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.     

轴向冲击下薄壁圆柱壳的屈曲行为的实验研究

由于薄壁圆柱壳比厚壁圆柱壳的不均匀性更大，薄壁圆柱壳的轴向动力屈曲比厚壁复杂得多。了解轴向冲击下薄壁圆柱壳的屈曲行为，有助于进行吸能构件设计。介绍了采用落锤实验进行圆柱壳的动力屈曲行为研究中，超薄壁圆柱壳的一些特殊屈曲行为，在实验中观察到随着径厚比的增加，折屈边数有相应增加的趋势，存在过渡区。经吸能特性分析，随着圆柱壳径厚比的增加，平均压垮载荷和一个基本变形单元能量吸收量增加，有效压缩距离和一个基本变形单元的初始长度增加，但有效压缩距离与基本变形单元长度之比保持不变；在壁厚相同的条件下，能量吸收量与圆柱壳半径成正比。     

轴向阶梯载荷下薄圆柱壳的弹性动力屈曲

对于轴向阶梯载荷下圆柱壳的非轴对称动力屈曲,将临界应力和屈曲惯性指数作为双特征参数求解。由屈曲瞬间的能量转换和守恒准则导出压缩波阵面上的屈曲变形补充约束方程。利用Galerkin方法求解失稳控制方程,得出包含双特征参数的代数特征值问题。该特征值问题满足补充约束方程的解给出动力屈曲的临界应力和惯性指数。     

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。     

轴向冲击载荷下圆柱壳的塑性动力屈曲

对于轴向冲击载荷下圆柱壳的轴对称塑性动力屈曲问题。将临界应力和屈曲惯性项指数参数作为双特征参数求解．由相邻平衡准则导出失稳控制方程、边界条件和波阵面上的连续条件．由失稳瞬间的能量转换和守恒准则，导出波阵面上的一个屈曲变形约束方程．由此得出定量求解2个特征参数和动力屈曲模态的完备定解条件．关于屈曲应力和屈曲波数的理论计算结果与已有实验吻合良好．     

一般边界条件下受轴向冲击圆柱壳的动力特性计算分析

在受轴向冲击圆柱壳的非冲击端引入轴向、周向、径向和径向旋转4个方向边界弹簧模拟一般边界条件。根据Love薄壳理论得到圆柱壳变形过程中的应力应变,并采用一种改进的Fourier级数方法表示圆柱壳沿坐标轴方向的位移。将应力应变以及位移代入圆柱壳的能量表达式,采用基于Hamilton方程的一阶变分法对能量表达式进行推导和变换,得到一般边界条件下受轴向冲击圆柱壳的自然频率以及动力屈曲临界载荷的判别式。计算分析了一般边界条件对受轴向冲击圆柱壳的自然频率和屈曲临界载荷的影响,以及不同边界条件圆柱壳屈曲模态的类型特点。结果表明：一般边界条件下自然频率随着冲击载荷增大而降低;随着轴向波数的增加圆柱壳自然频率及屈曲临界载荷增大,随着周向波数的增加屈曲临界载荷也增大;轴向、周向、径向和径向旋转各个方向边界刚度对圆柱壳自然频率和屈曲临界载荷的影响都是刚度系数越小,自然频率越低而临界载荷越大;圆柱壳受轴向冲击,边界条件的改变会影响屈曲模态。     

复合材料圆柱壳的非线性稳定性分析

本文应用能量变分方法,对加筋多层的复合材料圆柱壳,进行了非线性稳定性分析,处理了均匀轴压和横向载荷两种载荷情况。文中用卡门-佟聂耳方程考虑了柱壳失稳时的几何非线性影响,同时通过剪切模量的非线性变化考虑了复合材料的物理并线性影响。本文也分析了初始缺陷对于屈曲特性的影响。文中具体计算了硼/环氧圆柱壳失稳的数值算例。分析和计算表明,材料的剪切非线性和初始缺陷的几何非线性对圆柱壳的屈曲特性有着显著的影响。     

基于突变理论的弹性圆柱壳冲击扭转屈曲

本文将突变理论用于处理冲击载荷下弹性结构的屈曲问题,文中对无初缺陷的弹性圆柱壳给出了临界阶跃冲击扭矩.另外,本文还用数值方法求解了柱壳扭转时的非线性动力方程,并由B-R运动准则求得临界冲击扭矩。计算表明,这两个方法给出的结果是一致的。     

复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥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三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

Coupled size-dependent behavior of shear deformable microplates

The aim of the present study is to investigate the nonlinear motion characteristics of a shear deformable microplate based on the modified couple stress theory. The microplate is modeled via the third-order shear deformation theory retaining in-plane displacements and inertia. Using the Lagrange equations together with an assumed-mode method, five sets of second-order nonlinear ordinary differential equations of motion with coupled terms are obtained. These five sets of equations (two for the in-plane motions, one for the out-of-plane motion, and two for rotations) are transformed into ten sets of first-order nonlinear ordinary differential equations. These resultant equations are then solved by means of a direct time integration technique and the pseudo-arclength continuation method in order to analyze the nonlinear response of the system. Apart from the nonlinear analysis, the linear natural frequencies of the system are obtained using an eigenvalue analysis. Results are shown through frequency–response and force–response curves. Points of interest in the parameter space in the form of time histories, phase-plane portraits, and fast Fourier transforms are also highlighted. Moreover, a comparison is made between the motion characteristics of the system based on the modified couple stress and classical continuum theories.     

