改进共旋坐标法的Timoshenko梁单元非线性分析

为提高空间Timoshenko梁单元非线性问题的计算精度,在共旋坐标法的基础上,提出了一种改进的Timoshenko梁单元几何非线性分析方法。利用虚功原理得到改进空间梁单元的刚度矩阵;使用有限质点法中的逆向运动思路计算单元局部坐标系下的刚体旋转矩阵;根据整体坐标系与局部坐标系之间旋转角度的转化以及微分关系,求得空间梁单元的切线刚度矩阵;编制了相应的有限元程序,对多个经典的大变形结构进行几何非线性分析。计算结果印证了该文所提出改进方法的正确性,同时与传统共旋坐标法相比,具有更高的精度。     

三维动态八结点有限单元的建立及理论推导

本文为扩大动态有限单元法的应用范围,在 J.S.Przemieniecki 和 K.K.Gupta 等人的研究基础上建立了一种新的三维动态八结点单元,并对其进行了理论推导。通过算例验证了本文理论结果的正确性。     

基于共旋法与稳定函数的几何非线性平面梁单元

建立一个准确、高效的几何非线性梁单元对于描述杆系结构的非线性行为至关重要。该文基于共旋坐标法和稳定函数提出了一种几何非线性平面梁单元。该单元在形成中把变形和刚体位移分开,局部坐标系内采用稳定函数以考虑单元P-δ效应的影响,从局部坐标系到结构坐标系的转换则采用共旋坐标法以及微分以考虑几何非线性,给出了几何非线性平面梁单元在结构坐标系下的全量平衡方程和切线刚度矩阵;在此基础上根据带铰梁端弯矩为零的受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式。通过多个典型算例验证了算法与程序的正确性、计算精度和效率。     

计算圆筒动态应力强度因子的有限元方法与叠加积分方法

本文计算了厚壁筒的动态应力强度因子，研究了有限单元法计算动态应力强度因子的几个主要问题，提供了合理计算方案，本文还提供了计算厚壁筒动态应力强度因子的叠加积分法，方便于各种动态内压下的动态应力强度因子的计算。     

基于动态黏结滑移性能的钢筋混凝土分离式模型研究

基于钢筋混凝土黏结滑移机理,搭建能够描述循环荷载作用下钢筋混凝土之间黏结性能变化过程的动态黏结-滑移本构关系,并结合单弹簧联结单元法建立钢筋混凝土分离式模型.模型避免了人为选择法向刚度困难的问题,并通过局部坐标系求解钢筋单元解决工程配筋布置问题,保证了复杂受力条件下的计算精度与计算效率.结合混凝土损伤模型进行经典算例分...     

基于动态时间弯曲的轨道波形匹配方法

轨道平直度测量仪(简称平直尺)是轨道短波检测项目中非常重要的检测工具。由于平直尺测量范围有限,为了分析轨道短波的变化规律,需对所测波形进行匹配处理。首先对所测数据进行坐标转换,将待匹配数据统一在同一坐标系。传统匹配算法只能对坐标系内的曲线进行刚性的变换和匹配,无法解决不同坐标系下曲线的动态匹配问题。基于此提出了动态时间弯曲算法(DTW),通过对时间轴的弯曲和变形,找到最短弯曲路径,以及待匹配曲线间的单点对应关系,通过计算最短弯曲路径可衡量匹配的好坏。本文利用平直尺对标准铁轨进行实际测量,并将传统算法中常用的基于区域的匹配算法同动态时间弯曲法进行对比。实验结果表明,利用动态时间弯曲法可实现短波的动态匹配,匹配精度比传统匹配算法提高约10倍,匹配误差较小,稳定性较好。     

摩托车架结构动力优化设计

本文用有限单元法对某二轮摩托车架结构的动态特性进行了研究，将理论计算结果与实验模态分析结果作比较，确定了最终车架的有限元分析模型。     

基于有限单元柔度法和刚度法的几何非线性空间梁柱单元比较研究

分别基于有限单元柔度法和有限单元刚度法二阶分析理论,采用纤维模型梁柱单元编制了钢筋混凝土杆系结构二阶非线性分析程序;分别采用这两种方法对几个典型试验实例进行了计算机模拟分析,通过模拟分析结果的对比,对有限单元柔度法与有限单元刚度法处理几何非线性问题的效果与效率进行了比较研究。结果表明:对于几何非线性问题,尤其是对于处理下降段(非稳定阶段)问题,基于柔度法的梁柱单元无论从计算效率还是计算效果上都明显优于基于刚度法的梁柱单元,有限单元柔度法是目前处理杆系结构材料与几何双重非线性问题最为有效的分析方法。     

