冲击载荷下板杆组合结构的动态响应

结构受冲击载荷作用可能会变形甚至失效.合理的结构形式有助于增强结构的抗冲击性能.本文对冲击载荷作用下板杆组合结构的动力学行为进行了分析,采用有限元方法模拟冲击载荷下结构的大挠度变形模式和能量吸收特性,并研究了杆件长度对抗冲击性能的影响.     

冲击载荷下轻质夹芯拱最大刚度拓扑优化及动力响应

基于双向渐进结构优化方法（bi-directional evolutionary structural optimization,BESO）框架,将传统动态载荷优化法中的内外层迭代引入到ABAQUS-MATLAB平台集成优化中,改进动态载荷拓扑优化流程。对初速度为100 m/s的子弹冲击下的夹芯拱结构进行拓扑优化设计和动力学响应分析。优化后夹芯拱芯层的变形模式可分为3个对称的部分,跨中区域的中部和上部主要发生压缩变形,呈现类三角点阵桁架结构,边界区域上部发生拉伸变形,下部发生压缩变形,呈现C形型结构,跨中和边界之间的过渡区域以拉弯联合变形为主,呈现Y形结构。通过与两种等质量的拱结构对比,分析了3种结构在不同初速度的子弹冲击下结构的挠度以及芯层的能量吸收情况。结果表明:在相同的冲击速度下,优化后的结构挠度最小,芯层比吸能最高;当冲击速度较低时,优化后的结构的抗冲击性能优势并不明显;在所研究的冲击速度范围内,冲击速度越高,优化后结构的抗冲击性能越好。对比对称载荷与非对称载荷（冲击点偏移量为100%）下2种优化结构在不同载荷工况下的动态响应,结果表明:载荷工况不同,得到的最终优化结果也略有所不同,但在相同载荷下结构的响应相差较小,每种工况下得到的优化结果在相应工况下所展现的力学性能略优,但均明显优于传统结构。因此,在对称冲击载荷下优化所得的结构具有一定的普遍性。     

计入膜力塑性耗散效应的矩形板塑性动力响应

从能量的观点在小挠度理论中引入表征膜力塑性耗散效应的修正因子,基于刚性板块的总体平衡给出矩形板大挠度塑性动力响应的完全运动方程组,分析了理想刚塑性简支和固支矩形板在矩形脉冲和冲击载荷下包括移行塑性铰相的完全大挠度响应过程。解决了当矩形板的挠度达到厚度量级时弯矩、膜力的联合作用问题,理论预报的结果在板的挠度为10倍板厚的量级与实验结果符合良好,改进了只考虑弯矩作用的小挠度理论结果和模态近似估计。     

雨载作用下浮顶结构有限元分析的载荷修正法

浮顶结构的受力与变形之间存在着非线性的耦合关系,这给计算分析带来了很大的麻烦。为了解决这一问题,本文提出了单盘式浮顶结构在雨水载荷作用下有限元分析的载荷修正计算方法。通过对浮顶结构力学模型的分析,建立了浮顶结构载荷与单盘挠度之间的关系式,并基于这一关系式给出了浮顶结构有限元分析的载荷修正法和相应计算方案。载荷修正法的基本思想是,首先利用有限元方法对浮顶结构进行几何大变形非线性分析,然后通过迭代修正来调整载荷大小,使得计算得到的载荷与挠度满足给定关系式,最终获得浮顶结构的变形与受力情况。最后,将计算结果与试验结果进行了比较,验证了本文提出的计算方法的有效性和可靠性,为浮顶结构的进一步有限元分析打下基础。     

预制孔靶板在爆炸冲击波载荷作用下的动态响应

对四边固定带预制孔靶板在爆炸冲击波载荷作用下的动态响应问题进行了实验研究。通过设计 爆炸冲击波载荷对2种材料不同孔数、不同孔径的靶板的冲击工况,获得了各靶板的中心点挠度。通过分析, 得到了预制孔靶板中心点挠度与预制孔数、孔径的相关规律,结合无孔平板在爆炸冲击波载荷下的挠度公式, 建立了广义的靶板中心点挠度公式,可用于计算不同孔靶板的中心点挠度。研究结果可作为平板材料在破片 冲击波联合毁伤研究的基础,为杀爆战斗部威力评估提供一些依据。     

Lee极值原理与结构的大挠度塑性动力响应

本文介绍了利用Lee 极值原理确定结构的大挠度塑性动力响应的数值方法,给出了在均布冲击载荷作用下的理想刚塑性门形框架的大挠度进化模态解,指出如果模态形式取得合适,可使进化模态解接近于真实解.这样得到的门形框架的大挠度模态解与文献[8]中的实验结果和文献[9]中的大挠度完全解都符合得很好.     

