轴向应力波与弹塑性材料圆柱壳的动力屈曲

将弹塑性圆柱壳动力屈曲作为由于轴向应力波的传播而导致的分叉问题进行研究,找出该壳发生屈曲的机理,并讨论对各种支承的弹性和弹塑性壳在轴向阶梯载荷和脉冲载荷冲击下的屈曲问题.     

圆柱壳在径向冲击载荷作用下的弹性脉冲屈曲

当圆柱壳承受径向脉冲载荷时，如果其径厚比大于一特定值，圆柱壳将产生弹性动力屈曲．本文根据有关实验结果，假定变形模态，采用Ｌａｇｒａｎｇｅ方法分析了有限长薄圆柱壳（ａ／ｈ＝４８０）在余弦冲击载荷作用下的弹性脉冲动力屈曲．导出了动力屈曲方程组，借助数值方法求解方程，并与有关计算结果进行了比较．     

弹性介质中受轴向冲击载荷作用的圆柱壳的屈曲临界载荷计算分析

建立并求解了弹性介质中圆柱壳的径向位移控制方程,考虑边界条件及相容条件,得到了应力波传播及反射过程中圆柱壳的动力屈曲分叉条件.通过计算得到了不同时间段屈曲临界载荷与应力波波阵面到达圆柱壳的位置、弹性介质的刚度、壳体未嵌入弹性介质部分的长度与总长之比的关系.数值计算结果表明,弹性介质中的圆柱壳发生轴对称屈曲和非轴对称屈曲趋势一致;嵌入弹性介质部分越深、弹性介质刚度越大圆柱壳越难屈曲;屈曲临界载荷随着弹性介质刚度的增大经历了增长缓慢、增长迅速以及增长较慢3个阶段;应力波反射前波阵面通过分界面后,屈曲仅发生在应力波传播区域,反射波波阵面通过分界面前,临界载荷较小时屈曲先发生在反射端部,随着轴向阶数增大,屈曲覆盖整个圆柱壳区域,反射波波阵面通过分界面后,壳体发生的屈曲始终覆盖整个圆柱壳区域.     

周期载荷下超弹性圆柱壳的动力响应

研究了不可压超弹性圆柱壳在内表面周期载荷及突加常值载荷作用下的运动与破坏等动力响应问题．通过对所得描述圆柱壳内表面运动的非线性常微分方程解的数值计算和动力学定性分析,发现存在一个临界载荷;当突加常值载荷或周期载荷的平均载荷值小于这一临界值时,圆柱壳的运动随时间的演化是周期性的或拟周期性的非线性振动,而当其大于这一临界值时,圆柱壳将被破坏．另外,准静态问题的解可作为突加常值载荷作用下系统动力响应解的不动点,且不动点的性质与动力响应解及圆柱壳运动的性质有关．讨论了圆柱壳的厚度和载荷等参数对临界载荷值和圆柱壳运动特性的影响．     

吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法

针对一类天然纤维增强复合(natural fiber reinforced composite,NFRC)圆柱壳的屈曲问题展开研究,基于Reissner壳体理论和辛方法,建立了轴压NFRC圆柱壳在Hamilton体系下的屈曲控制方程.将原问题归结为辛空间下的辛本征问题,通过求解辛本征值和本征解可以直接获得高精度的临界载荷和解析的屈曲模态.数值算例分析了NFRC材料的吸湿老化过程对辛本征解表达式的影响,并详细讨论了老化时间、纤维含量和几何参数对NFRC圆柱壳屈曲行为的影响.     

非Lévy型正交各向异性开口圆柱壳屈曲问题的辛叠加解析解

该文基于笔者提出的辛叠加方法得到了经典解法难以直接获得的典型非Lévy型正交各向异性开口圆柱壳屈曲问题的解析解.首先，基于Donnell薄壳理论建立了正交各向异性开口圆柱壳屈曲问题的Hamilton体系控制方程，然后将非Lévy型边界下的原问题拆分为两个子问题，在Hamilton体系下利用分离变量和辛本征展开等数学手段对子问题进行求解，最后基于原问题边界条件，通过子问题解的叠加求得原问题的解析解.数值算例表明，辛叠加解析解与有限元数值解结果吻合良好.同时，定量研究了长度和厚度等参数对屈曲载荷的影响.相比于半逆解法等传统解析方法，辛叠加方法基于严格的数学推导，无需假定解的形式，可以获得更多类似问题的解析解.     

