弹性SHPB试件内部纵向应力波传播及所产生的横向约束应力

采用考虑横向惯性效应的Rayleigh-Love杆理论分析了一个弹性试件在分离式霍普金森压杆(SHPB)加载过程中的内部弹性波传播过程，运用Laplace变换和反变换方法，得到了试件内部各点的变形、速度、应变和应力解析解.通过数值计算，得到梯形入射波加载情况下，纵向应力在试件内部的连续变化过程，以及波传播所伴随的横向附加应力.计算表明：在试件/入射杆界面附近，初次加载所产生的横向附加应力最大，可达入射波平台的12%;在大部分试件区域，纵向应力波传播将造成入射波平台4%～6%的横向附加应力；材料的泊松比越大，或者杆/试件声阻抗比越小，所伴随的横向附加应力越大；梯形波的上升时间和试件长径比对横向附加应力影响不大.     

低频弹性波超材料的若干进展

超材料是一类新兴的具有超常物理性质的人造周期/拟周期材料, 能够改变电磁波、声波以及弹性波等在介质中的传播特性. 因在航天、国防以及民用科学等方面的巨大应用潜力, 超材料自被提出后便受到极大的关注并引发研究热潮. 弹性波超材料是超材料的一种, 能够基于弹性波与超材料结构的相互耦合作用实现对弹性波的操控. 带隙是评估弹性波超材料实现弹性波操控的重要工具, 其性质与超材料的材料参数、晶格常数以及局域振子的固有频率相关. 受制于超材料的承载能力、外观尺寸以及局域振子结构等因素, 利用传统超材料开启低频(约100 Hz)弹性波带隙依然存在较大困难. 文章首先简要介绍超材料开启弹性波带隙的基本原理, 然后从低频弹性波超材料基本结构与低频带隙实现方法、低频带隙优化与调控策略、低频带隙潜在应用等三个方面详细总结低频弹性波超材料的研究工作. 其中, 低频带隙超材料的基本结构主要包括布拉格散射型超材料、传统局域共振型超材料以及准零刚度局域共振超材料. 文章通过总结低频弹性波超材料的研究进展, 分析了目前研究中的不足并对未来低频弹性波的研究方向进行了展望.      

结构后屈曲分析中的混合Newton-Lanczos算法

本文提出一种适于结构非线性后屈曲分析的混合Newton-Lanczos算法。与当前流行的弧长法不同,本文提出的算法采用传统的载荷增量法进行逐步求解,可求出给定载荷下的结构变形且适于任意外加载荷。对于临界载荷附近的迭代应用了Lanczos法求解方程及相应变载技巧。文中给出的若干数值计算结果表明了该算法在结构非线性后屈曲分析中的适用性。     

简支梁大挠度弹性后屈曲载荷与变形的优化算法

针对简支梁结构大挠度后屈曲载荷与变形的计算问题,本文提出了一种直接求解其后屈曲载荷和变形的优化算法。在简支梁处于大挠度屈曲平衡状态下,将梁结构划分为有限子段,以待求后屈曲载荷为设计变量,根据起点的边界条件和每个子段满足的弯矩变形公式,累积计算出其他各个节点的坐标,以得到的终点坐标满足的边界条件构建目标函数模型。在此基础上,通过MATLAB编制优化程序分析了两个典型算例,并将理论结果与相关软件的计算结果进行对比,从而证明了本文算法的正确性。本文算法求解过程简单、快速,具有一定的实用性,为变截面结构大挠度弹性屈曲稳定性问题的研究提供了参考。     

刚体碰撞下直杆的塑性屈曲和后屈曲

研究了受刚体轴向碰撞直杆中塑性屈曲变形发展的机理.推导了增量形式的非线性动力方程,并用差分法求解,将特征值分析给出的初始局部屈曲位移作为方程解的初始条件.数值结果说明:随着轴向压缩波的传播,碰撞端附近发生的局部屈曲变形增长和向前传播,由半波形的初始模态发展成后屈曲高阶模态;在后屈曲变形的早期阶段无应变率逆转发生,切线模量理论适用于该阶段弯曲变形的计算.     

