子弹撞击作用下固支浅圆拱的弹塑性动力响应

基于大变形动力学微分方程并利用有限差分离散分析,研究了子弹撞击作用下固支浅圆拱的弹塑性动力响应。通过对响应不同时刻内力分布特征的分析,阐明了圆拱的响应模式和变形机制。研究表明,弹塑性响应过程可分为六个阶段。在响应早期,拱的变形以塑性弯曲挠动由撞击点向拱根部传播为主;在响应后期,则主要以轴力主导下的轴向拉伸变形为主。在高速撞击下,塑性弯曲挠动的不均匀性可以引起浅拱的反向弯曲变形。固支浅圆拱的动力响应对撞击速度的某个变化范围非常敏感,在此范围内,撞击速度的较小增加可以导致响应的很快增长,但动力响应随撞击速度连续变化,未发生突然的跳跃失稳。本文中计算结果同实验数据吻合较好。     

几何缺陷浅拱的动力稳定性分析

研究了几何缺陷对粘弹性铰支浅拱动力稳定性能的影响。从达朗贝尔原理和欧拉-贝努利假定出发推导了粘弹性铰支浅拱在正弦分布突加荷载作用下的动力学控制方程,并采用Galerkin截断法得到了可用龙格-库塔法求解的无量纲化非线性微分方程组。同时引入能有效追踪结构动力后屈曲路径的广义位移控制法,对含几何缺陷浅拱的响应曲线进行几何、材料双重非线性有限元分析。用这两种方法分析了前三阶谐波缺陷对浅拱动力稳定性能的影响,其中动力临界荷载由B-R准则判定。主要结论有:材料粘弹性使浅拱动力临界荷载增大且结构响应曲线与弹性情况差别很大;二阶谐波缺陷影响显著,它使动力临界荷载明显下降且使得浅拱粘弹性动力临界荷载可能低于弹性动力临界荷载。     

两端固支复合材料浅拱的动力屈曲分析

本文研究两端固支层合复合材料浅拱在阶跃载荷作用下的动力稳定性问题。通过对浅拱动力响应的数值计算结果,然后利用B-R动力屈曲准则,着重分析了集中阶跃载荷作用下几种铺层顺序及铺层数对浅拱动力临界载荷的影响,并给出了能够产生‘跳跃失稳’的最小的结构参数γ0。此外,在利用伽辽金法求解浅拱动力学控制方程时,通过取梁的自由振动模态和柱的静力屈曲模态作为浅拱的动力屈曲模态,分别进行计算并比较了二者的结果,进而讨论了二级数解的收敛性。     

考虑初始几何缺陷时复合材料层合浅拱的动态“跳跃”

考虑几何非线性但不计横向剪切效应，给出了复合材料合浅拱的动力方程，利用伽辽金法求出了均布阶跃载荷作用下，两端铰支、正交铺层的对称层合浅拱在计及初始几何缺陷情况下的动力响应，并由Ｂ－Ｒ准则分析了动力稳定性计算结果表明：初始缺陷对于结构参数γ较大的拱的临界动力载荷有很大的影响。     

复合材料层合浅拱的动态“跳跃”

本文考虑几何非线笥但不计横向剪切效应，给出了复合材料事浅拱的动力方程，并利用伽了辽金法求出了均布阶跃载荷作用下、两端铰支、对称铺层的层合浅的拱的动力响应是分析了动力稳定性。计算结果表明：不同的铺层顺序和结构几何参数对介载荷的影响很大。     

圆板动力反直观行为实验研究

对受子弹正向撞击的铝合金圆板进行了动力反直观行为的实验研究。描述了不同撞击速度下板的响应模式,发现了圆板中的反直观现象,即板的最终变形与子弹撞击方向相反,并记录了板在整个变形过程中典型点的位移历史曲线,进一步证实了结构动力响应的反直观行为是一种客观存在的弹塑性动力行为。     

集中质量撞击作用下刚塑性梁剪切和弯曲的联合响应

集中质量撞击作用下梁的刚塑性动力分析是结构碰撞的研究课题之一。很多学者曾做了详细的研究。实验表明,对于剪切强度较弱的梁,在集中质量撞击作用下梁内将出现明显的剪切滑移变形。因此,研究剪切变形对梁的动力塑性响应的影响是十分必要的,symonds、Nonaka和Oliveira曾采用方形的横向剪力和弯矩的屈服曲线研究了集中质量撞击作用下有限长梁的刚塑性动力分析。本文采用圆形屈服曲线进一步讨论了上述问题,目的是考察不同的屈服曲线对梁的动力塑性响应的影响。     

轴对称横观各向同性浅球壳受物体撞击的非线性动力响应分析

基于非线性扁壳理论和弹性接触力学,建立了横观各向同性浅球壳在其顶部受集中载荷作用的非线性运动微分方程,根据Hertz定律,考虑撞击物与浅球壳之间的弹性接触效应,确定了壳体顶部所承受的冲击力,它与撞击物的质量、初始速度、壳体的几何和物理性质等因素相关.对此非线性动力问题,采用正交配点法与时间增量法求解.算例中,讨论了撞击物的冲击速度、壳体的厚度及中曲面曲率半径对壳体所受冲击载荷及其位移响应的影响.     