黏弹性圆柱壳计及切变形和转动惯量时的动力学稳定性

根据修正的Timoshenko理论,在几何非线性中考虑了剪切变形和转动惯量,对黏弹性圆柱壳的动力稳定性进行了研究.根据Bubnov-Galerkin法,结合基于求积公式的数值方法,将问题简化为求解具有松弛奇异核的非线性积分-微分方程的问题.针对物理-力学和几何参数在大范围内的变化,研究壳体的动力特性,显示了材料的黏弹性对圆柱壳动力稳定性的影响.最后,比较了通过不同的理论得到的结果.     

轴向弹塑性应力波作用下直杆中的分叉问题

考虑了一个弹塑性直杆的动力屈曲问题,将其归结为轴向阶跃应力波的传播导致的分叉问题,分析了横向惯性效应的影响,并考虑了应力波反射的作用,给出了相应的屈曲条件,最后进行了数值分析,从中得到了一些有益的结论。     

复杂载荷下加筋圆柱壳非线性冲击屈曲研究

将加筋圆柱壳离散成为由圆柱壳和加强筋组成的壳体-肋骨系统,假设环向加筋与壳体在接触处刚性连接,由Hamilton变分原理推导出加筋圆柱壳结构的运动方程,以研究加筋圆柱壳在水下冲击载荷和静水压力以及动水压力组成的复杂载荷联合作用下的非线性屈曲行为。借助增量数值(在时域采用4阶Runge-Kutta方法)的方法来分析了加筋圆柱壳的非线性屈曲行为,经过算例分析验证了材料因素和初始缺陷对结构屈曲的重要影响。     

受轴向压缩圆柱壳塑性屈曲的内时分析

采用内时塑性本构方程的增量和全量表达式分析了受轴向压缩圆柱壳的塑性屈曲，得到了塑性屈曲临界应力与圆柱壳特征尺寸间的关系。对ＡＭＦ和铝合金圆柱壳塑性屈曲进行了分析，与实验结果的比较表明：除对于ＡＭＦ圆柱壳由内时塑性本构方程的全量表达式给出了较经典塑性理论全量分析略为保守的结果外，在其它杨合下，内时分析均给出了较经典塑性理论更符合实验数据的结果。     

The projective–iterative method and neural network estimation for buckling of elastic plates in nonlinear theory

The paper deals with a nonlinear buckling problem for von Karman elastic plates in bending. The simply supported and partially clamped plates are considered. A variational-projective approach with an iterative scheme is suggested for the calculation of eigenfunctions and the buckling loads for the studied problem. The convergence of the projective–iterative method is investigated. The bifurcation scenario is demonstrated by examples. Numerical results show the effectiveness of the proposed method. Prediction of the eigenvalues (which are the bifurcation points of the nonlinear problem) of the linearized problem with different sizes of the plate can also be done by an approximately trained neural network, as it is briefly demonstrated in this work.     

Duality Theory in Nonlinear Buckling Analysis for von Kármán Equations

The nonlinear eigenvalue problem in buckling analysis is studied for von Kármán plates. By using the general duality theory developed by Gao-Strang [1, 2] it is proved that the stability criterion for the bifurcated state depends on a reduced complementary gap function. The duality theory is established for nonlinear bifurcation problems. This theory shows that the nonlinear eigenvalue problem is eventually equivalent to a coupled quadratic dual optimization problem. A series of equivalent variational principles are constructed and a lower bound theorem for the first eigenvalue of the buckling factor is proved.     

