Finite difference analysis of simply supported RC slabs for blast loadings

A finite difference procedure that can account for strain-rate effects, both shear and flexural deformations, permits variations in cross-section geometry and strength and loading over the length of a component is proposed to accurately and efficiently analyze the dynamic response of a simply supported structural member under blast loads. A section-based layered analysis model that accommodates varying strain rates across a member’s cross-section is used to derive sectional moment–curvature relationships. A formula is derived to estimate the distribution of strain rate over the depth of a cross-section along the length of the member, and the corresponding strain rate effects are incorporated into the section-based layered analysis model. The Timoshenko beam equations that include both shear deformations and rotational inertia are solved numerically using an explicit finite difference scheme. The accuracy of the proposed finite difference analysis model is part validated using results of blast testing of reinforced concrete slabs with combinations of explosive weights and standoff distances. The results are also compared with those obtained by conventional single-degree-of-freedom (SDOF) analysis and finite element (FE) analysis using solid elements. The finite difference analysis procedure is both fast-running and accurate and most suitable for design office application, combining the speed of SDOF analysis and the detail and accuracy of FE analysis.     

Strain-rate dependency of the dynamic tensile strength of rock

Dynamic tension tests based on Hopkinson’s effect combined with the spalling phenomena were performed on Inada granite and Tage tuff to investigate the strain-rate dependency of the dynamic tensile strength of rock. The static tensile strengths were determined and compared with the dynamic tensile strengths. The fracture processes under various loading conditions were analyzed using a proposed finite element method to verify the differences between the dynamic and static tensile strengths and the strain-rate dependency. These analyses revealed that the differences were due to the stress concentrations and redistribution mechanisms in the rock. The rock inhomogeneity also contributed to the difference between the dynamic and static tensile strengths. An increase in the uniformity coefficient stimulated a reduction in the strain-rate dependency; i.e., the strain-rate dependency of the dynamic tensile strength was caused by the inhomogeneity of the rock. The fracture processes and principal stress fields in the specimens at high and low strain rates were analyzed to investigate fracture formations at various strain rates. Higher strain rates generated a large number of microcracks; the interaction of the microcracks interfered with the formation of the fracture plane. The observed dynamic tensile strength increase at a high strain rate was caused by crack arrests due to the generation of a large number of microcracks.     

Effects of microstructures on dynamic compression of Barre granite

The distribution and characteristics of microstructures (microcrack and grain) of Barre granite (BG) were investigated, and three orthogonal weak planes associated with the preferred orientations of microcracks were identified. It has been demonstrated that both the fracture toughness and the longitudinal wave speed depend on the direction of these weak planes. In this study, disk samples cut from one BG block are prepared for split Hopkinson pressure bar (SHPB) test. The axial directions of the samples are chosen to be parallel to the preferred direction of microcracks and the samples are grouped and denoted by Y (lowest P-wave velocity), Z (highest P-wave velocity), and X (intermediate P-wave velocity). Pulse-shaper technique is adopted to achieve equilibrium of dynamic stresses on both ends of the sample and constant strain rate during the dynamic loading. For samples within the same orientation group, the maximum stress achieved shows clear strain-rate sensitivity. The effect of microcracks on the dynamic compressive response of BG depends on the strain rate for a fixed loading duration (230 μs). For low strain-rate loading (70 s⁻¹) and high strain-rate loading (130 s⁻¹), the maximum dynamic stress achieved is not sensitive to the microcrack orientation; for intermediate strain rate (100 s⁻¹) loading, the maximum achieved stress for Y-samples is the largest. In addition, three dynamic compressive rock failure modes are identified: quasi-elastic, cracked, and fragmented. The correlation between the failure modes and the shape of the stress–strain curves is discussed.     

Behaviour of composite columns of closed cross-section under in-plane compressive pulse loading

In this work the dynamic stability analysis of composite columns of closed cross-section is performed. The columns are subject to pulse loading of finite duration. The influence of imperfection sensitivity, orthotropy level and lamination angle on the dynamic buckling load are investigated. The effect of material properties in elastic–plastic range is also studied. The numerical results obtained from FEM solution are presented in diagrams. The consequences of application of different dynamic stability criteria are discussed as well.     