Hopkinson曲杆型双向拉伸加载设计探讨

为了实现对材料或结构的双向高应变率同步拉伸加载,基于曲杆中弹性应力波传播理论和Hopkinson杆原理,首先在对称的人字形曲杆结构中同时产生和传递两路压缩波,再经过接触转接头反射形成沿拉伸加载杆传播的双向拉伸波,实现对试样的双向动态拉伸。同时,为理解人字形曲杆几何构形对弹性压缩波传播的影响规律,对该加载装置进行了动力学分析和ABAQUS有限元模拟。研究发现,理想方波构形的压缩弹性波经过曲杆传播后,方波的平台段随着杆弯曲角度的增大出现前高后低的倾斜现象,同时大曲率杆引起的波形失真更严重。为获取常规方波或梯形波的平台段,也可采用定量优化的锥形撞击杆,产生前低后高的加载波,来抵消曲杆传递中的倾斜失真。最后,为了验证该加载系统的有效性,搭建了小型人字形曲杆高应变率双向拉伸装置进行试验测试。结果表明,该装置实现了脉宽约为54 μs的双向拉伸加载波良好的同步,两路波形起始点时间差可以控制在约2.5 μs以内,幅值差约6×10?6。同时对2024铝合金试样进行了双向拉伸试验,取得良好的试验效果。     

理想直杆中轴向应力波的传播和反射导致的分叉问题

对阶跃载荷作用下弹性理想完善直杆中应力波的传播及其反射引起民的分叉问题进行了理论分析和数值计算，讨论了此类动力屈曲问题中横向惯性效应的影响；给出了一种进行后分叉分析的近似方法，得到了一些结论，在各类结构由于应力波的传播及反射引起的分叉问题具有指导意义。     

多孔材料中应力波的传播

针对多孔泡沫混凝土实验应力应变曲线的基本特点,提出并建立了一种可以考虑孔隙压实过程的材料本构模型及其数学形式.通过典型算例,分析了应力波在多孔材料中传播的耗散效应,指出多孔材料中的孔隙在被压实过程中能有效吸收应力波能量、降低应力波强度,在引起应力波衰减的诸因素中,孔隙压实所起的作用更大更显著.     

缺陷对玄武岩中声波波速影响的实验研究

岩体是具有多种微结构的复杂体,具有明显的频散效应.过去的研究基本上将岩体中的孔隙率作为研究岩体微观结构的参数,这种方法无法考虑到岩体中细观缺陷的局部影响.本文选用水泥砂浆为参考材料,通过在试件中预制裂缝来研究含缺陷玄武岩的弹性波传播特性.对含不同裂缝的试样进行了5种频率的声波测试.结果表明:缺陷对玄武岩的弹性波频散效应影响很大,随缺陷所占比例的增大而增大.同时单轴加载下的弹性波测试则说明,在0～20MPa范围内,玄武岩弹性波波速随压力增大开始时候有一定幅度的升高,到8MPa以后由于玄武岩硬度相对较高,波速基本保持在一定水平.     

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。     

含分层损伤复合材料层合板剩余压缩强度研究

准确预测含分层损伤层合板的剩余压缩强度,对复合材料具有十分重要 意义。本文基于层合板一阶剪切理论,建立了一种考虑复合材料多种损伤的含分层层合板刚度退化模型,通过数值算例分析了分层屈曲临界载荷与材料强度极限的关系以及刚度退化对含分层层合板前后屈曲行为的影响。     

Thermal post-buckling analysis of imperfect laminated plates using a higher-order shear deformation theory

Thermal post-buckling analysis is presented for a simply supported, composite laminated plate subjected to uniform or non-uniform tent-like temperature loading. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reddy's higher-order shear deformation plate theory, and include thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and post-buckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates. The effects played by transverse shear deformation, thermal load ratio, plate aspect ratio, total number of plies, fiber orientation and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form.     

