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。     

直杆塑性动力屈曲的双特征参数解

在关于轴向弹塑性压缩波下直杆塑性动力屈曲的研究中,将临界应力和屈曲惯性项指数参数作为一对特征参数求解．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定量求解两个特征参数和动力屈曲模态的完备条件。     

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。     

弹性压应力波下直杆动力失稳的机理和判据

基于应力波理论和失稳瞬间能量的转换和守恒,导出了一个直杆动力分岔失稳的准则:(1)直杆在发生分岔失稳的瞬间所释放出的压缩变形能等于屈曲所需变形能与屈曲动能之和;(2)在上述能量转换过程中,能量对时间的变化率服从守恒定律.应用临界条件(1)推导出的直杆动力失稳的控制方程和杆端边界条件以及连续条件,与应用哈密顿原理推导的结果完全相同,但不足以构成求解直杆动力失稳问题的完备定解条件.应用临界条件(2)导出压缩波前的附加约束方程.由此得出该问题的完备定解条件,导出包含两个特征参数的一对特征方程.从而建立了求解直杆动力失稳模态和两个特征参数(临界力参数和失稳惯性项指数参数即动力特征参数)的较严密理论方法.     

弹性压应力波下直杆动力失稳的机理的判据

基于应力波理论和失稳瞬间能量的转换和守恒,导出了一个直杆动力分岔失稳的准则：（1）直杆在发生分岔失稳的瞬间所释放出的压缩变形能等于屈曲所需变形能与屈曲动能之和;（2）在上述能量转换过程中,能量对时间的变化率服从守恒定律。应用临界条件（1）推导出的直杆动力失稳的控制方程和杆端边界条件以及连续条件,与应用哈密顿原理推导的结果完全相同,但不足以构成求解直杆动力失稳问题的完备定解条件,导出包含两个特征参数的一对特征方程。从而建立了求解直杆动力失稳模态和两个特征参数（临界力参数和失稳惯性项指数参数即动力特征参数）的较严密理论方法。     

轴向压应力波下圆柱壳弹性动力失稳的判据与机理

基于动力失稳瞬间能量的转换和守恒,推导提出了受轴向力圆柱壳弹性动力失稳的判据和两个临界条件,由第一个临界条件导出的圆柱壳弹性动力失稳的控制方程、边界条件、屈曲变形连续与利用Hamilton原理的结果完全相同,但不足以确定包含在本问题中的两个特定特征参数（临界载荷参数和动力特征参数）,由第二个临界条件导出压缩波前的屈曲变形约束方程,基于控制方程有满足边界条件、变形连续条件和波前约束方程的非平凡解的条件,导出关于两个特征参数的一对特征方程,基于特征方程的解,精确地计算出临界载荷参数和动力特征参数的值以及动力失稳态态,由此建立了轴向力作用下圆桩壳弹性动力失稳的特征值分析方法。     

应力波传播与屈曲耦合情况下结构动力屈曲控制方程探讨

从应力波作用下结构动力屈曲的特点出发,指出应力波作用下结构动力屈曲与结构中应力波传播的耦合导致时间成为结构动力屈曲的参变量,从而应力波作用下结构动力屈曲问题中结构的真实运动与邻近运动是不同时刻、不同扰动区域的比较,这使得其动力屈曲控制方程的建立不宜采用传统的等时积分变分原理;以压应力波作用下弹性直杆为例,应用能量守恒原理,根据屈曲时刻结构能量的转换关系,建立了弹性压应力波作用下半无限长直杆的动力屈曲控制方程,并得到了波前附加约束条件;最后,讨论了波前附加约束条件的物理意义,指出波前附加约束条件出现的根本原因是轴向应力波的传播与屈曲不能解耦。     

轴向应力波作用下圆柱壳塑性轴对称动力屈曲

运用有限元特征值分析方法对应力波作用下圆柱壳塑性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的特征方程,在分析中同时考虑了应力波效应及横向惯性效应,把圆柱壳塑性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳塑性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

轴向应力波作用下圆柱壳弹性轴对称动力失稳有限元特征值分析

本文运用有限元特征值分析方法对应力波作用下圆柱壳弹性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的有限元特征方程,在此方程中考虑了应力波效应及横向惯性效应,把圆柱壳弹性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳弹性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

应用阵面追踪法对散心爆轰波传播的数值模拟

考虑到爆轰波阵面曲率及化学反应区宽度的作用 ,由修正Hugoniot关系式解析求解了波后状态 ,应用阵面追踪法 (FTM)数值模拟了曲面散心爆轰波的传播。计算给出的散心爆轰波走时及波阵面上物理量都达到了波阵面曲率的一阶精度。     

Twin-characteristic-parameter solution of axisymmetric dynamic plastic buckling for cylindrical shells under axial compression waves

In the present investigation on the dynamic plastic buckling of cylindrical shells under axial compression waves, the critical axial stress and the exponential parameter of inertia terms in stability equations are treated as a couple of characteristic parameters. The criterion of transformation and conservation of energy in the process of buckling initiation is used to derive the supplementary restraint equation of buckling deformation at the fronts of axial elastic and plastic compression waves. The supplementary restraint equation, stability equations, boundary conditions and continuity conditions constitute the necessary and sufficient conditions of determining the two characteristic parameters. Two characteristic equations are derived for the two characteristic parameters. The critical axial stress or the critical buckling time, the exponential parameter of inertia terms and the initial modes of buckling deformation are calculated quantitatively from the solution of the characteristic equations.     

Characteristic-value analysis for plastic dynamic buckling of columns under elastoplastic compression waves

The characteristic-value analysis of plastic dynamic buckling is presented for columns under the action of elastoplastic compression wave caused by an axial-step load. Two critical conditions constituting a dynamic instability criterion are derived on the basis of transformation and conservation of energy. The governing equations, the boundary conditions and the continuity conditions derived by the use of the first critical condition are the same as those given by the adjacent-equilibrium criterion and are insufficient for determining two characteristic parameters involved in the governing equations. A supplementary restraint equation for buckling deformations at the plastic-wave front and the elastic-wave front is derived by the use of the second critical condition. Then, a couple of characteristic equations for two characteristic parameters are derived on the condition that the governing equations have non-trivial solutions satisfying the boundary conditions, the continuity conditions and the supplementary restraint equation. The critical-load parameters, dynamic characteristic parameter (exponent parameter of inertia term) and dynamic buckling modes are calculated from the solutions of the characteristic equations.     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.     

Buckling strength analysis of adhesively bonded aluminum hat sections

This paper provides an analytical solution for the critical buckling stress of adhesively bonded aluminum hat sections under static axial compression. The governing rectangular plate member of the structure is treated based on the differential equation for out-of-plane deflections of thin plates. Finite element eigenvalue buckling analysis is performed to verify the assumed simply supported boundary conditions for common edges between adjacent plate elements. Elastic restraint is applied to the two loaded edges of the rectangular plate, and the relative critical buckling stress is computed according to the transcendental equations. It is found from experiments that there is no adhesive bonding failure in the elastic buckling stage. The analytical solution yields buckling stress predictions which are in reasonable agreement with measured values.