Experimental and numerical analysis of the strain-rate effect on fully welded connections

This paper presents experimental and numerical results of dynamic cyclic tests carried out on two full-scale specimens of welded beam-to-column connections. In order to simulate the nonlinear dynamic behaviour of tested specimens, a fibre-based finite element beam is used to model beam and column members and a nonlinear rotational spring is also used to model welded connections. The effect of strain rate on beam and column behaviour is taken into account for each constitutive fibre using the Perzyna law. The effect of strain rate on welded connection is taken into account by extending the static Richard model to simulate its dynamic behaviour. The Krawinkler-Zoheri model, expressed as a function of normalized cumulative plastic strain, is introduced to quantify damage and degrading behaviour in terms of the strain-rate effect. The finite element Drain-2dx software is first upgraded for this purpose to carry out numerical investigations. The analytical results obtained from the numerical simulation, taking the strain rate effect and damage accumulation into account, predict well the structural dynamic behaviour up to failure of welded connections when compared with available experimental data.     

冻结黄土的单轴试验及其本构模型研究

冻土的强度及变形行为受加载速率及环境温度效应的影响。以冻结兰州黄土为对象,开展了一系列不同温度及加载速率下的常规单轴压缩、变速率压缩及加卸载蠕变回弹试验。基于常规单轴压缩试验结果,考虑了加载速率对变形行为的影响;通过变速率压缩试验,引入了一个与加载速率相关的率敏感性系数,构建一个新的考虑率效应的冻土强度关系式,解决了由试样离散性而对率效应试验研究带来的不利影响;运用加卸载蠕变回弹试验实现了对冻土变形中弹性、塑性变形的解耦,并获得了率无关弹性模量。以此为基础,在一定的温度、加载速率范围内建立了考虑率效应及温度效应的冻结黄土单轴唯像本构模型。通过试验验证,该模型能较好地模拟冻结黄土在不同温度和不同加载速率条件下的应力应变行为。     

考虑Cowper-Symonds黏塑性材料本构的向量式有限元三角形薄壳单元研究

薄壳结构的力学行为分析往往涉及显著的材料非线性效应,对爆炸、冲击等高速动力问题还需进一步考虑高应变率效应的影响。基于此,将可同时考虑应变硬化和应变率效应的Cowper-Symonds黏塑性材料本构模型（简称C-S模型）引入向量式有限元三角形薄壳单元,以实现金属薄壳结构的动力非线性分析。推导C-S模型的弹塑性增量分析步骤,并将其作为单独的计算分析模块引入薄壳结构的向量式有限元分析程序,适用于线弹性、理想弹塑性、双线性弹塑性和率相关C-S模型等4种材料模型条件下的薄壳结构分析。算例分析表明,所编制的向量式有限元程序可以有效实现非线性材料情况下薄壳结构的静、动力分析以及爆炸冲击作用下的非线性动力响应分析,验证了文中C-S模型理论推导和程序的正确、可靠。     

Dynamic behavior of a Mediterranean natural stone under tensile loading

Historical buildings are important structures commonly occurring in Mediterranean cities. The behavior of their constituent materials under high dynamic loads is fundamental to investigate the vulnerability of such structures under extreme dynamic events. The main aim of our investigation was to study the effect of high dynamic loading conditions on a classical porous natural stone from the Naples area, namely yellow tuff, used in hundreds of historical buildings and monuments in Naples and other Mediterranean cities. Hence, dynamic characterization was performed through high strain-rate failure tensile tests. A wide range of strain-rates was investigated, from 10^?5 s^?1 to 50 s^?1. The obtained data were processed to obtain stress–strain relationships at different strain-rate levels. The results reveal that Neapolitan yellow tuff presents a significantly strain-rate sensitive behavior, exhibiting dynamic tensile strength increasing with strain-rate, up to about three times that from quasi-static conditions in the case of very high strain-rates. Dynamic increase factors (DIFs) vs. strain-rate curves for tensile failure stress were also evaluated and discussed.     

爆炸荷载下钢筋混凝土简支板的有限差分分析

考虑应变率效应、剪切和弯曲变形、横断面几何尺寸、荷载情况,编制有限差分分析程序,精确有效地分析爆炸荷载下钢筋混凝土简支板的动力响应。与构件截面应变速率相适应,采用截面分层分析模型,建立截面矩与和曲率的关系。根据所提公式,将相应的应变率效应与截面分层分析模型相结合,沿构件长度方向,对构件纵向应变速率的分布进行评估。采用明确的有限差分方法,可得到包括剪切变形和转动变量的Timoshenko梁方程的数值解。结合爆炸量和距离,根据钢筋混凝土板爆炸试验的结果,验证所提有限差分分析模型的精确性。与传统的单自由度分析和有限元分析相比,有限差分分析程序快速、精确,结合了单自由度分析的速度和有限元分析精确的优势,十分适合于设计公司应用。     

