钢筋混凝土梁冲击试验数值模拟研究

摘要: 采用弹塑性损伤帽盖模型对筋混凝土梁冲击试验进行了数值模拟,数值模拟得到的碰撞力、梁体跨中挠度以及梁体破坏状况与实验情况吻合较好。在此基础上讨论了混凝土材料应变软化段、描述塑性体积的帽盖面、强度准则子午线形状、偏平面形状以及钢筋混凝土结构建模方式对冲击数值模拟的影响。     

On the central difference algorithm in discrete element modelling of impact

The paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach. It is revealed that the algorithm exhibits some different behaviour due to the inherent non‐linearity/discontinuity of the impact system. Particularly, for an elastic or slightly inelastic impact, the stable/unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion, and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability. Copyright © 2005 John Wiley & Sons, Ltd.     

Computation of the stress intensity factors of sharp notched plates by the fractal‐like finite element method

The fractal‐like finite element method (FFEM) is an accurate and efficient method to compute the stress intensity factors (SIFs) of different crack configurations. In the FFEM, the cracked/notched body is divided into singular and regular regions; both regions are modelled using conventional finite elements. A self‐similar fractal mesh of an ‘infinite’ number of conventional finite elements is used to model the singular region. The corresponding large number of local variables in the singular region around the crack tip is transformed to a small set of global co‐ordinates after performing a global transformation by using global interpolation functions. In this paper, we extend this method to analyse the singularity problems of sharp notched plates. The exact stress and displacement fields of a plate with a notch of general angle are derived for plane‐stress/strain conditions. These exact analytical solutions which are eigenfunction expansion series are used to perform the global transformation and to determine the SIFs. The use of the global interpolation functions reduces the computational cost significantly and neither post‐processing technique to extract SIFs nor special singular elements to model the singular region are needed. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Combined single and smeared crack model in combined finite‐discrete element analysis

Large‐scale discrete element simulations, combined finite‐discrete element simulations as well as a whole range of related problems, involve a large number of separate bodies that interact with each other and in general deform and fracture. In this context there is a need for a robust fracture algorithm applicable to simultaneous multiple fracturing of large numbers of bodies. In this work a fracture model for both initiation and propagation of mode I loaded cracks in concrete in the context of the combined finite‐discrete element method is reported. The algorithm is based on accurate approximation of experimental stress–strain curves for concrete in tension. Copyright © 1999 John Wiley & Sons, Ltd.     

A least‐squares coupling method between a finite element code and a discrete element code

This paper presents a coupling method between a discrete element code CeaMka3D and a finite element code Sem. The coupling is based on a least‐squares method, which adds terms of forces to finite element code and imposes the velocity at coupling particles. For each coupling face, a small linear system with a constant matrix is solved. This method remains conservative in energy and shows good results in applications. Copyright © 2014 John Wiley & Sons, Ltd.     

Introduction of imperfections in the cubic mesh of the truss‐like discrete element method

In the present version of the truss‐like discrete element method (DEM), masses are considered lumped at nodal points and interconnected by means of unidimensional elements with arbitrary constitutive relations. In previous studies of non‐homogeneous concrete cubic samples subjected to nominally uniaxial tension, it was verified that numerical predictions of fracture using DEM models are feasible and yield results that are consistent with the experimental evidence so far available, including the prediction of size and strain rate effects. In the DEM formulation, material failure under compression is assumed to occur by indirect tension. In previous simulations, it was verified that the response is satisfactorily modelled up to the peak load, when a sudden collapse usually occurs, characteristic of fragile behaviour. On the other hand, experimental stress versus displacement curves observed in small specimens subjected to compression typically present a softening branch, in part due to sliding with friction of the fractured parts of the specimens. A second deficiency of DEM models with a perfectly cubic mesh is that the best correlations with experimental results are obtained with material parameters that differ in tension and compression. This paper examines another cause of the excessively fragile behaviour of DEM predictions of the response of concrete elements subjected to nominally uniaxial compression, which is due to the regularity of the perfect cubic mesh, unable to capture nonlinear stability effects in the material. It is shown herein that the introduction of small perturbations of the DEM regular mesh significantly improves the predicting capability of the model and in addition allows adopting a unique set of material properties, which are independent of the nature of the loading.     