基于混合单元法的预应力混凝土梁非线性分析

利用共旋坐标法提出了一种预应力钢筋混凝土梁非线性分析的混合单元模型,在随转坐标系内,采用分层梁单元来模拟混凝土结构,带初应变的杆单元来模拟预应力钢筋,预应力钢筋杆元和混凝土梁元的变形协调则通过非线性刚臂来实现,通过刚臂单元两端节点位移和力的关系形成预应力钢筋对混合单元刚度矩阵的贡献,从而导出随转坐标系下预应力混凝土梁考虑材料非线性的切线刚度矩阵,几何非线性则由单元随转坐标系到结构坐标系的转换矩阵及其微分来体现,从而获得结构坐标系下混合单元模型的几何与材料双非线性切线刚度矩阵。数个钢筋混凝土及预应力钢筋混凝土梁非线性分析算例表明:所提出的混合单元模型能较好地分析预应力钢筋混凝土梁非线性性能,具有一定的实用价值。     

新型协同转动六节点三边形复合材料壳单元

为分析复合材料层合板壳结构,提出了一种协同转动六节点三边形复合材料曲壳单元。不同于现有的其它协同转动有限单元:1) 该单元中采用了增量可加的矢量型转动变量,因而在非线性增量求解过程中更新节点转动变量非常简单;2) 在计算应变能对局部节点变量的二阶偏微分时,微分的次序是可以交换的,并且通过链式微分计算应变能对整体节点变量的二阶偏微分时,微分的次序也是可以交换的,因此,得到的局部和整体坐标系下的切线刚度矩阵都是对称的;3) 在此有限单元公式中引入了混合公式法,以减轻膜闭锁和剪切闭锁的不利影响。对4个典型算例进行了分析,并与其他文献的结果进行对比,该文提出的单元的可靠性和计算效率得到了验证。     

有限元-无限元耦合单桩弹性分析法

本文提出有限元-无限元耦合单桩弹性分析法,阐述了耦合分析的基本原理,并将耦合分析结果与有限元和积分法结果进行了对比分析,表明耦合方法具有计算精度高,计算时间省的特点。本文最后通过一个实例分析,将理论分析结果与试桩的实测结果进行了分析对比,表明耦合方法能对桩的弹性性状作出较好地预见,同时表明,在对桩身沉降和内力进行分析时,考虑桩周土层的非均质性是重要的。     

THE PARTITION OF UNITY METHOD

A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a posteriori error estimation for this new method are also proved. © 1997 by John Wiley & Sons, Ltd.     

有限元线法的曲线单元

有限元线法是一种新近提出且正在开发中的一种新型结构分析方法。本文建立了有限元线法的曲线单元,并以弹性力学平面问题为例给出了相应的数值算例以表明曲线单元良好的适用性及有效性。     

A fast convergent iterative boundary element method on PVM cluster

This paper reports a fast convergent boundary element method on a Parallel Virtual Machine (PVM) (Geist et al., PVM: Parallel Virtual Machine, A Users' Guide and Tutorial for Networked Parallel Computing. MIT Press, Cambridge, 1994) cluster using the SIMD computing model (Single Instructions Multiple Data). The method uses the strategy of subdividing the domain into a number of smaller subdomains in order to reduce the size of the system matrix and to achieve overall speedup. Unlike traditional subregioning methods, where equations from all subregions are assembled into a single linear algebraic system, the present scheme is iterative and each subdomain is handled by a separate PVM node in parallel. The iterative nature of the overall solution procedure arises due to the introduction of the artificial boundaries. However, the system equations for each subdomain is now smaller and solved by direct Gaussian elimination within each iteration. Furthermore, the boundary conditions at the artificial interfaces are estimated from the result of the previous iteration by a reapplication of the boundary integral equation for internal points. This method provides a consistent mechanism for the specification of boundary conditions on artificial interfaces, both initially and during the iterative process. The method is fast convergent in comparison with other methods in the literature. The achievements of this method are therefore: (a) simplicity and consistency of methodology and implementation; (b) more flexible choice of type of boundary conditions at the artificial interfaces; (c) fast convergence; and (d) the potential to solve large problems on very affordable PVM clusters. The present parallel method is suitable where (a) one has a distributed computing environment; (b) the problem is big enough to benefit from the speedup achieved by coarse-grained parallelisation; and (c) the subregioning is such that communication overhead is only a small percentage of total computation time.     