实时温度下中细粒花岗岩动力响应与吸能特性试验研究

 基于改进的分离式霍普金森压杆,研究实时温度下中–细粒花岗岩的动力响应与吸能特性。结果表明：温度在20 ℃～500 ℃下,花岗岩全应力–应变曲线的弹性、塑性与应变软化3个阶段特征明显,700 ℃时的应力–应变曲线出现塑性屈服平台;应变率增加,岩石抗压强度增大,但随温度的升高应变率效应逐渐减弱;温度和应变率对岩石弹性模量的影响规律均不明显;应变率增加会使岩石单位体积的能量吸收能力提高,但不同温度下应变率对单位体积吸能的影响效果有较大差异;500 ℃及以下时峰值应变的应变率效应比较接近,但700 ℃时峰值应变的应变率敏感系数大幅增加;采用相同气压加载时,发现不同温度下应变率所处范围差异较大,而且气压对应变率的影响系数也不相同;500 ℃及以下,随应变率增加试样破坏形式从劈裂过渡到碎裂,700 ℃时试样则呈粉碎性破坏。     

加载速率对钢筋混凝土框架柱动态特性的影响

利用有限元软件ABAQUS,分别对钢筋混凝土框架柱在准静力和高应变率动态加载条件下的响应进行了数值模拟.探讨了加载速率对构件承载力、破坏形式的影响,并且对比了数值模拟结果和试验结果.通过比较高应变率与准静态加载下的分析结果,分析了应变率效应对钢筋混凝土柱的影响.研究结果表明,当考虑应变率效应时,钢筋混凝土柱的动态力学行...     

花岗岩在单轴冲击压缩荷载下的动态断裂分析

利用脉冲整形器改进后的分离式Hopkinson压杆(SHPB)系统,对新加坡Bukit Timah地区的花岗岩圆柱形试样进行了高应变率下的单轴压缩实验。实验结果发现:随着应变率的增加,不仅花岗岩材料的抗压强度增大,而且以轴向拉伸劈裂为主要破坏形式的破碎程度也有所提高,表现为碎块的尺寸减小和数量增加。针对上述花岗岩的动态特性,采用多裂纹相互作用的动态滑移型裂纹模型定量的分析了不同应变率下,材料的微裂纹的初始长度、角度、初始裂纹间距以及裂纹面的摩擦系数等微裂纹特征对材料动态强度及破碎的影响,将岩石类材料的宏观动力学特性与其细观微结构联系起来,合理地解释了花岗岩的动态强度及破碎程度的应变率相关性。     

Dynamic failure analysis on granite under uniaxial impact compressive load

High strain-rate uniaxial compressive loading tests were produced in the modified split Hopkinson pressure bar (SHPB) with pulse shaper on granite samples. It was shown that the failure of the granite cylinder was typical tensile splitting failure mode by sudden splitting parallel to the direction of uniaxial compressive loading at different strain rates. Besides, it was concluded that not only the strength of granite increased, but also the fragment size decreased and the fragment numbers increased with the increasing strain rate. To quantitatively analyze the failure phenomena, the numerical calculation based on a dynamic interacting sliding microcrack model was adopted to investigate the influence of microcrack with the different initial crack length, crack angle, crack space and friction coefficient on the macro-mechanical properties of granite under different strain rates. Accordingly, the strain-dependency of the compression strength and the fragmentation degree of granite was explained reasonably.     

砂岩黏性对抗拉强度加载率效应影响的试验研究

利用摆锤冲击加载SHPB试验装置,进行砂岩和人造岩心长杆冲击试验和动态巴西盘试验,测试砂岩和人造岩心的黏性系数,分析砂岩和人造岩心强度的加载率效应。利用试验和数值模拟相结合的方法得到绿砂岩、人造岩心A和B的黏性系数分别为100,10和5 k Pa·s。开展不同黏性岩石的动态巴西盘试验,测得砂岩和人造岩心试样的动态抗拉强度随着加载率的增大而增大,表现出一定的加载率相关性;证明了黏性对岩石强度加载率效应的影响,但两者并非正相关;在较小的加载速率下,岩石黏性导致试样中传播的应力波能量衰减,在巴西盘中心点起裂的裂纹沿加载直径方向扩展但是不足以使试样破坏成两半,从而验证了巴西盘裂纹起裂位置。     

Numerical simulation of Brazilian disk rock failure under static and dynamic loading