An adaptive non‐conforming finite‐element method for Reissner–Mindlin plates

Adaptive algorithms are important tools for efficient finite‐element mesh design. In this paper, an error controlled adaptive mesh‐refining algorithm is proposed for a non‐conforming low‐order finite‐element method for the Reissner–Mindlin plate model. The algorithm is controlled by a reliable and efficient residual‐based a posteriori error estimate, which is robust with respect to the plate's thickness. Numerical evidence for this and the efficiency of the new algorithm is provided in the sense that non‐optimal convergence rates are optimally improved in our numerical experiments. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of the discrete element method (DEM) and of the experimental evidence on concrete behaviour under static 3D compression

The authors successfully employed the discrete element method (DEM) in numerical determinations of the response up to and beyond failure of reinforced concrete structures subjected to impact and impulsive loadings in which tensile fracture, which is reliably predicted by DEM models, often controls the dominant failure modes. However, in impact problems when penetration occurs, the reliability of the approach in predictions of the structural response of the 3D compression zone that develops at the tip of the projectile has not yet been explicitly confirmed. In this context, in view of its complexity, the performance of the method is herein assessed and compared with available experimental results in static tests. By means of numerical simulations, it was previously verified that DEM models do predict, but overestimate, the strength increase observed on concrete cubes subjected to static multiaxial compression in relation with the unconfined strength, for confining (lateral) pressures up to about 20% of the unconfined compressive stress. For higher confining stresses, however, the DEM formulation underestimates the compressive strength increase observed in cubic and cylindrical samples, for the reasons examined in the paper, in which limitations of both the numerical predictions and experimental observations are thoroughly discussed.     

近断层钢筋混凝土框架结构地震倒塌机制分析

由于近断层地震动的特殊性,近断层混凝土结构的损伤倒塌较一般地震动下更为严重,其损伤过程和倒塌机制也更为复杂。采用改进的拆除构件法,对抗倒塌分析中传统的拆除构件法进行了改进,并结合近断层地震动下混凝土框架结构的反应特征,建立了典型10层钢筋混凝土框架模型,通过设置12种拆除工况,选取3条简谐波和3条实际近断层地震记录作为结构输入,进行动力弹塑性时程分析,研究了钢筋混凝土框架在近断层地震作用下的倒塌机制。研究表明,底层框架柱损伤对结构倒塌模式的影响较大,中、上部楼层框架柱损伤对结构倒塌模式的影响较小;框架柱不对称损伤对所在楼层层间位移的影响大于对称损伤的影响,角柱损伤的影响大于边柱损伤和中柱损伤的影响;即使结构的损伤部位不同,但也可能具有相同的倒塌模式;采用与结构基本周期相接近的简谐波作用能够从总体上模拟结构的整体倒塌模式。     

Numerical simulation of reinforced concrete structures under impact loading

This study presents the performance of a combined finite‐discrete element method for prediction of the structural response of reinforced concrete beams under impact loading. A combination of finite and discrete element methods enables the modelling of the concrete and the reinforcement before the concrete cracking, as well as a discontinuous nature of the concrete caused by fracture and fragmentation under high impact loading. Discretization of the concrete with triangular finite elements is coupled with one‐dimensional reinforcing bars embedded inside the concrete finite elements. The cracking in the concrete activates the joint elements used to simulate the non‐linear behavior of both concrete and reinforcement. Numerical analysis based on experimental test data has been carried out to simulate the main features of the reinforced concrete beams impacted by free‐falling drop‐weights. A high level of accuracy was demonstrated in various comparisons between the experimental tests and the analysis results, including peak displacement, crack pattern, damage level and failure modes of reinforced concrete beams.     

基于荷载时程分析法的钢筋混凝土与钢板混凝土墙冲击响应对比分析

为对比核电站核岛厂房钢筋混凝土结构(RC)与钢板混凝土结构(SC)外墙的抗冲击性能,基于荷载时程分析法,用显示非线性动力分析软件ANSYS/LS-DYNA仿真分析1/7.5比例飞机模型撞击RC、SC墙的冲击实验。将RC、SC墙破坏模式、混凝土碎片残余速度及背部钢板变形等计算结果与飞射物-靶体相互作用分析法计算结果及实验结果以及同厚度不同结构类别墙的计算结果进行对比。结果表明,基于荷载时程分析法计算结果有一定保守性,与实验结果吻合较好,且SC墙抗冲击性能优于RC墙,尤其背部钢板能有效约束混凝土撞击方向的运动及限制混凝土碎片飞溅。用于抗飞机撞击的SC结构墙体厚度可适当减薄。     

Failure behaviors of reinforced concrete beams subjected to high impact loading

To attain a better understanding of the failure behavior of reinforced concrete (RC) beams under impact load, series of high speed impact experiments were performed using an instrumented drop-weight impact machine. The test program was successful in providing a substantial volume of test data including impact loads, mid-span deflections, crack profiles and strains. These data was analyzed, focusing on the impact load characteristics and the impact behaviors of RC beams. Various characteristic values and their relationships were investigated such as the drop height, the static flexural load-carrying capacity, the input impact energy and the beam response values. Two empirical formulas were proposed to estimate the maximum and residual deflection of the beam based on the static flexural load-carrying capacity and the input impact energy. The applicability of the proposed equations was confirmed by comparison with the experimental results obtained by other researchers.     