金属梁在预应力下的冲击响应

工程结构在使用过程中，大部分构件处于预应力状态。为了理清预应力对金属梁在冲击载荷作用下响应的影响机理，对不同轴向预应力条件和不同冲击强度下金属梁的塑性变形规律进行了研究。通过自主设计的预应力加载装置和落锤试验机，实现对金属梁的预应力控制和冲击加载；借助商用软件建立数值模型，对相关工况进行模拟。数值模拟结果与试验结果有较好的一致性。通过对梁的剩余挠度进行对比发现，压预应力状态下的梁受冲击载荷作用所产生的中点剩余挠度会比无预应力时更大；而拉预应力状态下的梁，挠度的变化量与预应力之间没有较一致的规律。从能量角度进行分析发现，梁的塑性变形能来自外加动能和初始内能，外加动能的能量比越高，梁的能量吸收率就越高，且在低能量比时，压预应力下的能量吸收率相对较高，拉预应力下的相对较低；高能量比时，预应力对能量吸收率几乎无影响。压预应力下，梁的极限弯矩增大，长度缩小，增大了的塑性变形能分布在长度缩小了的梁内，必然会导致更大的剩余挠度；拉预应力下，梁的极限弯矩减小，长度增大，增大了的塑性变形能分布在长度增大了的梁内，剩余挠度则没有显而易见的规律。这在一定程度上解释了预应力对冲击载荷作用下金属梁变形的影响机理。     

简支梁中截面挠度计算的一种简易方法

介绍了一种首先利用简支梁的对称性找出等价悬臂梁, 然后利用叠加法求出等效悬臂梁自由端的挠度, 从而得到一般载荷作用下简支梁中间截面挠度的方法.     

球头落锤冲击下金字塔点阵夹芯板结构的动态响应实验

为研究金字塔点阵夹芯板结构在球头落锤碰撞冲击下的抗冲击性能,采用模型实验的方法,加工制作了金字塔点阵4层夹芯板实验模型。通过实验得到了金字塔点阵夹芯板结构在碰撞冲击载荷作用下的坍塌变形过程和变形模式,揭示了点阵结构夹芯层的吸能机理。结果表明,在球头落锤的中等强度冲击载荷下,整个夹芯板结构的最终变形可划分为迎冲面、夹层和背冲面3个区域,形成类似“三明治”式的变形模式。     

泡沫金属夹芯梁在重复冲击下的动态响应

为了研究重复冲击载荷作用下泡沫金属夹芯梁的动态响应,采用Abaqus数值仿真软件,基于可压碎泡沫模型（crushable foam）,建立了泡沫金属夹芯梁遭受楔形质量块冲击的有限元模型。通过将仿真获得的夹芯梁上下面板最终挠度与重复冲击实验结果进行对比,验证仿真方法的准确性。在此基础之上,分析了泡沫金属夹芯梁在楔形质量块重复冲击作用下的变形模式、加卸载过程以及能量耗散特性。结果表明,在重复冲击载荷作用下,夹芯梁的变形不断累积,上面板主要出现局部凹陷和整体弯曲,而芯层则是局部压缩,下面板表现为整体弯曲。在重复加卸载过程中,加卸载刚度随着冲击次数的增加而增大。随着冲击次数的增加,上面板和芯层的能量吸收增量不断减小,而下面板的能量吸收增量不断增加,且最终均趋于稳定。泡沫金属夹芯梁的塑性变形能增量不断减小,而回弹系数随着冲击次数逐渐增加,最后趋于稳定值。     

用“膜力因子法”分析简支刚塑性圆板的大挠度动力响应

在板的变形过程中,当其挠度与厚度同量级时,膜力的作用与弯矩的作用同样重要;当其挠度超过厚度甚至接近板的面内尺寸的量级时,相对于弯矩的作用,膜力的作用是更主要的。本文发展了一种基于能量平衡的简便的“膜力因子法”,有效地解决了当板的挠度达到厚度量级时弯矩和膜力联合作用问题;用这种方法并结合塑性膜阶段的分析成功地求解了简支刚塑性圆板在冲击载荷作用下的大挠度塑性响应问题。所得结果与Florence实验结果符合良好,比已有理论近似结果有所改进。     

Analysis of the large deflection dynamic plastic response of simply-supported circular plates by the “membrane factor method

Based on energy equilibrium, a new procedure called the Membrane Factor Method is developed to analyze the dynamic plastic response of plates with deflections in the range where both bending moments and membrane forces are important. The final deflection of a simply-supported circular rigid-plastic plate loaded by a uniformly distributed impulse is obtained. In comparison with other approximate solutions, the present results are found to be simpler and in better agreement with the corresponding experimental values reoorded by Florence. The project supported by a fund from the National Educational Committee.     

