张弦梁(桁架)结构的找形方法——分级卸载法

对张弦梁(桁架)结构的找形问题进行了深入研究,根据该类结构的受力特点,提出了分级卸载法。该方法无需假定结构零状态几何,而可以一次得到对应于初状态(即预应力态)几何的结构施工放样尺寸(即零状态几何),并通过分级加载对该方法的精度进行了检验。     

双向张弦梁找形的有限元法

根据双向张弦梁上弦压力和下弦拉力在节点产生的竖向分力与撑杆高度之间的关系推导了单元刚度矩阵,根据外荷载与上弦和下弦在节点产生的竖向分力相等的原则建立了以撑杆高度为未知数的双向张弦梁找形的线性有限元列式并编制了有限元程序,给出了张弦梁计算时下弦拉索初应变确定方法和张拉控制方法;通过对平屋顶和曲面屋顶双向张弦梁2个算例找形计算和受力分析验证了找形方法的正确性以及撑杆高度与屋面形状的无关性,本文给出的计算方法将撑杆高度作为未知量,考虑了上弦为曲面时拱的作用,计算方便、结果准确.     

基于动力松弛法的松弛索杆体系找形分析

索杆张力结构施工成形分析需要解决一个松弛态索杆系统的平衡形态求解问题,该问题可归结为一个给定构件原长的受荷索杆机构系统的找形问题。文中利用动力松弛法进行该类松弛索杆体系的找形分析。由于不建立刚度矩阵,避免了体系几何不稳定性所引起的刚度矩阵奇异问题。该方法采用悬链线索单元模型,可以考虑索大垂度效应。文中还推导了反映索原长和内力之间关系的悬链线索单元协调方程。通过一个正交松弛索网算例分析,考察了该找形方法的计算精度和收敛性。最后还模拟了一个索穹顶的施工成形过程,表明了该找形方法用于索杆张力结构施工成形分析的有效性。     

张拉膜结构的有限元分析

应用有限元程序ANSYS进行了薄膜结构的找形分析和荷载分析．张拉结构受力后将产生较大的位移,因此需要采用非线性理论．通过一系列计算,可以发现影响找形结果的因素有：单元的划分,初始弹性模量的选取,膜的预张力,边索和脊索的预张拉力值及其比值．在实际工程中,由于膜结构建筑要求和边界条件的限制,找到具有极小曲面性质的初始平衡形状较难,因此,一般把应力的差值控制在一定的范围内．工程实例计算结果表明：在风荷载作用下膜结构的竖向位移反应比较大,风吸力通常是索膜结构设计的控制因素．     

A simple finite element method for Stokes flows with surface tension using unfitted meshes

This paper presents a simple finite element method for Stokes flows with surface tension. The method uses an unfitted mesh that is independent of the interface. Due to the surface force, the pressure has a jump across the interface. Based on the properties of the level set function that implicitly represents the interface, the jump of the pressure is removed, and a new problem without discontinuities is formulated. Then, classical stable finite element methods are applied to solve the new problem. Some techniques are used to show that the method is equivalent to an easy‐to‐implement method that can be regarded as a traditional method with a modified pressure space. However, the matrix of the resulting linear system of equations is the same as that of the traditional method. Optimal error estimates are derived for the proposed method. Finally, some numerical tests are presented to confirm the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Flexible bridge decks suspended by cable nets. A constrained form finding approach

The initial geometry of structures made of cables is steered by the cable tensioning forces. In a cable net the geometrical shape and the internal force distribution cannot be dealt as separate issues: the set of geometries defines also the feasible sets of the internal forces. During the last decades, many different approaches have been proposed to deal with the form finding of cable structures. The most efficient one is the so called Force Density Method (FDM), proposed by Schek, which allows to conforming cable nets for structural applications without requiring any further assumption, neither on the geometry, nor on the material properties. An Extension of the Force Density Method, the EFDM, makes it possible to set conditions in terms of fixed nodal reactions or, in other words, to fix the position of a certain number of nodes and, at the same time, to impose the intensity of the reaction forces. Through such an extension the EFDM enables us to deal with form finding problems of cable nets subjected to given constraints and in particular to treat mixed structures, made of cables and struts. In this paper we consider cable nets interacting with members having flexural behaviour. For a given cable assembly and for a given loading condition, aim of this work is to find that particular pretensioning system which replaces both the static and the kinematic functions of the inner reactions of a flexural elastic continuous beam. It is, for instance, the case of the bridge decks suspended by cables, shaped in various forms. The specialization of the EFDM to this type of problem is presented and a progressive set of examples shows the efficiency and the versatility of this approach in contributing to the design of new creative forms.     

