带钢域杆件的弹塑性分析

本文采用Ｇｉｂｅｒｓｏｎ单分量模型描绘杆件的弹塑性状太民，推导并建立了带刚域杆件考虑材料非线性的单元刚度矩阵，该表达式适用于求解可简化为“平面等效框架”的任意结构的弹塑性分析问题。     

考虑大位移影响的解析型压扭杆单元

为提高压扭杆件内力和变形分析的精度和效率,以Vlasov扭转理论为基础,根据压扭杆件位移控制方程,考虑大位移和截面翘曲影响,构建了压扭杆的单元位移形函数,采用势能原理建立了压扭杆势能泛函。利用势能驻值变分原理得出了解析型压扭杆单元列式,并推导了用于杆件内力分析的单元刚度矩阵。将其与理论解、插值多项式单元进行对比,结果表明:该文构造的单元计算压扭杆转角及翘曲率和临界荷载的精度高于插值多项式单元,且不需划分单元,即可保证计算结果与理论解一致,满足了高精度、高效率的要求,可应用于解决实际工程问题。     

改进的基于弹性核法的曲梁有限梁段法

基于弹性核法的曲梁有限梁段法,在求解曲梁单元刚度矩阵时,因柔度矩阵的表达式繁琐,难以直接求逆得到单元刚度矩阵的解析表达式.相关文献及曲梁的梁段有限元程序均采用数值方法求逆,得其刚度矩阵.该文提出一个矩阵求逆理论,并证明之.依此理论推导出曲梁单元刚度矩阵的解析解,并提出对曲梁有限梁段法的改进.算例验证了公式的正确性和可靠...     

多边形比例边界有限元非线性高效分析方法

比例边界有限元法作为一种高精度的半解析数值求解方法,特别适合于求解无限域与应力奇异性等问题,多边形比例边界单元在模拟裂纹扩展过程、处理局部网格重剖分等方面相较于有限单元法具有明显优势。目前,比例边界有限元法更多关注的是线弹性问题的求解,而非线性比例边界单元的研究则处于起步阶段。该文将高效的隔离非线性有限元法用于比例边界单元的非线性分析,提出了一种高效的隔离非线性比例边界有限元法。该方法认为每个边界线单元覆盖的区域为相互独立的扇形子单元,其形函数以及应变-位移矩阵可通过半解析的弹性解获得;每个扇形区的非线性应变场通过设置非线性应变插值点来表达,引入非线性本构关系即可实现多边形比例边界单元高效非线性分析。多边形比例边界单元的刚度通过集成每个扇形子单元的刚度获取,扇形子单元的刚度可采用高斯积分方案进行求解,其精度保持不变。由于引入了较多的非线性应变插值点,舒尔补矩阵维数较大,该文采用Woodbury近似法对隔离非线性比例边界单元的控制方程进行求解。该方法对大规模非线性问题的计算具有较高的计算效率,数值算例验证了算法的正确性以及高效性,将该方法进行推广,对实际工程分析具有重要意义。     

钢筋混凝土框剪结构非线性地震反应分析

本文采用壁式框架来分析框架─剪力墙结构的非线性地震反应,假定弯曲刚度沿杆轴按抛物线分布,导出了考虑剪切变形的单元刚度矩阵,将古典刚度法或高斯消元法用以形成该时间间隔内的瞬时抗侧移刚度矩阵,用适合非线性动力计算的数值方法求解动力方程。     

考虑节点刚度的网壳杆件切线刚度矩阵

本文采用Timoshenko梁柱理论,推导出网壳杆件的切线刚度矩阵。该矩阵不仅考虑了两个主轴方向弯曲的耦合作用。而且考虑了节点刚度以及节点体大小的影响,对于位移的高阶项没有任何省略,其精度比C．Oran的切线刚度矩阵有很大程度的提高。通过对一单层网壳结构的算例分析,证明了该分析模型的正确性。     

基于分段悬链线理论的悬索分析矩阵迭代法

通过分析现有悬索计算的主要方法,在分段悬链线解析计算方法的基础上,结合求解非线性方程组的牛顿迭代法,提出了适用于悬索分析的矩阵迭代方法.根据解析推导给出了悬索矩阵迭代法的切线刚度矩阵构造方法,分析了刚度矩阵的特点,针对特定的工程问题列出了悬索找形的迭代计算流程.该方法计算量小,效率高,计算精度能够满足实际工程需要.通过与其他文献的数值计算结果进行对比,验证了所研究方法的可靠性.该方法适用于悬索桥、货运索道等各类悬索结构的分析计算.     

