生长对超弹性球壳变形和稳定性的影响

应用连续介质力学有限变形理论建立受内压作用不可压超弹性球壳大变形问题的力学模型, 且运用基于变形梯度张量极分解的弹性体积生长理论分析生长对不可压超弹性球壳变形和稳定性的影响. 通过对球壳变形与内压关系式的数值计算得到不同生长条件下球壳的变形曲线和应力分布曲线及由生长引起的残余变形和残余应力分布. 计算结果表明生长对球壳变形特性有明显的影响, 生长影响球壳可产生不稳定变形的临界壁厚和临界内压, 且在某些情况下可改变球壳的稳定性. 生长在球壳中可产生一定的残余变形和残余应力, 对球壳中的应力分布有一定的影响. 另外当生长的程度足够大时, 即便没有外力作用,球壳仅在生长引起的残余应力作用下也可产生不稳定变形.      

热超弹性薄板非对称拉伸的分岔和稳定性

本文应用超弹性材料的有限变形理论分析了在面内等双向拉伸死载荷作用下不可压热超弹性方形薄板发生非对称变形的分岔及其稳定性问题.给出了方板变形的分岔曲线和临界载荷,发现对受面内等双向拉伸载荷作用的均匀方板,当拉伸载荷值较小时,方板双向等伸长变形,发生对称的拉伸变形;但当此载荷值大于某一临界值时,从方板的对称拉伸变形中分岔出非对称的变形,方板在两个方向的变形不再相等.通过变形发生分岔前后的能量比较发现,分岔后的对称变形是不稳定的,而非对称变形是稳定的.同时,给出了板中的应力分布曲线,并由不同温度下变形的分岔曲线和应力分布曲线讨论了温度对方板变形和板中的应力分布的影响.     

热超弹性圆筒的不稳定性

应用有限变形弹性理论分析了受内压和轴向拉伸作用的不可压热超弹性圆筒发生非均 匀变形的不稳定性问题. 受内压和轴向拉力作用的薄壁圆筒，当内压较小时，圆筒发生稳定 的均匀膨胀变形；当内压大于某一临界值时，圆筒产生复杂的非均匀变形，其一部分膨胀变 形很大，形如``灯泡'状，而另一部分仅仅是轻微膨胀，且此时的变形是不稳定的. 但对厚 壁圆筒而言，不论压力如何，总是发生稳定的均匀膨胀变形. 根据圆筒的变形曲线，给出了 圆筒可以发生不稳定变形的临界厚度. 同时，讨论了轴向拉伸和温度场对圆筒变形的影响.     

拉压性能不同材料全量型本构关系及厚壁筒的应力分析

将经典全量理论作了推广，考虑了应力状态及塑性体积变形对拉压性能不同材料的塑性行为的影响。应用该本构模型分别计算了厚壁筒在内压和外压作用下的应力分布。给出了径向应力、环向应力和轴向应力沿壁厚的分布图。将本文的计算解与拉压性能相同(不考虑体积变形、强化曲线唯一)的幂函数强化材料的厚壁筒的理论解进行了比较。结果表明，材料的拉压性能不同对厚壁筒的环向应力和轴向应力影响较大。因此，对于拉压性能不同材料，考虑到其对应力状态及塑性体积变形敏感时，是不能将其简化成拉压性能相同、体积不可压缩、强化曲线唯一的理想材料。     

在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。     

弹性圆柱壳在轴向应力波传播过程中的非对称屈曲

讨论弹性圆柱壳端部受冲击载荷作用，在应力波传播过程中的非对称屈曲问题。通过求解扰动方程得到了动态屈曲的分叉条件、临界载荷和屈曲模态。数值结果表明，当壳壁厚不很薄时，轴对称屈曲临界载荷比非对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低。不同的冲击载荷，屈曲模态也将不同。     

钢质圆柱壳在侧向爆炸荷载下的动力响应

将壁厚为2.75mm、外径为100mm的钢质圆柱壳置于75g裸装圆柱形压装TNT药柱产生的爆炸场中进行冲击实验,获得了不同装药条件下圆柱壳的变形破坏特征。实验表明:非接触爆炸条件下,壳壁迎爆面局部破坏呈现碟型凹陷,同时沿壳体轴线方向产生了整体屈曲变形,且装药距离较大或药柱轴线与壳体轴线垂直放置情况下对壳体损伤程度较大;而接触爆炸时,壳壁发生破裂形成破口及破片。利用动力有限元程序LS-DYNA及Lagrangian-Eulerian流固耦合方法对圆柱壳的非线性动态响应过程进行数值模拟,分析了壳壁的屈曲变形过程及迎爆曲面中心点速度、位移时程曲线,计算结果与实验吻合较好。并基于数值计算确定了壳壁发生破裂的临界装药距离。     

含孔边裂纹球壳的断裂分析

在依据Reissner理论得出的球壳裂纹尖端应力应变场展开式基础上,采用局部—整体分析法和权函数方法分别计算承受内压的含孔边裂纹球壳的应力强度因子.在有限元的模式中考虑剪切变形的影响,并对奇异元模式的应力应变场展开式的项数选择、奇异元最佳尺寸的选取进行了分析.本文计算和分析了在不同几何尺寸,不同开孔大小以及不同剪切参量条件下承受内压的含孔边裂纹球壳的应力强度因子及其变化规律.     

电活性聚合物圆柱壳静态与动态电压下的响应及稳定性

摘要：在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场。这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏。本文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题。采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程。给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏。同时,也讨论了厚度和边界条件对临界电压的影响。圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动。给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性。采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏。最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论。     

一种内压膨胀系统的动态响应分析

论文采用LS-DYNA非线性动力学有限元程序,对一种曲边柱壳-多体内压膨胀系统在均布内压作用下的动态膨胀过程进行了数值分析,获得了曲边柱壳动态响应规律.文中分析了各种因素对曲边柱壳的变形模式及其应力、应变变化规律的影响；模拟了曲边柱壳在内部压力和外围变形体共同作用下的耦合变形运动过程.模拟计算结果与试验现象基本一致.     