钢筋混凝土梁桥船舶撞击连续倒塌数值模拟

详细介绍了钢筋混凝土桥梁船撞倒塌模拟涉及的材料模型和单元失效指标等问题,建立某连续梁上部、下部结构、支座和船舶结构精细有限元模型,将弹塑性损伤帽盖模型用于混凝土,弹塑性随动强化模型用于钢筋,对船舶撞击钢筋混凝土连续梁引起的结构连续倒塌过程进行了数值模拟,揭示了连续梁桥结构的船撞倒塌机理。     

An improved discrete Kirchhoff quadrilateral element based on third‐order zigzag theory for static analysis of composite and sandwich plates

A new improved discrete Kirchhoff quadrilateral element based on the third‐order zigzag theory is developed for the static analysis of composite and sandwich plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid‐surface. The usual requirement of C¹ continuity of interpolation functions of the deflection in the third‐order zigzag theory is circumvented by employing the improved discrete Kirchhoff constraint technique. The element is free from the shear locking. The finite element formulation and the computer program are validated by comparing the results for simply supported plate with the analytical Navier solution of the zigzag theory. Comparison of the present results with those using other available elements based on zigzag theories for composite and sandwich plates establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The accuracy of the zigzag theory is assessed by comparing the finite element results of the square all‐round clamped composite plates with the converged three‐dimensional finite element solution obtained using ABAQUS. The comparisons also establish the superiority of the zigzag theory over the smeared third‐order theory having the same number of degrees of freedom. Copyright © 2006 John Wiley & Sons, Ltd.     

A computational model for failure analysis of fibre reinforced concrete with discrete treatment of fibres

Failure patterns and mechanical behaviour of high-performance fibre reinforced cementitious composites depend on the distribution of fibres within a specimen. In this contribution, we propose a novel computational approach to describe failure processes in fibre reinforced concrete. A discrete treatment of fibres enables us to study the influence of various fibre distributions on the mechanical properties of the material. To ensure numerical efficiency, fibres are not explicitly discretized but they are modelled by applying discrete forces to a background mesh. The background mesh represents the matrix while the discrete forces represent the interaction between fibres and matrix. These forces are assumed to be equal to fibre pull-out forces. With this approach experimental data or micro mechanical models, including detailed information about the fibre-matrix interface, can be directly incorporated into the model.     

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

Numerical study of the interfaces of 3D‐printed concrete using discrete element method

3D concrete printing is an additive manufacturing method which reduces the time and improves the efficiency of the construction process. Structural behavior of printed elements is strongly influenced by the properties of the material and the interface surfaces. The printing process creates interface surfaces between layers in the horizontal and vertical directions. The bond strength between layers is the most critical property of printed elements. In this paper, the structural behavior of printed elements is studied using the discrete element method. The material is modelled using discrete particles with bonding between them. A new discrete model of a multilayer geometry is presented to study the behavior of the interfaces of printed concrete. The layers are made up of randomly placed particles to simulate the heterogeneous nature of concrete. The numerical model is developed to simulate the flexural behavior of multilayer specimens. A four‐point flexural test is simulated considering the interface surfaces between layers. This numerical model provides relevant results to improve the behavior of this kind of structural elements. The aim of this work is to provide a discrete element model to predict the mechanical behavior of 3D concrete printed components.     

Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method

Free vibration characteristics of thick skew plates reinforced by functionally graded carbon nanotubes (CNTs) reinforced composite are presented. Discrete singular convolution (DSC) method is used for the numerical solution of vibration problems via geometric mapping technique. Using the geometric transformation via a four-node element, the straight-sided quadrilateral physical domain is mapped into a square domain in the computational space. Then the method of discrete singular convolution with some singular kernels such as Regularized Shannon's delta (RSD) and Lagrange's delta kernels (LDK) have been used for spatial discretizing of the resulting governing equation of motion. Calculated results have been presented in order to show the effects of volume fraction of CNT, skew angles, CNT distribution types, plate aspect ratio and length-to-thickness ratio on the frequency of CNT reinforced skew plate. The current results are compared with the related results available in the literature and obtained by different methods. It is shown that reasonable accurate results are obtained for free vibration of nanocomposite plates with less computational effort for higher modes. Several test examples for different plate have been selected to demonstrate the convergence properties, accuracy, and simplicity in numerical implementation of DSC procedures. This approach has verified the accuracy and applicability of DSC method to the class of problem considered in this study. Furthermore, in the numerical examples in the scope of the study, the results obtained with DSC method using a coarser grid are more accurate than the values obtained by finite elements and differential quadrature (DQ) methods. It is also revealed that the method of discrete singular convolution is a promising and potential approach for computational mechanics of nonrectangular plates with nanocomposite reinforced.     

Time reversibility of the discrete element method

An algorithm is presented for discrete element method simulations of energy-conserving systems of frictionless, spherical particles in a reversed-time frame. This algorithm is verified, within the limits of round-off error, through implementation in the LAMMPS code. Mechanisms for energy dissipation such as interparticle friction, damping, rotational resistance, particle crushing, or bond breakage cannot be incorporated into this algorithm without causing time irreversibility. This theoretical development is applied to critical-state soil mechanics as an exemplar. It is shown that the convergence of soil samples, which differ only in terms of their initial void ratio, to the same critical state requires the presence of shear forces and frictional dissipation within the soil system.