轴向冲击载荷作用下弹性圆柱壳横向弯曲动态屈曲

研究在轴向冲击载荷下弹性圆柱壳动态屈曲问题.通过构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题.辛本征解反映了局部的压缩屈曲模态和整体的弯曲屈曲模态,特别是在冲击端为自由支承边界时的特殊屈曲方式.数值结果给出了具体的临界载荷和屈曲模态规律.     

辛方法和弹性圆柱壳在内外压和轴向冲击下的动态屈曲

针对有内压或外压的弹性圆柱壳在轴向冲击载荷耦合作用下的动态屈曲问题,构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛方法。该方法直接得到非轴对称的屈曲模态。数值结果给出了圆柱壳问题的临界载荷和屈曲模态以及一些规律。     

辛方法在弹性圆板屈曲问题中的应用

在辛几何空间中将临界载荷和屈曲模态归结为辛本征值和本征解问题,从而形成一种辛方法.研究和讨论了轴对称屈曲和非轴对称屈曲问题,它们分别属于零本征值问题和非零本征值问题.以弹性圆板屈曲问题作为研究对象,借助于系统的能量构造出哈密顿体系,得到了该体系下的所有的本征解.数值结果给出了圆板和圆环板问题的临界载荷和屈曲模态.数值结果表明:对应低阶屈曲模态的临界载荷相对较小且屈曲模态在周向的波纹数也较少,说明在屈曲过程中低阶屈曲模态容易出现,特别是轴对称屈曲更容易发生;对应较大分支数的临界载荷,其值相对较大且屈曲模态在径向的波纹更加复杂;同时物理常数和几何参数也会直接影响临界载荷的大小.     

Hamilton体系下功能梯度梁的热冲击动力屈曲分析

在Hamilton体系下,基于Euler梁理论研究了功能梯度材料梁受热冲击载荷作用时的动力屈曲问题;将非均匀功能梯度复合材料的物性参数假设为厚度坐标的幂函数形式,采用Laplace变换法和幂级数法解析求得热冲击下功能梯度梁内的动态温度场:首先将功能梯度梁的屈曲问题归结为辛空间中系统的零本征值问题,梁的屈曲载荷与屈曲模态分别对应于Hamilton体系下的辛本征值和本征解问题,由分叉条件求得屈曲模态和屈曲热轴力,根据屈曲热轴力求解临界屈曲升温载荷。给出了热冲击载荷作用下一类非均匀梯度材料梁屈曲特性的辛方法研究过程,讨论了材料的梯度特性、结构几何参数和热冲击载荷参数对临界温度的影响。     

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。     

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。     

悬臂高梁在静动态载荷作用下侧向失稳的实验研究

本文进行了平头圆柱形弹体对铝合金悬臂高梁自由端正撞击引起侧向失稳的实验研究．通过多种不同尺寸梁的实验，研究了梁在静动态载荷下的侧向失稳临界载荷值及屈曲模态．最后给出一个在撞击载荷下，计算悬臂高梁侧向失稳临界冲击动能值的经验公式．     

冲击载荷作用下矩形薄板的弹性动力屈曲

为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲,根据动力屈曲发生瞬间的能量转换和守恒准则,导出板的屈曲控制方程和波阵面上的补充约束条件,真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件,建立了该问题的完整数值解法,对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究,定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明:板的厚宽比一定时,临界屈曲长度随冲击载荷的增大而减小;由于屈曲时的横向惯性效应,应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍;随着边界约束逐渐减弱,板临界力参数逐渐减小,动力特征参数逐渐增大。     

弹塑性梁在轴向应力波下的动态屈曲

本文考虑轴向应力波效应，利用分叉理论研究各种支承半无限长弹塑性梁的动态屈曲问题。在轴向阶梯载荷和脉冲载荷冲击下得到了梁的临界屈曲载荷及初始屈曲模态。其结果与实验现象相一致。同时也为研究结构动态屈曲问题提供了有效途径。     

面内阶跃载荷下矩形薄板的塑性动力屈曲

对于面内阶跃载荷作用下矩形薄板的塑性动力屈曲问题,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,由动力屈曲发生瞬间的能量转换和守恒准则,导出波阵面上的屈曲变形补充约束条件。失稳控制方程、边界条件、塑性波阵面上的连续条件和补充约束条件构成了定量求解两个特征参数和动力屈曲模态的完备条件。研究了矩形薄板塑性动力屈曲过程中板的厚宽比、冲击载荷大小、屈曲模态和临界屈曲长度之间的关系。     

Dynamic buckling of cylindrical shells subject to an axial impact in a symplectic system

This paper discusses the dynamic pre-buckling of finite cylindrical shells in the propagation and reflection of axial stress waves. By introducing the Hamiltonian system into dynamic buckling of structures, the problem can be described mathematically in a symplectic space. The solutions of Hamiltonian dual equations shown in canonical variables are obtained. The problem is reduced to the determination of eigenvalues and eigensolutions, with the former indicating critical buckling loads and the latter buckling modes. Numerical example presented shows phenomena of axisymmetric and non-axisymmetric dynamic buckling subject to impacts of axial load.     

