合浅球壳的结构特点,基于有限元分析软件ANSYS,采用层合壳单元建立有限元模型,分析了几种壳体参数对浅球壳自振频率的影响,并采用函数逼近法和梯度寻优法相结合的方法对壳体参数进行优化设计,给出了壳体参数的最优组合,使壳体的一阶自振频率为最大,改善了壳体的动态特性,为复合材料层合浅球壳的结构设计提供了有价值的理论依据,也为进一步进行结构动力学分析奠定基础.     

Creep bending of thin-walled shells and plates by consideration of finite deflections

A phenomenological constitutive model for the characterization of creep-damage processes of metals is applied to the numerical analysis of thin-walled shells and plates. The governing equations of the theory of shallow shells are used taking into account geometrical nonlinearities connected with finite time-dependent deflections by moderate bending. The solutions of the initial-boundary value problem are obtained for thin rectangular plates in order to show the influence of geometrical nonlinearity on results of time-dependent deformation and stress redistribution as well as on estimations of the failure time.     

Thermomechanical postbuckling analysis of functionally graded plates and shallow cylindrical shells

Summary. In this paper, an analytic solution is provided for the postbuckling behavior of plates and shallow cylindrical shells made of functionally graded materials under edge compressive loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituents. The fundamental equations for thin rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection, and the solution is obtained in terms of mixed Fourier series. The effect of material properties, boundary conditions and thermomechanical loading on the buckling behavior and stress field are determined and discussed. The results reveal that thermomechanical coupling effects and the boundary conditions play a major role in dictating the response of the functionally graded plates and shells under the action of edge compressive loads.     

The fundamental solutions of orthotropic shallow shells

Summary A set of partial differential equations governing orthotropic shallow shells with arbitrary quadratic midsurface is reduced into an eight order partial differential equation with one function as unknown. By use of the method of plane wave decomposition this partial differential equation is transformed into an ordinary differential equation. The fundamental solutions for orthotropic shallow shells are presented in the form of a definite integral. The calculation of the fundamental solutions is discussed in detail.     

Static and dynamic snap-through of orthotropic spherical caps

This paper presents the results of a study on the axisymmetric snap-through buckling of orthotropic shallow spherical shells subjected to a total-area uniform pressure. Both static and dynamic buckling of the orthotropic caps are investigated according to the classical thin shell theory and Reissener's shallow shell assumptions.

To take moderate rotation and initial imperfection into account, a set of nonlinear differential governing equations is derived in terms of the mid-surface displacement and a stress function.

Two types of imperfection, and damping (in the dynamic case) are included to simulate real structures. It is seen that imperfections play an important role in the reduction of buckling loads for both static and dynamic analyses. Damping, on the other hand, increases the dynamic buckling load. The finite difference scheme is applied to represent spatial and time derivatives, and the block elimination method is used to solve the resulting difference equations.     

纤维增强复合材料迭层圆柱壳的几何非线性分析

本文从非线性弹性理论出发,在小应变、中等小转动的前提下,全面考虑了变形对于平衡方程的影响,导出了和传统理论不同的壳体非线性理论;并用摄动法和伽略金法分别求解了四边不可动固支正交各向异性复合材料迭层园桂壳块以及考虑横向剪切的四边可动简支园桂形扁壳的非线性弯曲问题。计算表明:变形较大时,变形对所有平衡方程的影响都是值得注意的。