Large deflection dynamic response of composite laminated plates under in-plane loads

An analytical solution is presented for the dynamic buckling behaviour of a laminate subjected to time-dependent uniformly distributed normal and shear in-plane loads based on the Classical Lamination Theory and accounting for moderately large deflections. The assumed load-time variation is either linear or of a pulse type. The Galerkin method is applied and the obtained nonlinear differential equations are solved numerically by the Runge-Kutta method. The parametric study performed revealed three distinct phases in the undamped centre deflection time-history of a laminate. No significant deformations are produced in phase I, while the subsequent phase II reflects the dynamic buckling behaviour, exhibiting a rapid increase of the deformations. These magnitudes follow an oscillating motion in phase III, analogous to the loading condition under consideration. Relatively large initial imperfection values change completely the response of the laminate, by eliminating both the characteristic dynamic buckling phase II and the oscillations of phase III.     

脉冲载荷下裂纹损伤梁的动力屈曲

研究含初始缺陷裂纹梁一端固定，另一端被一质量块沿轴向以某一速度进行碰撞而导致的动力屈出问题。根据Hamilton原理导出考虑初始缺陷及横向剪切变形时裂纹梁的动力屈曲控制方程，并应用线弹簧理论将裂纹引入到屈曲控制方程中，用有限差分法对控制方程进行求解，基于B-R动力屈曲判断准则，确定临界冲击速度。比较了裂纹梁与无裂纹梁的临界冲击速度和屈曲模态，针对裂纹梁主要考察了不同的冲击块质量、初挠度形状等因素对屈曲模态的影响。     

基于双特征参数解的直杆弹性动力后屈曲研究

利用差分方法求解动力后屈曲非线性方程解，研究了弹性直杆的2类轴向碰撞屈曲问题．将双特征参数解得出的含有小幅值参数的初始动力屈曲模态作为非线性后屈曲解的初始条件．理论计算的结果与文献中的实验数据达到了很好的一致，由此验证了双特征参数方法的正确性．研究结果还揭示了碰撞过程中屈曲变形扩展和发展的机理，以及轴向应力波和屈曲变形的相互作用规律．     

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。     

剪切可变形梁热过屈曲解析解

该文导出了面内热载荷作用下,梁过屈曲问题的精确解。首先基于非线性一阶剪切变形梁理论,推导了控制轴向和横向变形的基本方程。然后,将3 个非线性方程化简为一个关于横向挠度的四阶非线性积分-微分方程。该方程与相应的边界条件构成了微分特征值问题。直接求解该问题,得到了热过屈曲构形的闭合解,这个解是外加热载荷的函数。利用精确解,得到了临界屈曲载荷的一阶结果与经典结果的解析关系。为考察热载荷、横向剪切变形以及边界条件的影响,根据得到的精确解给出了两端固定、两端简支以及一端固定一端简支边界条件下的具体数值算例,讨论了梁在面内热载荷作用下的过屈曲行为,并与经典结果进行了比较。该文得到的精确解可以用于验证或改进各类近似理论和数值方法。     

考虑剪切效应的轴对称脱层圆板的后屈曲分析

基于Von Karman板理论,考虑横向剪切变形,建立了具脱层的轴对称层合圆板的后屈曲控制方程。应用正交配点法,将后屈曲控制方程、边界条件、以及连续条件转化为非线性方程组,然后进行迭代求解。讨论了不同脱层深度和脱层半径对层合圆板的屈曲及后屈曲特性影响,且与有关文献的结果进行了比较。     

Coupled longitudinal-transverse-rotational behaviour of shear deformable microbeams

In this paper, for the first time, the nonlinear motion characteristics of a hinged-hinged third-order shear deformable microbeam are examined, based on the modified couple stress theory and the third-order shear deformation theory. The extensibility of the microbeam is modelled by taking into account the longitudinal displacement. The nonlinear equations governing the longitudinal, transverse, and rotational motions are derived by means of Hamilton's principle in conjunction with the modified couple stress theory (to take into account small-scale effects). The three coupled nonlinear partial differential equations are discretized via the Galerkin method and the resulting set of ordinary differential equations is solved by means of the pseudo-arclength continuation technique and via direct time-integration. The effects of the system parameters on the behaviour of the microbeam are studied. Results are presented in the form of frequency-responses and force-responses. Points of interest in the parameter space are also highlighted in the form of time histories, phase-plane portraits, and fast Fourier transforms (FFTs). Moreover, the similarities and differences in the response of the system obtained via the modified couple stress and classical continuum mechanics theories are discussed.     

Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro–thermo-mechanical loadings using HDQM

Nonlinear buckling response of a composite cylindrical shell made of polyvinylidene fluoride (PVDF), is investigated. A two-dimensional smart model surrounded by an elastic foundation subjected to combined electro–thermo-mechanical loading is considered. The nonlinear strain terms based on Donnell’s theory are taken into account using the first shear deformation theory. The Hamilton’s principle is employed to obtain coupled differential equations, containing displacement and electric potential terms. Harmonic differential quadrature method (HDQM) is applied to obtain the critical buckling load for clamped supported mechanical and free electric potential boundary conditions at both ends of the smart cylinder. Results indicate that the critical buckling load increases when piezoelectric effect is considered.