计及二阶效应的一种变截面梁精确单元刚度阵

推导一种精确的Bernoulli-Euler变截面梁单元,解决了传统变截面梁单元在结构稳定性分析中存在的计算精度较低的问题,以常见的外形沿轴向按线性变化的变截面梁为例,给出梁单元的精确刚度阵。放弃传统有限元通过插值理论构建变形场,并通过虚位移原理获取单元刚度阵的方法,直接从计入二阶效应的单元平衡微分方程中得到变截面梁的载荷位移关系,进而得到有限元格式的变截面梁精确刚度阵。借助于变截面梁单元刚度阵,可导致与精确的微分方程解析法同样的计算精度。通过与几个经典算例和ANSYS计算结果比较表明:该精确刚度阵可直接应用于结构稳定性分析,获得变截面梁结构精确的欧拉临界力。     

基于静力凝聚的高精度变截面梁单元及其几何非线性分析研究

基于Euler-Bernoulli梁单元基本假定,通过静力凝聚获得截面特性沿单元轴向连续变化的变截面梁单元高精度刚度矩阵,并提出一种基于随动坐标法求解变截面梁杆结构大位移、大转动、小应变问题的新思路。首先依据插值理论和非线性有限元理论推导出三节点变截面梁单元的切线刚度矩阵,然后使用静力凝聚方法消除中间节点自由度,从而得到一种新型非线性两节点变截面梁单元。结合随动坐标法,在变形后位形上建立随动坐标系,得到变截面梁单元的大位移全量平衡方程。实例计算表明,该新型变截面梁单元具有较高的计算精度,可应用于变截面梁杆系统大位移几何非线性分析。     

考虑构件弹性的电动Stewart并联机构刚度建模与仿真

基于集总解析建模方法和构件有限元分析建立包含驱动副、被动万向铰链和运动杆件弹性变形以及预载作用下的Stewart机构刚度矩阵模型。采用添加虚拟铰链等效构件弹性的方式,将分支等效为一系列刚性构件经由主、被动副以及虚拟铰链连接的形式,给出了运动关节和虚拟铰链变量对机构末端位姿的运动学Jacobian矩阵的数值计算方法,应用虚功原理得到静平衡方程,最终建立了机构无预载以及预载下的刚度矩阵模型。该模型不仅考虑了控制环路刚度,还将构件柔性的有限元分析结果与解析建模相结合,在降低计算成本的同时保证了精度。通过一机构分析实例,考察了两种模型下刚度分布的差异。     

与圆弧形曲梁连结的框架柱则移刚度

从悬臂直梁出发，可以推导出线刚度与固定端弯矩及铰支端转角的相互关系，进而通过该关系推导出曲梁的折算线刚度。如果考虑楼板的刚度足够大，利用传统的D值法可以直接计算出相关柱的侧移刚度。如果考虑楼板的刚度是有限的，则可以通过建立平衡方程和协调方程得出曲梁中部柱子的位移与其它柱子位移之间的关系，进而可以对曲梁中部柱子侧移刚度的修正系数进行调整，最终可以求出曲梁中部柱子的侧移刚度。     

考虑剪切作用的盾构隧道管片接头力学模型研究

目前使用较广泛的盾构隧道管片接头研究模型往往视切向为刚性,大多考虑了轴力与弯矩的共同作用而忽视了剪力作用。然而剪切力可能会使接头位置发生剪切位移,严重时可能引起管片剪切破坏、隧道错台等。该文将轴向、切向和转动三个方向的位移作为已知荷载,分别推导接头区域内螺栓与混凝土结构的刚度矩阵,然后对刚度矩阵进行合成,得到管片接头考虑剪切时的力学模型。并以狮子洋盾构隧道工程为依托,对比了有限元法与该模型的计算结果。研究表明,模型与有限元法计算的结果规律相同,两者具有较好的一致性。该文建立的模型考虑了轴向、剪切及弯曲三个方向上荷载的耦合作用,使之更符合接头的实际情况。研究成果对补充管片接头力学模型有一定参考价值。     

A reliable three‐node triangular plate element satisfying rigid body rule and incremental force equilibrium condition

