复合材料层合开顶扁球壳在集中冲击下的非线性动力屈曲

研究了具有刚性中心的复合材料层合开顶扁球壳在中心集中冲击载荷作用下的非线性动力屈曲问题。通过增加横向转动惯量项得到中心集中冲击下复合材料层合开顶扁球壳非线性稳定性的控制方程，采用Galerkin方法得到以刚性中心位移表达的冲击动力响应方程，并用Runge-Kutta方法进行数值求解，应用Budiansky-Roth准则（简称B—R准则）确定冲击屈曲的临界荷载；讨论了壳体几何尺寸对复合材料层合开顶扁球壳冲击屈曲的影响。     

含单分层损伤复合材料层合梁的动力屈曲研究

采用有限差分（FDM）方法求解了含初始缺陷和单个分层损伤复合材料层合梁的轴向刚性质量块撞击的脉冲动力屈曲问题。基于Hamilton原理导出了考虑所有惯性影响以及一阶横向剪切变形（FSDT）影响时单个分层损伤复合材料梁的非线性动力屈曲控制方程；采用B—R准则判断梁动力屈曲时刻，同时确定刚性质量块的临界冲击速度。重点研究脱层、冲击速度、初始几何缺陷等因素对复合材料层合梁脉冲动力屈曲的影响。     

径向冲击下复合材料层合圆柱壳的动力屈曲

采用Lagrange方程导出包含横向剪切变形和转动惯量的复合材料层合圆柱壳径向脉冲屈曲控制方程;用四阶Runge-Kuta方法对方程数值求解,寻找占优屈曲模态数及对应于允许初缺陷放大值时的临界冲击速度;通过计算碳/环氧材料角铺设层合圆柱壳,讨论了横向剪切变形、壳体几何尺寸、铺层角度等因素对层合圆柱壳动力屈曲的影响.     

轴向冲击下复合材料圆柱壳的非对称动力屈曲

基于一阶剪切变形理论和非扁壳型几何方程，由Ｈａｍｉｌｔｏｎ原理导出包含初始几何缺陷的复合材料圆柱壳的非线性动力方程，Ｇａｌｅｒｋｉｎ方法得以位移形式表达的动力屈曲控制方程，通过有限差分方法求解，并由类似Ｂ－Ｒ准则方法判断动力屈曲是否发生；讨论了冲击速度，初始几何缺陷等因素对动力屈曲可能产生的影响。     

径向载荷作用下复合材料圆柱壳的非线性动力屈曲

采用半解析法求解径向阶跃载荷作用下复合材料圆柱壳的非线性动力屈曲。基于一阶剪切变形理论，由Hamilton原理推导出包含横向剪切变形以及几何初缺陷的圆柱壳的非线性动力方程，位移及载荷沿周向采用级数展开，由Galerkin方法得到微分方程组，通过有限差分法求解；根据响应情况，由B—R准则判定屈曲，确定屈曲临界载荷。     

土中浅埋层合扁球壳的非线性动力响应

本文建立了考虑横向剪切影响、纤维增强对称正交铺设层合扁球壳的非线性动力方程。应用一维波阻法分析了土与结构的相互作用,对冲击波作用下土中浅埋周边弹性支承层合扁球壳的非线性动力响应问题进行了探讨。数值计算中考虑了各种材料参数及横向剪切变形对动力响应的影响。      

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。     

复合材料层合板的混沌运动分析

建立了四边简支纤维增强复合材料层合薄板在受到x轴方向面内激励和横向激励联合作用下的动力学方程,考虑了复合材料层合板主参数共振和1:1内共振的情况,利用二阶Galerkin离散和多尺度方法得到四维直角坐标形式下复合材料层合板系统的平均方程。然后利用规范形理论化简平均方程得到简单规范形。应用Kovacic等人提出的高维Melnikov方法研究复合材料层合薄板的脉冲混沌运动,理论分析发现在参数激励和外激励作用下系统存在smale马蹄意义下的混沌运动并存在脉冲跳跃轨道。     

波纹扁球壳的非线性动态屈曲

研究了用于传感器弹性元件波纹扁球壳的非线性动态屈曲问题。建立了波纹扁球壳的非线性振动微分方程,根据突变理论建立了该壳体动态屈曲的突变模型,得到了动态屈曲的临界方程。     

