钢筋混凝土框架结构破坏性能的离散单元法模拟

离散单元法是模拟结构破坏的一种有效的分析方法。通过引入节点单元和考虑混凝土的非线性对矩形离散单元模型进行了改进,并给出了改进后离散单元模型的破坏准则和基本方程以及弹簧系数等计算参数的确定;改进后的模型采用了双链表技术,提高了模型的计算效率。对在爆炸荷载作用下的钢筋混凝土框架结构的倒塌破坏过程进行了模拟,结果表明:采用改进后的离散单元法可以有效地模拟钢筋混凝土框架结构的倒塌破坏过程。     

瞬动态问题有限元网格单元修正的自适应分析

本文基于一种先进的非结构化网格生成系统和对于有限元离散误差的分析，将网格单元修正的自适应分析方法应用于二维瞬动态问题的研究，由于有限元近似求解的精度很大程度取决于所离散的网格质量，并且动态问题的数值解在不同时段变化较大以及由于波动求解中半离散化方法所引入的离散化的弥散现象，而网格单元修正的自适应分析方法能够在不同时段形成最佳网格来进行计算，使有限元分析的可靠性和近似程度得到提高；文中对地下圆形隧道     

混凝土材料与结构破坏过程模拟分析

采用离散单元法对混凝土材料和混凝土结构破坏机理进行分析。在细观尺度上将混凝土材料视为由粗骨料、水泥砂浆及界面过渡区三相组成,建立了混凝土材料的离散元模型;在宏观尺度上将混凝土视为均质材料建立了混凝土结构离散单元模型。计算分析结果表明:细观尺度上的二维离散单元模型可以用来很好地模拟混凝土材料的单轴受力破坏过程,但不能很好地模拟复合受力状态下的混凝土材料的破坏;宏观尺度上的离散单元模型可以很好地模拟钢筋混凝土构件的破坏过程,但模拟结果对单元的形状有较大的依赖性;宏观尺度上的离散单元模型可以很好地模拟结构的倒塌过程,但计算效率有待提高。     

聚合物注塑内应力和翘曲变形的数值模拟

由聚合物粘弹性理论和注塑成型原理出发,考虑了聚合物玻璃态的非线性粘弹性响应,采用新的四元件粘弹性力学模型模拟计算注塑制品冷却过程中内应力的形成与发展。在此基础上,采用改进的Allman膜单元[1]和离散Kirchhoff板单元[2]组合生成的板壳单元,模拟计算注塑件的翘曲变形,计算结果与实验结果一致,计算精度有所提高。     

二节点曲线索单元非线性分析

本文提出了二节点曲线索单元,对拉索结构进行非线性分析。这种单元不仅能模拟大跨度索元的初始形态,而且能克服目前广泛使用的二节点直线杆单元精度不高,多节点曲线索单元自由度大,内插点坐标难以确定等缺点。文中采用修正的Lagrangian坐标描述法,由卡氏第一定理推导并得出了刚度矩阵的显示表达式,编制了相应的程序,并对若干算例进行了计算与比较,分析结果表明此单元模型有较好的精度,能适用于塔桅结构、张拉结构等大跨结构形式的非线性分析。     

文丘里粉体喷射器内部颗粒运动特性的联合仿真

采用计算流体力学-离散单元法(CFD-DEM)耦合方法,对文丘里粉体喷射器内部5种不同粒径球形颗粒组成的颗粒群的气力输送过程进行数值模拟;分析颗粒的运动轨迹,发现部分颗粒在吸收室的底部聚集,颗粒在文丘里喷射器内部的运动集中分布在输送管道的中下部位,小尺寸颗粒速度较快,颗粒尺寸越大,颗粒与颗粒碰撞次数越多,颗粒与壁面碰撞次数越少;采用离散单元法-有限单元分析(DEM-FEA)耦合方法对颗粒与壁面碰撞引起的壁面应力变化进行分析。结果表明,喷射器在喷嘴出口处附近和吸收室底部出现应力峰值。     