Buckling and post-buckling analyses of size-dependent piezoelectric nanoplates

This paper attempts to investigate the buckling and post-buckling behaviors of piezoelectric nanoplate based on the nonlocal Mindlin plate model and von Karman geometric nonlinearity. An external electric voltage and a uniform temperature rise are applied on the piezoelectric nanoplate. Both the uniaxial and biaxial mechanical compression forces will be considered in the buckling and post-buckling analysis. By substituting the energy functions into the equation of the minimum total potential energy principle,the governing equations are derived directly, and then discretized through the differential quadrature(DQ) method. The buckling and post-buckling responses of piezoelectric nanoplates are calculated by employing a direct iterative method under different boundary conditions. The numerical results are presented to show the influences of different factors including the nonlocal parameter, electric voltage,and temperature rise on the buckling and post-buckling responses.     

BUCKLING ANALYSIS OF STRETCHABLE FERROELECTRIC THIN FILM ON ELASTOMERIC SUBSTRATES

The thin stiff films on pre-stretched compliant substrates can form wrinkles, which can be controlled in micro and nanoscale systems to generate smart structures. Recently, buck- led piezoelectric/ferroelectrie nanoribbons have been reported to show an enhancement in the piezoelectric effect and stretchability, which can be applied in energy harvesting devices, sensors and memory devices instead of polymeric polyvinylidine fluoride （PVDF）. This paper studies the buckling and post-buckling process of ferroelectric thin films bonded to the pre-stretched soft layer, which in turn lies on a rigid support. Nonlinear electromechanical equations for the buckling of thin piezoelectric plates are deduced and employed to model the ferroelectric film poled in the thickness direction. Two buckling modes are analyzed and discussed： partially de-adhered buck- ling and fully adhered buckling. Transition from one buckling mode to the other is predicted and the effect of piezoelectricity on the critical buckling condition of piezoelectric film is examined.     

Secondary buckling of a flat plate under uniaxial compression : Part 1: theoretical analysis of simply supported flat plate

While studies of post-buckling behavior and load-carrying capacities of thin plates subjected to uniaxial compression have been limited to stable conditions, further post-buckling loading generates an unstable condition. The secondary buckling which occurs with snap-through to higher-order deflections under such unstable conditions has not been analyzed in detail as yet. In the first part of this paper, a thin square plate under uniaxial compression, which is simply supported along four edges, is considered. A method based on the second variation of the total potential energy is then proposed for evaluating the stability of the post-buckling equilibrium state and inevitable secondary buckling is derived analytically. The effects of various factors, such as initial imperfections, assumed virtual displacement pattern, post-buckling deflection pattern and in-plane boundary conditions, on the secondary buckling values are discussed. In part 2, secondary buckling of clamped plates is analyzed by use of the finite element method and the resultant numerical results are compared with experimental results.     

Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical–cylindrical shells

Here, the nonlinear thermo-elastic buckling/post-buckling characteristics of laminated circular conical–cylindrical/conical–cylindrical–conical joined shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach. The nonlinear governing equations, considering geometric nonlinearity based on von Karman’s assumption for moderately large deformation, are solved using Newton–Raphson iteration procedure coupled with displacement control method to trace the pre-buckling/post-buckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, material properties and number of circumferential waves on the nonlinear thermo-elastic response of the different joined shell systems.     

The buckling behavior of uniformly heated thin circular cylindrical shells

The results of buckling tests on uniformly heated, clamped, thin circular cylindrical shells are presented and discussed. Particular attention is paid to both the actual buckling process and the ensuing post-buckling behavior. Load vs. end-shortening curves are included. The possibility of “snap-through” buckling which occurs at a value of end shortening greater than that corresponding to the maximum supported load is experimentally verified. A comparison of the present experimental results with available theory is made. It is observed that the experimental values of the buckling temperature can be substantially greater than the temperatures calculated by linear theory from the experimental buckling loads; however, the buckling stresses are the same whether the loading is thermal or mechanical.