含缺陷的固支梁受冲击载荷作用的实验研究

本文报导了含缺陷的固支梁受圆柱形飞射物撞击的实验过程和实验结果,分析和讨论了输入能量、切口深度、质量比等参数对非完善梁塑性动力响应特性的影响。     

端部受斜撞击作用悬臂梁的弹塑性动力响应模式

基于大变形动力控制方程并利用有限差分离散分析,研究了斜撞击作用下弹塑性悬臂梁的动力响应．通过对屈服函数以及弯矩、轴力在动力响应过程中分布规律的分析,阐明了斜撞击下恳臂梁的弹塑性动力响应模式和斜撞击的轴向分量对变形机制的影响．研究表明,弹塑性响应过程可划分为四个阶段,对应的变形模式为：“压缩塑性区扩展”模式,“广义移行塑性铰”和“压缩塑性区收缩”混合模式,“驻定塑性铰”模式,“弹性自由振动”模式．与刚塑性分析所假定的两相变形模式比较,弹塑性应响分析证实了响应早期的瞬态轴向压缩模式和梁根部“驻定塑性铰”模式的存在性,肯定了刚塑性分析所假定变形模式的主要特征．斜撞击的轴向分量在撞击发生的瞬时主导了梁的变形,使梁呈现同承受横向冲击明显小同的变形规律．随着响应的深入,轴向分量迅速衰减,其对截面屈服的贡献非常微弱,由横向分量引起的弯曲挠动在大部分时间内主导和控制梁的变形．数值计算结果表明,斜撞击载荷的质量、撞击速度和角度是影响梁动力响应的重要因素．     

In-plane buckling of prismatic funicular arches with shear deformations

The in-plane buckling behavior of funicular arches is investigated numerically in this paper. A finite strain Timoshenko beam-type formulation that incorporates shear deformations is developed for generic funicular arches. The elastic constitutive relationships for the internal beam actions are based on a hyperelastic constitutive model, and the funicular arch equilibrium equations are derived. The problems of a submerged arch under hydrostatic pressure, a parabolic arch under gravity load and a catenary arch loaded by overburden are investigated. Buckling solutions are derived for the parabolic and catenary arch. Subsequent investigation addresses the effects of axial deformation prior to buckling and shear deformation during buckling. An approximate buckling solution is then obtained based on the maximum axial force in the arch. The obtained buckling solutions are compared with the numerical solutions of Dinnik (Stability of arches, 1946) [1] and the finite element package ANSYS. The effects of shear deformation are also evaluated.     

钢管混凝土圆弧桁架拱平面内徐变稳定分析

核心混凝土的徐变会增加钢管混凝土拱肋的屈曲前变形,降低结构的稳定承载力,因此只有计入屈曲前变形的影响,才能准确得到钢管混凝土拱的徐变稳定承载力。基于圆弧形浅拱的非线性屈曲理论,采用虚功原理,建立了考虑徐变和剪切变形双重效应的管混凝土圆弧桁架拱的平面内非线性平衡方程,求得两铰和无铰桁架拱发生反对称分岔屈曲和对称跳跃屈曲的徐变稳定临界荷载。探讨了钢管混凝土桁架拱核心混凝土徐变随修正长细比、圆心角和加载龄期对该类结构弹性稳定承载力的影响,为钢管混凝土桁架拱长期设计提供理论依据。     

冲击作用下刚塑性拱的大变形响应分析

本文对受集中冲击作用的深圆拱的刚塑性动力响应进行了理论分析和数值计算，用瞬时构形法得到了问题的全程解，提出发生反向弯曲的必要条件和反向弯曲变形的近似分析方法，确定了反向弯曲出现的临界冲击速度范围，并讨论质量比，能量比和支承条件对结构的响应时间，塑性形区域和最变形的影响。本文理论分析结果与实验数据吻合。     

Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force

In this paper an integral equation solution to the linear and geometrically nonlinear problem of non-uniform in-plane shallow arches under a central concentrated force is presented. Arches exhibit advantageous behavior over straight beams due to their curvature which increases the overall stiffness of the structure. They can span large areas by resolving forces into mainly compressive stresses and, in turn confining tensile stresses to acceptable limits. Most arches are designed to operate linearly under service loads. However, their slenderness nature makes them susceptible to large deformations especially when the external loads increase beyond the service point. Loss of stability may occur, known also as snap-through buckling, with catastrophic consequences for the structure. Linear analysis cannot predict this type of instability and a geometrically nonlinear analysis is needed to describe efficiently the response of the arch. The aim of this work is to cope with the linear and geometrically nonlinear problem of non-uniform shallow arches under a central concentrated force. The governing equations of the problem are comprised of two nonlinear coupled partial differential equations in terms of the axial (tangential) and transverse (normal) displacements. Moreover, as the cross-sectional properties of the arch vary along its axis, the resulting coupled differential equations have variable coefficients and are solved using a robust integral equation numerical method in conjunction with the arc-length method. The latter method allows following the nonlinear equilibrium path and overcoming bifurcation and limit (turning) points, which usually appear in the nonlinear response of curved structures like shallow arches and shells. Several arches are analyzed not only to validate our proposed model, but also to investigate the nonlinear response of in-plane thin shallow arches.     