车身结构分析中的三节点七自由度梁单元

为了高精度计算公共客车骨架结构的应力以及外膜皮对套车结构的影响,本文提出了一种新的空问梁单元。这种单元共有三个节点点,每个节点除常用的六个自由度外,还增加了一个翘曲扭转位移自由度以考虑梁截面的翘曲效应。该梁单元与八节点空间膛单元配合,可以提高梁、膛、板组合结构的计算精度。本文还给了一个实际的算例,部分计算值和实测值的比较证明该梁单元的工作性能是很好的。     

烟囱定向爆破仿真模拟

介绍了离散单元法的计算模型以及阻尼、时步等关键参数的选择原则，对烟囱定向爆破进行了仿真模拟，并与工程实际进行了比较。     

三维弹性体移动接触边界元法的一类新方案

基于对二维弹性体移动和滚动接触边界元法的前期研究,将其中的协调离散方案推广到三维问题,提出了针对给定移动方向的三维弹性体移动接触的一种边界元协调离散方案。其中在接触面上的位移和面力都能在边界元离散意义下精确满足,因此能保持边界元法在位移计算、特别是应力计算中高精度的优势。该方案将可能接触区分成大小相等的直角三角形单元,每个直角三角形单元有6个节点,其中3个角节点是固定节点,另外在每条边上有一可动节点。可动节点的位置确定于与其接触的另一面上对应单元的固定节点及其连线的位置。在每一瞬时,每个单元可由可动节点连线分成4个三角形子单元,在每个子单元上边界位移与面力线性分布。文中给出了一些算例来验证所提出算法的有效性和高精度。     

薄板弯曲分析的多边形流形单元

一般的数值流形方法均采用三角形、四边形单元进行计算。对于工程中的有些实际问题, 多边形单元能更好的适应复杂计算域形状。为此, 研究了采用多边形流形单元进行数值计算的方法。采用任意几何区域的Delaunay三角网格构造出新的凸多边形网格, 并以此单元作为计算的流形单元。采用改进的Wachspress插值函数作为多边形流形单元的权函数。为说明该方法的有效性, 将该流形方法应用于薄板弯曲计算, 推导出用于薄板弯曲分析的流形格式和单元矩阵。计算结果表明:较一般有限元法, 计算精度和收敛速度有很大提高。     

Refined triangular discrete Kirchhoff plate element for thin plate bending,vibration and buckling analysis

A refined triangular discrete Kirchhoff thin plate bending element RDKT which can be used to improve the original triangular discrete Kirchhoff thin plate bending element DKT is presented. In order to improve the accuracy of the analysis a simple explicit expression of a refined constant strain matrix with an adjustable constant can be introduced into its formulation. The new element displacement function can be used to formulate a mass matrix called combined mass matrix for calculation of the natural frequency and in the same way a combined geometric stiffness matrix can be obtained for buckling analysis. Numerical examples are presented to show that the present methods indeed, can improve the accuracy of thin plate bending, vibration and buckling analysis. © 1998 John Wiley & Sons, Ltd.     

Refined 15‐DOF triangular discrete degenerated shell element with high performances

A refined discrete degenerated 15‐DOF triangular shell element RDTS15 with high performances is proposed. For constructing the element displacement function, the exact displacement function of the Timoshenko's beam is used as the displacement on the element boundary, and the re‐constitute method for shear strain matrix is adopted. The proposed element can be used in the analysis of both moderate thick and thin plates/shells. Numerical examples presented show that the new model indeed possesses higher accuracy in the analysis of thin and thick plates/shells, and that it can pass the patch test required for the Kirchhoff thin plate elements, and also passed the inf–sup test for free cylindrical shell problems and satisfied both the bending‐ and membrane‐dominated test. Copyright © 2004 John Wiley Sons, Ltd.     