双层石墨烯系统稳态受迫振动问题中的辛方法

针对悬臂石墨烯系统提出一种求解其稳态受迫振动问题的辛解析方法。基于Eringen非局部理论,将石墨烯层板受迫振动问题导入哈密顿体系。采用边界条件分解技术,将问题化为三种边界条件的子问题。通过辛解析方法,得到由辛本征值和辛本征解表示的双层石墨烯系统受迫振动问题的解析解表达式。数值结果表明,辛本征解级数具有很好的收敛性和精度,并与文献结果吻合;在一定的外载激励下可发生同向振动模式和反向振动模式;在一定的参数下,得到一些新的现象和结论。     

The thermal effect on axially compressed buckling of a double-walled carbon nanotube

The thermal effect on axially compressed buckling of a double-walled carbon nanotube is studied in this paper. The effects of temperature change, surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic double-shell model with thermal effect is presented for axially compressed buckling of a double-walled carbon nanotube embedded in an elastic matrix under thermal environment. Based on the model, an explicit formula for the critical axial stress is derived in terms of the buckling modes of the shell and the parameters that indicate the effects of temperature change, surrounding elastic medium and the van der Waals forces. Based on that, some simplified analysis is carried out to estimate the critical axial stress for axially compressed buckling of the double-walled carbon nanotube. Numerical results for the general case are obtained for the thermal effect on axially compressed buckling of a double-walled carbon nanotube. It is shown that the axial buckling load of double-walled carbon nanotube under thermal loads is dependent on the wave number of axially buckling modes. And a conclusion is drawn that at low and room temperature the critical axial stress for infinitesimal buckling of a double-walled carbon nanotube increase as the value of temperature change increases, while at high temperature the critical axial stress for infinitesimal buckling of a double-walled carbon nanotube decrease as the value of temperature change increases.     

Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

In this paper,a new analytical method of symplectic system.Hamiltonian system,is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain.In the system,the fundamental problem is reduced to all eigenvalue and eigensolution problem.The solution and boundary conditions call be expanded by eigensolutions using ad.ioint relationships of the symplectic ortho-normalization between the eigensolutions.A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space.The results show that fundamental flows can be described by zero eigenvalue eigensolutions,and local effects by nonzero eigenvalue eigensolutions.Numerical examples give various flows in a rectangular domain and show effectivenees of the method for solving a variety of problems.Meanwhile.the method can be used in solving other problems.     

Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.     

Stokes 流问题中的辛本征解方法

通过引入哈密顿体系，将二维Stokes流问题归结为哈密顿体系下的本 征值和本征解问题. 利用辛本征解空间的完备性，建立一套封闭的求解问题方法. 研究结果 表明零本征值本征解描述了基本的流动，而非零本征值本征解则显示着端部效应影响特点. 数值算例给出了辛本征值和本征解的一些规律和具体例子. 这些数值例子说明了端部非规则 流动的衰减规律. 为研究其它问题提供了一条路径.     

Symplectic solution system for reissner plate bending

Based on the Hellinger-Reissner variatonal principle for Reissner plate bendingand introducing dual variables, Hamiltonian dual equations for Reissner plate bending werepresented. Therefore Hamiltonian solution system can also be applied to Reissner platebending problem, and the transformation from Euclidian space to symplectic space and fromLagrangian system to Hamiltonian system was realized. So in the symplectic space whichconsists of the original variables and their dual variables, the problem can be solved viaeffective mathematical physics methods such as the method of separation of variables andeigenfunction-vector expansion. All the eigensolutions and Jordan canonical formeigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail, and their physical meanings are showed clearly. The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed. It is showed that the alleigensolutions for zero eigenvalue are basic solutions of the Saint-Venant problem and theyform a perfect symplectic subspace for zero eigenvalue. And the eigensolutions for nonzeroeigenvalue are covered by the Saint-Venant theorem. The symplectic solution method is notthe same as the classical semi-inverse method and breaks through the limit of the traditional semi-inverse solution. The symplectic solution method will have vast application.