基于质量守恒的缆索计算理论与找形解析算法

旨在解决既有缆索计算理论的基本假定不合理问题,基于质量守恒原则推导了精细化缆索计算理论;根据拉格朗日坐标建立了考虑缆索截面变形后受拉刚度变化的改进弹性悬链线计算理论。研究结果表明,精细化缆索计算理论与改进的分段悬链线计算理论具有等价性;自重下跨度为888 m的缆索找形计算案例中,精细化缆索计算理论与悬链线方程理论的缆力及高程差值分别为61.5 kN和-158.7 mm,与弹性悬链线理论计算差值对应分别为1.9 kN和0.5 mm;受外载下跨度为1038 m缆索找形计算案例中,推导的精细化缆索计算理论与悬链线方程理论缆力差值分别为77.8 kN,与弹性悬链线理论无应力长度计算差值控制为1.0 mm。精细化缆索单元计算理论及缆索找形算法可作为缆索承载结构体系一种完备的精细化计算理论与方法。     

张力索杆结构最小势能分析方法与结构特性研究

张力索杆结构为柔性多态体系,计算方法复杂。本文基于势能最小化迭代建立平衡态的最小势能方法,推导了体系势能、下降向量及步长列式,建立势能最小化共轭梯度法迭代格式,并用VC++编程实现了算法。通过正交四边形网格索网数值分析算例验证了程序正确性,并分析了新型六边形网格马鞍形双曲索网和索杆张拉整体结构的非线性荷载特性。研究表明最小势能迭代分析是一种有效的柔性张力结构非线性分析方法。     

Application of subregion function method for solving beam-board structure

In this paper,the solution to the structure consisting of a bead and a board is given as aresult of the application of the subregion function method which was suggested in ref.[1].The same problem is also computed with finite element method.The comparison betweenthe two results shows that the application of the subregion function in the method of weightedresiduals is practical and effective,especially for solving compound structures.     

A new method for finding special solutions of nonlinear diffusion equation

A straightforward and concise method is proposed to construct special solutions of nonlinear diffusion equation. Many new special solutions obtained. We believe this method is effective on solving other nonlinear differential equations.     

张拉结构非线性分析的五节点等参单元

本文针对张拉结构的特点，提出了一种五节点等参数单元有限元模型，采用四次多项式作为位移插值函数及单元初始形状函数，并假定索是理想柔性的且满足虎克定律，基于修正的Ｌａｇｒａｎｇｉａｎ坐标描述法，建立了非线性有限元基本方程和切线刚度矩阵，利用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法进行了实例计算。结果表明：本文方法精度极高，可供大跨度索网，索穹顶，拉线塔等张拉结构分析，设计时采用。     

斜拉桥索力张拉过程的最优控制

以影响结构为基础,通过拉索张拉过程的结构分析,建立了张拉过程的最优控制数学模型,并采用综合参数法进行求解。该方法不但适合斜拉桥索力张拉过程,而且能够应用于悬索桥、拱桥的施工控制中,对同类问题有重要的参考价值。     

基于牛顿-拉夫逊的拉压不同模量问题的数值求解

针对拉压模量不同引起的材料本构非线性,首先,通过引入改进的Heaviside函数将本构方程连续光滑化;然后,基于特征值与特征向量的求导策略,推导有限元求解模型中切线刚度矩阵的列式;最终,提出基于牛顿-拉夫逊迭代格式的拉压不同模量问题的数值求解算法。数值算例验证了本文算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于工程分析中大规模计算问题的求解。     