A numerical simulator based on RFPA (Rock Failure Process Analysis) is used to study the deformation and failure process of a Brazilian disk of heterogeneous rock when subjected to static and dynamic loading conditions. In this simulator, the heterogeneity of rock is considered by assuming that the material properties of elements conform to a Weibull distribution; an elastic damage-based law that considers the strain-rate dependency is used to describe the constitutive law at mesoscopic scale; and a finite element program is employed as a basic stress analysis tool. The simulator is firstly validated by simulating the dynamic spalling of a homogeneous rock bar and by comparing with the theoretical and experimental results. Then, the failure process of a Brazilian disk of rock subjected to static and dynamic loading is numerically simulated, and the numerical results are compared with the available experimental results. Particular attention is given to the typical failure patterns of the rock disk when the incident compressive stress waves with different amplitudes are applied. The numerical simulation also identifies the failure mechanisms of rock during dynamic failure processes that are closely related to the propagation of the stress wave.     

绢云母石英片岩和砂岩的SHPB试验研究

 利用液压伺服压力试验机和波形整形器改进后的? 100 mm分离式霍普金森压杆(SHPB)试验装置,研究绢云母石英片岩和砂岩在50～160 s－1应变率等级下的准静态力学性能及其在不同冲击压缩荷载作用下的波形曲线、动态抗压强度、比能量吸收以及破坏形态的应变率效应问题。试验结果表明,绢云母石英片岩和砂岩的动态抗压强度、比能量吸收以及破坏形态均表现出显著的应变率相关性,但弹性模量的应变率相关性较弱。综合绢云母石英片岩和砂岩动态力学性能的对比结果可知,砂岩比绢云母石英片岩对应变率的变化更敏感。从材料的微观结构特征和能量吸收的角度对岩石动态破坏过程进行分析,探寻岩石破坏的本质。研究成果可为其他类型的脆性材料动态力学性能的研究提供参考。     

Dynamic failure analysis on granite under uniaxial impact compressive load

High strain-rate uniaxial compressive loading tests were produced in the modified split Hopkinson pressure bar (SHPB) with pulse shaper on granite samples. It was shown that the failure of the granite cylinder was typical tensile splitting failuremode by sudden splitting parallel to the direction of uniaxial compressive loading at different strain rates. Besides, it was concluded that not only the strength of granite increased, but also the fragment size decreased and the fragment numbers increased with the increasing strain rate. To quantitatively analyze the failure phenomena, the numerical calculation based on a dynamic interacting sliding microcrack model was adopted to investigate the influence of microcrack with the different initial crack length, crack angle, crack space and friction coefficient on the macro-mechanical properties of granite under different strain rates. Accordingly, the strain-dependency of the compression strength and the fragmentation degree of granite was explained reasonably. __________ Translated from Chinese Journal of Geotechnical Engineering, 2007, 29(3): 385–390 [译自: 岩土工程学报]     

混凝士动态力学性能的试验研究

混凝土结构在爆炸与冲击载荷下的安全分析通常是结构的应力波效应和材料的应变率效应。而混凝土结构中的应力波传播特性实际上又依赖于混凝土在高应变率下率型本构关系。本文利用改装的杆径为74mm的直锥变截面式大尺寸Hopkinson压杆对混凝土材料进行冲击压缩实验,得到应变率约100s-1下的应力-应变全曲线及方程,得出混凝土具有敏感的应变率效应。     

加载速率对岩石动态断裂韧度影响的实验研究

为了获得岩石在高加载速率作用下的动态断裂韧度值并分析加载速率的影响,由分离式霍普金森压杆入射杆杆端附加劈尖及其基座对边切槽圆盘试样施加动态劈裂载荷。把应变片粘贴在裂纹尖端附近获得裂纹扩展时间;将劈裂载荷时间历程及裂纹扩展时间输入有限元计算模型,获得试样的起裂动态断裂韧度值。结果表明,在加载速率18.85×104MPa.m1/2s-1以下,大理岩的动态断裂韧度值随着加载速率的增大而上升,但上升趋势逐渐减弱。断裂韧度数值在高加载速率下呈现出明显的离散性。     

钢筋混凝土构件动力加载试验数据库

钢筋混凝土结构在地震作用下会产生应变率效应,受该效应影响,结构的抗震性能将产生变化。因此,在对钢筋混凝土结构进行抗震性能分析及设计时应考虑应变率效应的影响。对国内外已有研究的钢筋混凝土构件在不同加载速率下的相关试验进行力学模型等效和试验数据处理,分析了钢筋混凝土构件在不同加载速率下力学性能的一般变化趋势,并以此为基础建立了钢筋混凝土构件动力加载试验数据库,该数据库界面友好、检索方便,包含了钢筋混凝土梁、柱、节点和剪力墙构件的数据。