弹侵彻混凝土靶的法向膨胀理论

基于描述材料在高速高压冲击下的动态行为的方程,建立了相应的冲击波前为一般曲面的方程．通过分析,针对混凝土材料,提出了可给出弹体减速度时间历程解析解的法向膨胀理论．它不仅适用于球形弹头和柱形弹头,也适用于其他类型的弹头,如锥形弹头和卵形弹头等;它不但适用于垂直侵彻,也适用于斜侵彻．     

着角与攻角联合作用下薄芳纶层合板抗平头弹侵彻性能

为探究着角和攻角对薄芳纶层合板抗平头弹侵彻性能的影响,建立了三维有限元仿真模型,对4 mm厚芳纶层合板在着角单独作用下以及着/攻角联合作用下的弹道行为进行了计算.通过弹丸的剩余速度、靶板的极限弹道速度及穿孔能量阈值反映了芳纶层合板的抗侵彻性能,分析了其在不同工况下的变形与破坏机理.结果表明：薄芳纶层合板的弹道极限速度随初始着角的增加先减小后增大;随着入射速度的增大和初始着角的减小,着角改变量和攻角改变量均有减小的趋势;对于固定的着角,负攻角不利于子弹侵彻,正攻角有利于侵彻.     

弹着点对钢筋混凝土侵彻深度的影响北大核心CSCD

在弹体侵彻钢筋混凝土研究领域,侵彻深度的离散性普遍存在于试验和经验公式中,弹着点位置的不同是造成此离散性的主要原因之一.为探究由弹着点位置造成的侵彻深度离散性并揭示其机理,参照公开发表的侵彻试验,建立了三种典型弹着点位置的有限元模型,对比分析出了三种典型弹着点位置侵彻过程差异的主要原因,依据数值计算结果归纳了表征侵彻深度离散性的表达式,提出了弹体侵彻钢筋混凝土侵彻深度是一个范围值的基本思想,并对表达式进行了初步验证.结果表明,造成侵彻深度离散性的主要因素是弹体撞击钢筋的数目和弹体接触钢筋的持续时间,此离散性随着弹径与钢筋网眼尺寸比值的增大而减小.     

有限变形下的混凝土动态本构关系研究

讨论有限变形和小变形假设下本构关系的区别,并将其运用于混凝土的弹-粘塑性本构关系研究,提出了一个应变率相关的动态力学模型．模型基于Ottosen的4参数屈服准则,分别考虑混凝土在硬化阶段和软化阶段加载面的不同变化规律,建立冲击荷载下的混凝土本构关系．该模型可以应用于冲击载荷下混凝土材料响应的模拟．引进Green-Naghdi客观率建立有限变形的混凝土模型．根据大量实验结果对应变率和材料强度的关系提出合理假设,使模型可以反映混凝土大变形的动态力学行为,为相关工程问题的研究提供有益的思路和有效的工具．     

几个与Ros等周亏格相关的逆Bonnesen型不等式

研究了平面卵形区域的Ros等周亏格问题,利用R~2中卵形区域的Ros定理及其加强形式,著名的等周不等式,给出R~2中卵形区域与Ros等周亏格相关的几个逆Bonnesen型不等式.     

混凝土轴拉加卸载随机损伤模型的建立与试验验证

为了分析及深入探讨混凝土在受拉加载及卸载情况下的力学特性,基于随机损伤本构关系提出了一种混凝土轴拉加卸载模型,推导出了混凝土加卸载的应力 应变关系表达式.为了印证理论表达式,进行了混凝土轴向拉伸及加卸载的试验研究,测得了混凝土的材料参数及其相应的轴拉加卸载应力-应变曲线.结合模型的计算结果,对混凝土的轴拉加卸载试验结果进行了对比分析,结果表明:混凝土轴拉加卸载模型能够预测混凝土的极限强度,同时能描述混凝土的强度软化、加载过程中的弹模折减及卸载后的塑性变形.     