有限元方法中的光滑积分伪弱形式

提出了一种光滑积分伪弱形式,将光滑积分拓展至被积函数非偏导项求解。结合光滑应变技术和伪弱形式,可实现有限元系统方程统一光滑积分求解,即对刚度矩阵和质量矩阵中的应变矩阵和形函数矩阵均可进行光滑积分处理,并转化为光滑子域的边界积分。光滑积分伪弱形式与光滑应变技术比较,增加了形函数矩阵不定积分处理过程,且没有降低有限元求解对形函数连续性的要求。不过,伪弱形式改变了单元积分的求解形式,连续质量矩阵求解也无需坐标映射和雅可比矩阵计算。以轴对称二维问题为研究对象,结果表明极度不规则三角形和四边形单元光滑积分伪弱形式在静态和动态有限元方程求解中也具有很好的精度。     

基于模糊推理网的高层结构智能型式优化方法与系统

首先,给出了一种改进加权模糊推理网,建立了基于该推理网的结构性能评价过程与方法,该网兼有模糊综合评判、模糊推理与模糊推理网等算法共同优点;然后,给出了一种基于模糊综合评判的优选法,将其与六个目标级性能的评价网集成,形成了兼有性能评价与优选功能的集成推理网络系统,给出了该集成系统的网络结构图及其决策函数,同时,建立了基于上述方法的结构智能型式优化支持系统;最后,给出了工程实例,结果与实际吻合。实践表明:该方法能以直观的方式表征、存储与利用领域专家在型式优化时的知识与策略,并克服了传统基于模糊逻辑与神经网络的型式优化系统的不足,是解决具有多目标、多层次及不确定信息的型式优化问题的有效方法。     

人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度,利用微分求积-积分求积,即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程,首先利用IQ法离散与时间相关的Dirac函数,再利用DQ法把控制方程转化为二阶常系数微分方程,最后利用Newmark算法求解微分方程。以某钢结构连廊为例,利用DQ法计算结构自振频率并与解析解进行对比,结果验证了节点选取和边界条件施加的合理性,再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应,计算结果表明,DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。     

A higher order subdomain method for finding local stress fields in composites

The problem of finding local and volume averaged stresses in a two-dimensional heterogeneous solid is formulated in terms of fundamental point load solutions (Green's function) leading to singular integral equations. The resulting equations are solved approximately using a subdomain method in which closed form solutions for a rectangular subdomain are obtained and utilized to find the full field solution. Previously, closed form solutions for a rectangular subvolume had been found, but only for the case of an assumed constant strain. In the present paper the solution is obtained for a quadratic form which includes not only the usual constant term but also linear and quadratic terms. The advantages of using the higher order solutions is illustrated by finding the local field in a periodic composite with square fibers. The numerical solution takes less than 90 CPU s on a workstation. The solution yields average properties independent of the reference modulus as would be expected for an accurate solution of the singular integral equation and the effective transverse modulus vs volume fraction is close to that from Christensen's model developed for round fibers.     

Hopkinson曲杆型双向拉伸加载设计探讨

为了实现对材料或结构的双向高应变率同步拉伸加载,基于曲杆中弹性应力波传播理论和Hopkinson杆原理,首先在对称的人字形曲杆结构中同时产生和传递两路压缩波,再经过接触转接头反射形成沿拉伸加载杆传播的双向拉伸波,实现对试样的双向动态拉伸。同时,为理解人字形曲杆几何构形对弹性压缩波传播的影响规律,对该加载装置进行了动力学分析和ABAQUS有限元模拟。研究发现,理想方波构形的压缩弹性波经过曲杆传播后,方波的平台段随着杆弯曲角度的增大出现前高后低的倾斜现象,同时大曲率杆引起的波形失真更严重。为获取常规方波或梯形波的平台段,也可采用定量优化的锥形撞击杆,产生前低后高的加载波,来抵消曲杆传递中的倾斜失真。最后,为了验证该加载系统的有效性,搭建了小型人字形曲杆高应变率双向拉伸装置进行试验测试。结果表明,该装置实现了脉宽约为54 μs的双向拉伸加载波良好的同步,两路波形起始点时间差可以控制在约2.5 μs以内,幅值差约6×10⁻⁶。同时对2024铝合金试样进行了双向拉伸试验,取得良好的试验效果。

     

Residual a posteriori error estimate two-grid methods for the steady Navier-Stokes equation with stream function form

Residual based on a posteriori error estimates for conforming element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.     

A subspace expanding technique for global zero finding of multi-degree-of-freedom nonlinear systems

A subspace expanding technique(SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom(MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highlyefficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation,and optimization problems in complex MDOF nonlinear dynamic systems.