冲击载荷下复合材料层合杆的动力屈曲

研究复合材料层合杆被一质量块以某一速度沿轴向进行碰撞而导致的动力屈曲现象,采用不同的横向剪切理论,并用差分方法对杆的动力屈曲方程进行求解。文中考察了冲击块质量、初挠度、应力波、横向剪切等因素对临界冲击速度以及屈曲模态的影响。     

Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method

Hygrothermal stresses due to the change in environmental condition may induce buckling and dynamic instability in the composite shell structures. In the present investigation, the hygrothermoelastic buckling behavior of laminated composite shells are numerically simulated using geometrically nonlinear finite element method. The orthogonal curvilinear coordinate is used for modeling a general doubly curved deep or shallow shell surface. The geometrically nonlinear finite element formulation is based on general nonlinear strain–displacement relations in the orthogonal curvilinear coordinate system. The present theory can be applicable to thin and moderately thick shells. The mechanical linear and nonlinear stiffnesses, and the nonmechanical nonlinear geometric stiffness matrices and the hygrothermal load vector are presented. It is also observed that during the present numerical solution of nonlinear equilibrium equation, in order to construct the nonlinear stiffness matrices for the first load step, the initial deformation can be assumed as zero or any computer generated small random number or the properly scaled fundamental buckling mode shape. To verify the present formulations and finite element code, the present results are compared well with those available in the open literature. Parametric studies such as thickness ratio and shallowness ratio on buckling are performed for spherical, truncated conical and cylindrical composite shell panels. The buckling behavior and deflection shapes are characterized by multiple wrinkles along unreinforced direction at higher moisture concentrations or temperature rise.     

Nonlinear dynamic stability of laminated composite shells integrated with piezoelectric layers in thermal environment

This paper reports the nonlinear dynamic stability characteristics of laminated composite cylindrical (CYL) and spherical (SPH) shells integrated with piezoelectric layers using the finite element method. The shells are subjected to a thermal environment in addition to the in-plane periodic load and the electric load. The theoretical formulation considers Sanders?? approximation for doubly curved shells, and von Kármán type nonlinear strains are incorporated into the first-order shear deformation theory (FSDT). The formulation includes the effects of transverse shear, in-plane and rotatory inertia. The in-plane periodic load is taken as the parametric excitation in the governing equation. The nonlinear matrix amplitude equation is obtained by employing Galerkin??s method. The correctness of the formulation is established by comparing the authors?? results with those available in the published literature. Detailed parametric studies are carried out to investigate the effects of different parameters on the dynamic stability characteristics of laminated composite shells.     

具有夹层的正交异性复合材料圆锥壳体的非线性轴对称屈曲分析

研究均布载荷作用下边缘可移夹支具有正交异性复合材料表层和软夹心的夹层圆锥壳非线性轴对称屈曲问题.利用变分原理导出具有正交各向异性表层夹层圆锥壳在均匀外压作用下的非线性轴对称屈曲问题的基本方程,采用修正迭代法[8]求得了可移夹支边界条件下壳体临界屈曲载荷的解析表达式,对几种典型的纤维增强复合材料表层夹层圆锥壳给出了数值结果和图表,讨论了几何参数和物理参数对临界屈曲载荷的影响。     

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。      

双层柱面网格扁壳的非线性稳定性分析

基于等效夹层壳思想的双层网格扁壳非线性弯曲理论,对双层柱面网格壳体在均布压力作用下的非线性稳定性问题进行研究,采用伽辽金方法求得了简支边界条件下双层柱面网格扁壳的非线性载荷-位移关系式和临界屈曲载荷的解析表达式,讨论网壳结构几何参数对临界屈曲载荷的影响。     

Stability analysis of generally laminated conical shells with variable thickness under axial compression

Abstract

The buckling of generally laminated conical shells having thickness variations under axial compression is investigated. This problem usually arises in the filament wound conical shells where the thickness changes through the length of the cone. The thickness may be assumed to change linearly through the length of the cone. The fundamental relations for a conical shell with variable thickness applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy have been derived. Nonlinear terms of Donnell equations are linearized by the use of adjacent-equilibrium criterion. Governing equations are solved using power series method. This procedure enables us to investigate all combinations of classical boundary conditions. The results are verified in comparison with Galerkin method and the available results in the literature. Effects of thickness function coefficient, semi-vertex angle, lamination sequence, length to diameter ratio, and initial thickness of the cone on the buckling load are investigated. It is observed that these parameters have considerable effects on the critical buckling load of a conical shell.     

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。