关于n型卵形线

敲(,,尸)是卵形技C上一默的切校拯坐镖,而川,)是它的曲举年视t11,那磨风甲)的富里埃保数是一专关”,(,)一专厂”,(,)co吕左砂d砂,(几=l,2.二sin介甲d甲. 当龄任何卵形技恒有a,=O,b:二0. 若a,=a。二··二a二二o;bZ二b3=··一b。二。而心 1,b叶:中至少有一不焉o,科疽检卵形袋焉牲型卵形技. 野粉n型卵形援,虞介藩田蹬明了它至少有2n 2佃填默.GanaPatbi!3]特别研究赏n二2待的卵形技(殊氏卵形技),蹬明了疽踵卵形接至少有三徊外切正方形.是咽事臂使吴德篡{4j注意到了圃粉n型卵形筱的外切正方形的侗数尚题,在他的输文中解决了常n二2(Zm l)特的…     

正则卵形线的一些性质

本文建立正则卵形线的弦切角与曲率关系,利用此关系以研究弧上曲率的变化是比较方便的,由此不仅简单的得到S. B. Jackson之结果(系2)及W. C. Graustein之曲线之性质(系3);而且得到下列正则卵形线之性质: 定理1.一正则卵形弧具有顶点之充份及必要条件是有一圆存在,此圆与弧至少相切于二点,若此卵形弧有一段弧是圆弧的话,则此二切点不同在此圆弧上。定理2.设A_1,A_2,…,A_(2n)依次为一正则卵形线之顶点。A_1,A_3,…,A_(2n-1)之曲率为极小;A_2,A_4,…,A_(2n)之曲率为极大。顺次连结各顶点成一内接多角形,则     

R3中卯形闭曲面的等周亏格的上界的注记

利用R^3中卵形结果的高斯曲率不等式以及著名的等周不等式,将R^3中卵形闭曲面的高斯曲率K应用到空间曲面的等周亏格的上界估计中,得到了R^3中卵形闭曲面的等周亏格的一个新的上界,并给出其简单证明．     

关于平面卵形区域的等周亏格上界的几点注记

利用平面卵形区域的Ros'定理及其加强形式,给出平面R²中卵形区域的等周亏格的几个上界估计.     

Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile

This paper demonstrates the application of both numerical simulation and empirical equation in predicting the penetration of a concrete target by an ogive-nosed projectile. The results from the experiment performed by Gran and Frew [In-target radial stress measurements from penetration experiments into concrete by ogive-nose steel projectiles, Int. J. Impact Eng. 19 (8) (1997) 715–726] are used as a benchmark for comparison. In the numerical simulations a 3.0-caliber radius-head steel ogival-nose projectile with a mass of 2.3 kg is fired against cylindrical concrete target with a striking velocity of 315 m/s. The simulation, performed using AUTODYN 2-D, assesses three numerical schemes, namely Langrange, Euler–Lagrange coupling and smooth particles hydrodynamics SPH–Lagrange coupling, in predicting the maximum depth of penetration and the radial stress–time response of the concrete target. When assessing the three solution techniques we hypothesize that the effect of strain rate on strength for the concrete target does not adversely affect the prediction on the maximum depth of penetration and the radial stress–time response of the concrete target. In the empirical approach the penetration equation developed by Forrestal et al. [An empirical equation for penetration depth of ogive-nose projectiles into concrete targets, Int. J. Impact Eng. 15 (4) (1994) 395–405] is used to determine the maximum depth of penetration and the deceleration–time response. The deceleration–time response for the projectile using the empirical approach is compared with those obtained from the numerical simulations. Results from both the numerical and empirical approaches are consistent. The calculated depth of penetration from both approaches yield relatively good agreement with that obtained from the experiment. The numerical simulations using each of the three numerical schemes are also able to reproduce the profiles from the radial stress measurements. Simulations using the SPH numerical scheme give the best overall agreement. The good overall agreement with the experimental radial stress measurements and consistent results between both empirical and numerical approach, enhanced the confidence in engineers and ballisticians when using these two approaches in complementing full-scale testing.     