Electromechanical responses and instability of electro-active polymer cylindrical shells

Based on the theories of finite deformation elasticity, electromechanical responses and instability of an incompressible electro-active polymer (EAP) cylindrical shell, which is subjected to an internal pressure and a static electric field, are studied. Deformation curves and distribution of stresses are obtained. It is found that an internal pressure together with an electric field may cause the unstable non-monotonic deformation of the shell. It is also shown that a critical thickness for the shell exists, and the shell may undergo the unstable deformation if its thickness is less than this critical value. In addition, the effects of the electric field, axial stretch, thickness, and internal pressure on the instability of the shell are discussed.     

Instability of a Charged Droplet in an Inhomogeneous Electrostatic Field of a Rod of Finite Thickness

The instability of a charged droplet of an ideal liquid in an inhomogeneous electrostatic field of a rod of finite thickness maintained at a constant electrostatic potential is investigated within the framework of analytic asymptotic calculations. It is shown that the mode amplitudes and the drop oscillation frequencies increase with the rod thickness. The critical conditions of instability of the droplet reduce by several times as compared with the critical conditions of implementation of its instability in the electrostatic field of an infinitely thin filament maintained at a constant electrostatic potential. An analytic dependence between the charge and field parameters, critical for implementation of the instability of a charged droplet in an inhomogeneous electrostatic field and dependent on the rod thickness, is found.     

绕径旋转横观各向同性圆球壳的变形和应力分析

本文用三维弹性力学理论研究绕径旋转横观各向同性圆球壳的变形和应力分布，给出任意厚度圆球壳的位移和应务的封闭形式解以及数值结果。研究表明球壳上的位移和应力大小与旋转角速度的平方成正比，球面内的正应力远大于径向正应力和剪应力。     

Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory

By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material (FGM) are examined. To take small scale effects into consideration in a more accurate way, a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory. The variation of material properties associated with FGM nanoshells is supposed along the shell thickness, and it is modeled based on the Mori-Tanaka homogenization scheme. With a boundary layer theory of shell buckling and a perturbation-based solving process, the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly. It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime, while the nonlocal size dependency leads to the decreases of them. Moreover, the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.     

Analysis of an elasto-plastic thick walled sphere loaded by internal and external pressure

The non-linear behaviour of a thick walled sphere under internal and external pressure is considered. The material is assumed to be incrementally elasto-plastic in the classical sense. No restriction on the magnitude of the deformation is imposed. For internal pressure a solution is obtained in terms of closed integrals. It is shown that the three dimensional solution reduces exactly to the membrane solution when the thickness of the shell becomes very small.Numerical examples are given for some practical materials used in the aerospace industry. It is shown that at a certain critical pressure instability of the second kind (inflation) is obtained.     

圆柱壳在外压和轴向冲击联合作用下的稳定性实验研究

本文利用AMT铝合金三种不同厚度的圆柱壳,在常外压和不同轴向冲击载荷作用下的柱壳塑性动力屈曲问题。实验发现除了通常文献中提到的临界速度Vc1外,还有一个使柱壳发生较大变形而破坏时所对应的一个临界遵度Vc2。文章重点研究Vc2与轴向变形。柱壳厚度等之间关系以及柱壳屈曲形式。     

Higher order zig-zag theory for smart composite shells under mechanical-thermo-electric loading

A higher order zig-zag shell theory based on general tensor formulation is developed to refine the predictions of the mechanical, thermal, and electric behaviors. All the complicated curvatures of surface including twisting curvatures can be described in a geometrically exact manner in the present shell theory because the present theory is based on the geometrically exact surface representation. The in-surface displacement fields are constructed by superimposing the linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface free conditions of transverse shear stresses. Thus the proposed theory has only seven primary displacement unknowns and they do not depend upon the number of layers. To assess the validity of present theory, the developed theory is evaluated under the thermal and electric load as well as under the mechanical load of composite cylindrical shells. Through the numerical examples, it is demonstrated that the proposed smart shell theory is efficient because it has the minimal degrees of freedom. The present theory is suitable in the predictions of deformation and stresses of thick smart composite shells under the mechanical, thermal, and electric loads combined.     

Asymptotic limits and wrinkling patterns in a pressurised shallow spherical cap

The asymmetric bifurcation problem for a shallow spherical cap is examined. The applied pressure can act either external or internal to the cap and both cases are treated here. Assuming a non-linear axisymmetric basic state, the linearised bifurcation equations for the pressurised shell are investigated in the limit when the thickness of the cap is much less than the maximum rise of the shell mid-surface. Within this regime the wrinkling patterns in both cases are confined to a narrow zone near the edge of the shell, making it possible to solve asymptotically the corresponding equations and derive analytical predictions for both the critical pressure and the corresponding number of wrinkles. Some comparisons with direct numerical simulations are included as well.     

Elastoplastic analysis of nonlinearly hardening variable thickness annular disks under external pressure

Based on von Mises’ yield criterion, deformation theory of plasticity and Swift’s hardening law, elasto-plastic deformation of variable thickness annular disks subjected to external pressure is studied. A nonlinear shooting method using Newton’s iterations with numerically approximated tangent is designed for the solution of the problem. Considering a thickness profile in the form of a general parabolic function, the condition of occurrence of plastic deformation at the inner and outer edges of the annular disk is investigated. A critical disk profile is determined and the corresponding elastic–plastic stresses as well as the residual stress distribution upon removal of the applied pressure are computed and discussed.