Computer simulation of a twisted nanotube buckling

We develop procedures for solving the problems of dynamic nanostructure deformation and buckling numerically. The procedures are based on discretization with respect to time of the nonlinear equations of molecular mechanics whose matrices and vectors are determined using the Morse potential for the central forces of interaction between atoms and fictitious truss elements accounting for the variations of the angle between atomic bonds. To determine the critical values of deformation parameters and the shapes of buckling nanostructures we use a stability loss criterion for solutions to nonlinear ordinary differential equations on a finite time interval. We implemented our procedures in the PIONER code, using which we solve the problem of a twisted nanotube buckling in the conditions of a quasistatic deformation. To determine the postcritical equilibrium modes we solve the same problem in a dynamic formulation. We show that the modes of equilibrium configurations of the nanotube in the initial postcritical deformation correspond to a buckling mode obtained both at the bifurcation point of quasistatic solutions and at the quasibifurcation point of dynamic solutions.     

On the numerical solution of some finite-dimensional bifurcation problems

We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.     

Bifurcation problems for discrete variational inequalities

The buckling of a beam or a plate which is subject to obstacles is typical for the variational inequalities that are considered here. Birfurcation is known to occur from the first eigenvalue of the linearized problem. For a discretization the bifurcation point and the bifurcating branches may be obtained by solving a constrained optimization problem. An algorithm is proposed and its convergence is proved. The buckling of a clamped beam subject to point obstacles is considered in the continuous case and some numerical results for this problem are presented.     

球壳的环向剪切屈曲

通过球壳微元初始屈曲的微分几何分析,推导出一组新的精确的屈曲分支方程,并且应用Galerkin变分法研究铰支球壳承受环向剪切力时的整体稳定性,构造了接近分支点变形状态的屈曲模式,首次求得了从扁球壳到半球壳大范围内的扭转屈曲临界特征值,临界荷载强度和临界应力.     

2D elastic analysis of the sandwich panel buckling problem: benchmark solutions and accurate finite element formulations

This paper is concerned with the elastic stability of a sandwich beam panel using classical elasticity. An exact solution for the buckling problem of a sandwich panel (wide beam) in uniaxial compression is presented. Various formulations that correspond to the use of different pairs of energetically conjugate stress and strain measures for the infinitesimal elastic stability of the sandwich panel are discussed. Results from the present two-dimensional analyses to predict the global and local buckling of a sandwich panel are compared with previous theoretical and experimental results. A new finite element formulation for the bifurcation buckling problem is also introduced. In this new formulation, terms that influence the buckling load, which have been omitted in popular commercial codes are pointed out and their significance in influencing the buckling load is identified. The formulation and results presented here can be used as a benchmark solution to establish the accuracy of numerical methods for computing the buckling behavior of thick, orthotropic solids.     

2D elastic analysis of the sandwich panel buckling problem: benchmark solutions and accurate finite element formulations

This paper is concerned with the elastic stability of a sandwich beam panel using classical elasticity. An exact solution for the buckling problem of a sandwich panel (wide beam) in uniaxial compression is presented. Various formulations that correspond to the use of different pairs of energetically conjugate stress and strain measures for the infinitesimal elastic stability of the sandwich panel are discussed. Results from the present two-dimensional analyses to predict the global and local buckling of a sandwich panel are compared with previous theoretical and experimental results. A new finite element formulation for the bifurcation buckling problem is also introduced. In this new formulation, terms that influence the buckling load, which have been omitted in popular commercial codes are pointed out and their significance in influencing the buckling load is identified. The formulation and results presented here can be used as a benchmark solution to establish the accuracy of numerical methods for computing the buckling behavior of thick, orthotropic solids.     

Modelling and bifurcation analysis of internal cantilever beam system on a steadily rotating ring

Using Hamilton variation principle, a nonlinear dynamic model of the system with a finite deforming Rayleigh beam clamped radially to the interior of a rotating rigid ring, under the assumption that the constitutive relation of the beam is linearly elastic, is discussed. The bifurcation behavior of the simple system with the Euler-Bernoulli beam is also discussed. It is revealed that these two models have no influence on the critical bifurcation value and buckling solution in the steady state. Then we use the assumption model method to analyse the bifurcation behavior of the steadily rotating Euler-Bernoulli beam and get two different types of bifurcation behavior which physically exist. Finite element method and shooting method are used to verify the analytical results. The numerical results confirm our research conclusion. Project supported by the National Natural Science Foundation of China (Grant No. 19332022) and Space High Technology Foundation of China.