Non-linear in-plane analysis and buckling of pinned–fixed shallow arches subjected to a central concentrated load

This paper is concerned with an analytical study of the non-linear elastic in-plane behaviour and buckling of pinned–fixed shallow circular arches that are subjected to a central concentrated radial load. Because the boundary conditions provided by the pinned support and fixed support of a pinned–fixed arch are quite different from those of a pinned–pinned or a fixed–fixed arch, the non-linear behaviour of a pinned–fixed arch is more complicated than that of its pinned–pinned or fixed–fixed counterpart. Analytical solutions for the non-linear equilibrium path for shallow pinned–fixed circular arches are derived. The non-linear equilibrium path for a pinned–fixed arch may have one or three unstable equilibrium paths and may include two or four limit points. This is different from pinned–pinned and fixed–fixed arches that have only two limit points. The number of limit points in the non-linear equilibrium path of a pinned–fixed arch depends on the slenderness and the included angle of the arch. The switches in terms of an arch geometry parameter, which is introduced in the paper, are derived for distinguishing between arches with two limit points and those with four limit points and for distinguishing between a pinned–fixed arch and a beam curved in-elevation. It is also shown that a pinned–fixed arch under a central concentrated load can buckle in a limit point mode, but cannot buckle in a bifurcation mode. This contrasts with the buckling behaviour of pinned–pinned or fixed–fixed arches under a central concentrated load, which may buckle both in a bifurcation mode and in a limit point mode. An analytical solution for the limit point buckling load of shallow pinned–fixed circular arches is also derived. Comparisons with finite element results show that the analytical solutions can accurately predict the non-linear buckling and postbuckling behaviour of shallow pinned–fixed arches. Although the solutions are derived for shallow pinned–fixed arches, comparisons with the finite element results demonstrate that they can also provide reasonable predictions for the buckling load of deep pinned–fixed arches under a central concentrated load.     

Dynamic large deformation response of rigid plastic arches under impact

This paper presents a theoretical analysis of the dynamic large deformation response of highly circular arches under impact. By the Instantaneous Configuration Method (ICM), the solutions of the entire large deformation response process of the problem are obtained. The influences of the mass ratio, the energy ratio and the supported condition on the final deformation, the response time and the occurrence of plastic deformation are discussed in detail. The necessary condition for occurrence of the local reverse bending phenomenon has been found. An approximate method is provided to describe the phenomenon. The numerical results are in good agreement with experimental data.     

Nonlinear analysis and buckling of elastically supported circular shallow arches

Arches are often supported elastically by other structural members. This paper investigates the in-plane nonlinear elastic behaviour and stability of elastically supported shallow circular arches that are subjected to a radial load uniformly distributed around the arch axis. Analytical solutions for the nonlinear behaviour and for the nonlinear buckling load are obtained for shallow arches with equal or unequal elastic supports. It is found that the flexibility of the elastic supports and the shallowness of the arch play important roles in the nonlinear structural response of the arch. The limiting shallownesses that distinguish between the buckling modes are obtained and the relationship of the limiting shallowness with the flexibility of the elastic supports is established, and the critical flexibility of the elastic radial supports is derived. An arch with equal elastic radial supports whose flexibility is larger than the critical value becomes an elastically supported beam curved in elevation, while an arch with one rigid and one elastic radial support whose flexibility is larger than the critical value still behaves as an arch when its shallowness is higher than a limiting shallowness. Comparisons with finite element results demonstrate that the analytical solutions and the values of the critical flexibility of the elastic supports and the limiting shallowness of the arch are valid.     

Long-term non-linear behaviour and buckling of shallow concrete-filled steel tubular arches

This paper presents a theoretical analysis for the long-term non-linear elastic in-plane behaviour and buckling of shallow concrete-filled steel tubular (CFST) arches. It is known that an elastic shallow arch does not buckle under a load that is lower than the critical loads for its bifurcation or limit point buckling because its buckling equilibrium configuration cannot be achieved, and the arch is in a stable equilibrium state although its structural response may be quite non-linear under the load. However, for a CFST arch under a sustained load, the visco-elastic effects of creep and shrinkage of the concrete core produce significant long-term increases in the deformations and bending moments and subsequently lead to a time-dependent change of its equilibrium configuration. Accordingly, the bifurcation point and limit point of the time-dependent equilibrium path and the corresponding buckling loads of CFST arches also change with time. When the changing time-dependent bifurcation or limit point buckling load of a CFST arch becomes equal to the sustained load, the arch may buckle in a bifurcation mode or in a limit point mode in the time domain. A virtual work method is used in the paper to investigate bifurcation and limit point buckling of shallow circular CFST arches that are subjected to a sustained uniform radial load. The algebraically tractable age-adjusted effective modulus method is used to model the time-dependent behaviour of the concrete core, based on which solutions for the prebuckling structural life time corresponding to non-linear bifurcation and limit point buckling are derived.