Experiments on viscoplastic response of circular plates to impulsive loading

Tests are described of circular plates of mild steel and commercially pure titanium loaded impulsively by means of explosive sheet. Three loading geometries were used, with magnitudes such that final deflections in the range from one to about seven plate thicknesses were produced. Clamping against radial as well as transverse deflections at the edge was provided. Both materials exhibit strong plastic rate sensitivity. Parameters describing this behavior were obtained from stress-strain tests at low to intermediate rates together with published data for high strain rates. The measured final deflections and response times are compared with predictions of the mode approximation technique as extended to large deflections of viscoplastic structures.     

An Improved Upper Bound to Maximum Deflections of Elastic-Plastic Structures at Shakedown

ABSTRACT

A method is presented providing an upper bound to the maximum shakedown deflections for elastic-perfectly plastic structures. The influence of plastic zones is taken into account. Residual stresses required by the Melan theorem can be expressed in terms of stresses due to ideal plastic hinges and of stresses due to the finite extent of plastic zones. Making use of this fact a bound on the total energy dissipated in a shakedown process as well as a bound to the permanent displacement have been derived. This bound permits an estimate of the deflections at shakedown. Application of the method is illustrated by means of two examples.     

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。     

Response of circular clamped plates to square-wave stress pulses

An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular stress pulses over a small circular region. The stress pulses were transmitted to the plates through a 1/2-in.-diam shock bar and the strain-time responses of the plates were measured. The stress-wave interactions between the bar and the plates were measured for a number of thicknesses and the effect of the applied stress on the extent of the plastic deformation was determined. It was found that the elastic response was accurately predicted by the theory of Sneddon and the plastic response behaved according to a simple modification of this theory. The interaction between the stress pulse and plates of various thickness was theoretically predicted and found to be in excellent agreement with experimental measurements. The final plate deflections were theoretically predicted using a rigid viscoplastic theory and was in substantial agreement with the data. From this theory, the data were analyzed to determine the visco-plastic constant or relaxation time of the material. It is proposed that this testing arrangement is a suitable and convenient method for determining dynamic yield properties under biaxial-loading conditions.     

Large Deflection of a Circular Plate on Elastic Foundation under Symmetrical Load

ABSTRACT

The large deflection of a clamped circular plate on elastic foundation under nonuniform but symmetrical loads has been investigated following Berger's approximate method. The deflections are obtained in the form of an infinite series involving Bessel functions. Graphs are plotted for deflections, bending moments, and bending stresses for various values of foundation modulus and load functions.     

大挠度弯曲直梁混合变量最小势能原理的应用

应用大挠度弯曲直梁混合变量最小势能原理,求解均载两端固定大挠度柱面弯曲板条的轴向挠度分布和轴向弯矩分布．实例计算表明:该方法简单实用、精度高,是一种计算大挠度柱面弯曲板条变形的有效方法．     

Bending of simply-supported circular timber beam strengthened with fiber reinforced polymer简

The bending behavior of the circular cross-section timber beam strengthened with a fiber reinforced polymer (FRP) sheet is investigated. The tight bonding is on the interface between the surface of a timber beam and the reinforcement layer of the FRP sheet. An analytical expression for the bending moment-curvature relation is presented, and its failure modes are analyzed. The governing equation for nonlinear small deflection of the FRP-strengthened circular timber beam is established, and the corresponding numerical method is given. The bending deformation of the simply-supported circular timber beam strengthened with the carbon fiber reinforced polymer (CFRP) sheet subject to a uniform load is studied numerically. The influence of the angle and thickness of the CFRP layer as well as the timber strength on the bending deflection of the FRP-strengthened circular timber beam is examined. It is revealed that, with the increases of the thickness and angle, the deflection of the CFRP-strengthened circular timber beam is decreased, and its carrying capacity and ductility are increased. However, when the angle of the layer reaches a certain value, the deflection will no longer decrease with the increase of the angle. At the same time, the nonlinear bending moment-curvature relation of the CFRP-strengthened circular timber beam is simplified as an approximate bilinear constitutive model. The approximate deflections of the simply-supported circular timber beam strengthened with the CFRP sheet are obtained. The results are compared with the linearly elastic bending and nonlinear bending models, showing that the mid-span deflections of a CFRP-strengthened circular timber beam with the approximate bilinear constitutive model are greater than those with the nonlinear constitutive model. The results of its stiffness analysis are on the safe side.     

Lee's extremum principle and the large deflection response of dynamically loaded plastic structures

An approximate method based on Lee's extremum principle is introduced to study the large deflections of dynamically loaded plastic structures. As an example, the evolutionary mode of an impulsively loaded rigid-perfectly plastic portal frame is determined and then compared with the experimental results [8] and with the large deflection complete solution obtained previously [9]. It is found that the evolutionary modal solution may approach the complete solution if the modes are appropriately chosen.