陶瓷/金属复合靶板受可变形弹体撞击的理论分析模型

针对弹体撞击陶瓷/金属复合靶板的问题,将弹体的变形、陶瓷面板的碎裂和金属背板的变形结合起来,建立了新的可变形弹体垂直撞击陶瓷/金属靶板的理论分析模型．模型中计入了弹体刚性区长度和运动速度、塑性变形区长度、横截面积和运动速度的变化以及弹体对靶板的侵入速度和深度;对陶瓷面板考虑了陶瓷锥体积和抗压强度的变化;对金属背板的变形,根据其塑性变形功、外力功及其动能守恒原理,得到金属背板的运动方程．最后对具体算例进行了分析,得到了各物理量随时间的变化,给出了一些有价值的规律．结果表明,模型能较好地描述撞击过程中的有关规律;与实验结果和数值模拟结果进行对比,吻合较好,说明了模型的有效性．     

Projectile motion with Mathematica

This note describes how to use the computer algebra system (CAS) Mathematica to analyse projectile motion with and without air resistance. For a projectile fired from ground level with an initial velocity ν ft/s at an angle θ degrees from the horizontal (0 < θ < 90°), it is well known that in the absence of air resistance, the projectile follows a parabolic path. However, this is not true if air resistance is taken into account. In the presence of air resistance, the equations of motion become complicated, thus making traditional handcalculation methods quite ineffective, and a powerful CAS such as Mathematica becomes an invaluable tool to better understand projectile motion. The note discusses how Mathematica can be used to create simulated experiments of projectiles with and without air resistance. These experiments result in several conjectures, leading to theorems.     

长杆弹高速斜穿甲工程计算公式

本文提出了一个实用的高速斜穿甲公式.它是根据本文提出的高速碰撞时应以应力冲量.而不是以应力本身作为破坏参数而导出的.所得公式与大量已有试验数据相符得很好.     

Reply to “Comments on “Model for cover cracking due to corrosion expansion and uniform stresses at infinity””

Corrosion of rebar in concrete under service conditions is a dynamic, continuous and interaction process between rebar, corrosion products and concrete. Both the penetration depth and the rate of penetration are functions of time.     

Well-posedness of a moving-boundary problem with two moving reaction strips

We deal with a one-dimensional coupled system of semi-linear reaction-diffusion equations in two a priori unknown moving phases driven by a non-local kinetic condition. The PDEs system models the penetration of gaseous carbon dioxide in unsaturated porous materials (like concrete). The main issue is that the strong competition between carbon dioxide diffusion and the fast reaction of carbon dioxide with calcium hydroxide–which are the main active reactants–leads to a sudden drop in the alkalinity of concrete near the steel reinforcement. This process–called concrete carbonation–facilitates chemical corrosion and drastically influences the lifetime of the material. We present details of a class of moving-boundary models with kinetic condition at the moving boundary and address the local existence, uniqueness and stability of positive weak solutions. We also point out our concept of global solvability. The application of such moving-boundary systems to the prediction of carbonation penetration into ordinary concrete samples is illustrated numerically.     

一类发烟装液弹装填率的数学模型

装液弹的装填率对弹的安全可靠性极其重要 .如果装液弹的装填率不合理 ,不是造成弹腔容积的浪费 ,就会造成弹内压过大 ,易于破坏密封性能引起渗漏甚至破裂而造成损失和危险 .本文通过对一类发烟装液炮弹弹内压力分析 ,得出了弹内压力计算公式 .在分析压力诸因素时 ,我们运用了固体热膨胀理论 ;考虑了液体的压缩性 .这是本文区别于以往压力计算的两个特点 .通过这类发烟装液炮弹内压压力曲线的分析 ,导出了装液 (炮 )弹弹腔空隙率合理选定最后的数学模型 (PLT方程——可由此确定合理的装填率 ) ,由此所计算的空隙率数据与国外文献值相符 ,并引入了“预极限温度”的概念 .可以相信 ,所谓“预极限温度”,将是装液 (炮 )弹 (或任何装液容器 )设计者必须认真考虑的问题     

Analysis of projectile motion in view of fractional calculus

The projectile motion is examined by means of the fractional calculus. The fractional differential equations of the projectile motion are introduced by generalizing Newton’s second law and Caputo’s fractional derivative is considered to use the physical initial conditions. In the absence of air resistance it is found that at certain conditions, the range and the maximum height of the projectile obtained by using the fractional calculus give the same results of the classical calculus. It is also found that, unlike the classical projectile motion, the launching angle that maximizes the horizontal range is a function of the arbitrary order of the fractional derivative α. Moreover, in a resistant medium, the parametric equations are expressed in terms of Mittag-Leffler function and the results agree with those of the classical projectile as α → 2. Moreover, the trajectories of the projectile are discussed in graphs and compared with those of the classical calculus. In order to explore the validity of modelling the projectile motion by the fractional approach, we compared our results with the experimental data of mortar.