广义协调平板型三角形壳元

本文构造了一种具有三个角点十八个自由度的平板三角形壳元GST18。其拉伸与弯曲部分分别由含旋转自由度的三角形膜元和薄板弯曲三角形元组成。广义协调方法的采用,使得该单元的收敛性得到保证。在结点上引入了平面内旋转自由度,从根本上克服了单元共面刚度矩阵出现奇异这一困难。对平面膜元采用了缩减积分方案,使该单元不会产生薄膜闭锁现象。数值算例表明,本文提出的GST18薄壳元是计算精度优于同类单元的可靠、实用的单元。     

材料损伤开裂的数值模拟方法

针对数值模拟材料损伤开裂的现有方法——空单元技术和嵌入过程区中结点力释放方法,提出了释放空单元内结点力的新模拟方法,既可解决原有空单元技术未曾明确的残余应力的释放问题,又可避免采用嵌入过程区方法时所引入的大量重叠结点。己有算例表明,本方法具有模型简明,操作便利的特点。     

广义协调元方法的收敛性

本文从弹性力学平面问题理论及分区广义势能原理入手，说明广义协凋元方法的基本理论，讨论了广义协调元方法的特点；并证明了按边协调和周协调条件构造的广义协调元的解的收敛性与唯一性。     

Dynamic response of finite sized elastic runways subjected to moving loads: A coupled BEM/FEM approach

The transient response of a finite elastic plate, resting on an elastic half-space, and subjected to moving loads is considered here. Both the cases of an elastic foundation alone, as well as a finite sized elastic plate resting on an elastic foundation are considered. The numerical methods employed are: (1) the time-domain boundary element method for the elastic foundation and (2) a combination of the time-domain boundary element method for the soil and the semi-discrete finite element method for the finite sized elastic plate. Both constant as well as linear-time-interpolation schemes are included in the BEM. The integration is carried out analytically in time. The analytical solution for a moving point load on an infinite elastic plate resting on an elastic half-space is derived here. This is used as a benchmark against which the present numerical solution is compared with. The accuracy of the numerical method is also verified by comparing the solutions with some existing numerical results; the comparison with the solutions based on a Winkler foundation model reveals the limitations of the applicability of such a model, especially in the cases of high velocities of the moving load. This is because neither the inertia of the foundation, nor the behaviour of the foundation as a continuum, can be properly accounted for in Winkler's model. A parametric study is conducted, and the influences of velocity of the moving load, load distribution, etc. on the dynamic response of the soil/runway system are investigated. Furthermore, the present computational method is applied to the problem of a transport airplane taxiing on a concrete pavement resting on a typical soil. The responses of pavements are presented for different taxiing velocities.     

基于有限元与边界元耦合法的波浪力分析

利用有限元与边界元耦合法对三维无界区域中直立圆柱所受的波浪力进行进行计算,把整个求解区域分成内域或外域两部分,在内域采用有限元法,对外域采用边界元法,数值计算的结果与理论解吻合良好,表明该方法有效。     

Control of analyses with isoparametric elements in both 2‐D and 3‐D

This paper presents an extension of the computation method for the error in the constitutive relation to include isoparametric elements. Developed over the past few years at ENS Cachan's laboratory, this technique is based on the strict building of admissible displacement and stress fields. This building process, validated for several types of 2‐D and 3‐D straight finite elements (triangles and quadrilaterals, tetrahedra and hexahedra), cannot be extended to isoparametric elements. For such elements, the method consists of seeking an approximation of the statically admissible stress field by solving a high‐degree finite element problem on each element. This technique, as implemented in our error computation code, which is associated both with a method of computing optimal sizes and with meshers able to respect a size map, allows us to optimize 2‐D and 3‐D meshes. Examples demonstrate the capabilities of the proposed method. Copyright © 1999 John Wiley & Sons, Ltd.