A FLAT TRIANGULAR SHELL ELEMENT WITH LOOF NODES

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiencies are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal configuration of the element is similar to the SemiLoof element, and the formulation is an improvement of a previous formulation. The element is used for both linear statics, linear buckling and geometrical non-linear analysis, and numerical examples are presented to show the robustness, accuracy and quick convergence of the element.     

A fast multipole boundary element method for solving the thin plate bending problem

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex notation of the kernel functions, expansions and translations in the fast multipole BEM are presented. Finally, a few numerical examples are presented to show the accuracy and efficiency of the fast multipole BEM in solving thin plate bending problems. The bending rigidity of a perforated plate is evaluated using the developed code. It is shown that the fast multipole BEM can be applied to solve plate bending problems with good accuracy. Possible improvements in the efficiency of the method are discussed.     

Refined discrete quadrilateral degenerated shell element by using Timoshenko's beam function

A refined discrete degenerated 20‐DOF quadrilateral shell element RQS20 is proposed. The exact displacement function of the Timoshenko's beam is used as the displacement on the element boundary. The re‐constitute method for shear strain matrix is adopted. The proposed element can be used for the analysis of both moderately thick and thin plates/shells, and the convergence for the very thin case can be ensured theoretically. Numerical examples presented show that the new model indeed possesses higher accuracy in the analysis of thin and thick plates/shells, and that it can pass the patch test required for the Kirchhoff thin plate elements. Most important of all, it is free from the membrane and shear locking phenomena for extremely thin plates/shells, on the one hand, and it can also avoid the phenomenon of oscillatory solutions for thick plates/shells case on the other. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

New finite element model for analysis of Kirchhoff plate

A new kind of approach to formulate an isotropic thin plate bending element is presented. The strain energy of the element is decomposed into two parts: an integral concerning the first strain invariant and a line integral around the elemental boundary. The former can be discretized by quasi-conforming technique¹ and the latter can be directly calculated using the interpolation of the deflection and its normal slope along the element boundary. By this method, an assumed first strain invariant quadrilateral element (AFSIQ) is derived. The procedure of formulating the element and the numerical examples show that the new kind of element not only simplifies the formulation considerably but also has excellent accuracy.     

Corotational non‐linear analysis of thin plates and shells using a new shell element

A new three‐node triangular shell element is developed by combining the optimal membrane element and discrete Kirchhoff triangle (DKT) plate bending element, and is modified for laminated composite plates and shells so as to include the membrane‐bending coupling effect. Using appropriate shape functions for the bending and membrane modes of the element, the ‘inconsistent’ stress stiffness matrix is formulated and the tangent stiffness matrix is determined. Non‐linear analysis of thin‐walled structures with geometric non‐linearity is conducted using the corotational method. The new element is thoroughly tested by solving few popular benchmark problems. The results of the analysis are compared with those obtained using existing membrane elements. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed plate bending elements based on least‐squares formulation

A finite element formulation for the bending of thin and thick plates based on least‐squares variational principles is presented. Finite element models for both the classical plate theory and the first‐order shear deformation plate theory (also known as the Kirchhoff and Mindlin plate theories, respectively) are considered. High‐order nodal expansions are used to construct the discrete finite element model based on the least‐squares formulation. Exponentially fast decay of the least‐squares functional, which is constructed using the L₂ norms of the equations residuals, is verified for increasing order of the nodal expansions. Numerical examples for the bending of circular, rectangular and skew plates with various boundary conditions and plate thickness are presented to demonstrate the predictive capability and robustness of the new plate bending elements. Plate bending elements based on this formulation are shown to be insensitive to both shear‐locking and geometric distortions. Copyright © 2004 John Wiley & Sons, Ltd.     

Refined nine-parameter triangular thin plate bending element by using refined direct stiffness method

Based on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non-conforming elements is proposed. The formulation is similar to that of the direct stiffness method (DSM), but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured. The well-known BCIZ nine-parameter triangular thin plate bending element is refined by the RDSM to yield a new nine-parameter thin plate bending element RT₉. Numerical examples are presented to show that the present model passes the patch test and possesses high accuracy.