Abstract

This paper proposes a simple method for deriving the geometric stiffness matrix (GSM) of a three‐node triangular plate element (TPE). It is found that when the GSM of the element is combined into the global one of the structure, this structural stiffness matrix becomes symmetric and satisfies both the rigid body rule and incremental force and moment equilibrium (IFE) conditions, which are basically two fundamental conditions for analysis of mechanics. The former condition has been widely used in the community of mechanics; while the latter one, to our best knowledge, has never been considered. Advantages with the GSM derived are that derivations only need simple matrix operations without cumbersome non‐linear virtual strain energy derivations and tedious numerical integrations and more appealingly, this derived GSM can be explicitly given for applications. In addition, based on IFE and the rigid body rule conditions, a reasonable GSM for the three‐node TPE must be asymmetric; however, an asymmetric matrix usually gives rise to tedious numerical calculation especially in geometrically nonlinear problems and further, greatly influences computation efficiency. Fortunately, the skew‐symmetric parts of the derived GSM can be canceled out once they are merged into the global stiffness matrix of the structure. In this regard, this structural stiffness matrix becomes a symmetric one and thus enhances its effectiveness. Finally, several examples are provided for validating the robustness of the derived GSM.     

索的非线性有限元与调索方法研究

介绍了索单元几何非线性刚度的各种模拟方法并进行了评述,采用悬链线理论推导了一种新的柔性索单元切线刚度矩阵及单根柔索的各种非线性计算公式,用变形后线密度q的回代来反应弹性伸长和温度的影响,概念清晰、公式简洁、迭代效率高;还介绍了用增量调索法、绝对索力调索法、无应力索长调索法进行索单元张力的施加及调整的原理,而无应力索长并配合螺母旋转角度调索法可实现任意次序调索,操作性强、效率高、精度好。     

Implementation of a new algorithm for evaluating 3D fracture analysis

This paper presents a new method for calculating the elastic stress intensity factors for 3D structural components under complex loads and with complex geometry. To this end, a hybrid element formulation was developed where the hybrid element has its stiffness matrix corrected to exactly reflect the existence of the true 3D crack geometry within the element. To obtain the stiffness matrix of the hybrid element, this approach involves the combined use of the redundant force method together with the displacement field results arising from the finite element alternating technique (FEAT). This matrix was subsequently used together with a standard commercial finite element package to obtain the force field of the nodes. Finally, these forces were used to determine the stress intensity factors along the crack front. This procedure was validated by comparison with results available in the literature.     

Free vibration analysis of arches using curved beam elements

The natural frequencies and mode shapes for the radial (in‐plane) bending vibrations of the uniform circular arches were investigated by means of the finite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two‐node six‐degree‐of‐freedom arch element, the elemental stiffness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia effect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall stiffness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the finite element method based on the conventional straight beam element and good agreements were achieved. Copyright © 2003 John Wiley & Sons, Ltd.     

任意非对称断面薄壁箱梁一维有限元分析

根据薄壁箱梁的实际支承特点,设置支承坐标系并在支承坐标系中建立变形协调的相容条件,针对任意非对称断面薄壁箱梁,导出了考虑拉(压)弯扭翘空间耦合分析的单元刚度矩阵及等效节点力公式。此外,提出了通过设置具有线刚度、转动刚度、扭翘刚度的假想弹簧单元,对薄壁箱梁的复杂约束条件进行处理的一般方法。所得到的刚度矩阵表明,只有当忽略翘曲变形对截面转角的影响时,轴向拉压才只与水平弯曲及竖向弯曲相耦合,而与约束扭转不再耦合。算例结果表明了分析方法的有效性。     

任意截面预应力混凝土细长柱的非线性分析

提出了轴力和双向弯曲作用下任意截面混凝土和预应力混凝土细长柱的非线性有限元计算模型。分析时既考虑了由单元变形和轴力二次矩引起的几何非线性效应,也考虑了由材料非线性应力应变关系和截面刚度矩阵引起的材料非线性效应。推导了非线性全过程分析的标准有限元公式,得到的单元刚度矩阵可分割成三个子矩阵,分别反映了材料非线性、材料非线性和单元大位移的耦合、轴力二次矩等三种不同的非线性作用效应。计算分析结果和试验结果吻合较好。     

Experimental and numerical performance of corrugated fibreboard at different orientations under four‐point bending test

This paper presents experimental work, finite element (FE) model, and analytical solution for predicting the four‐point bending on C‐flute corrugated fibreboard (CFB) when oriented at different angles. The angles of the CFB samples used in this research study were 0° (cross‐machine direction) and 30°, 45°, 60°, and 90° (machine direction). The CFB was assumed as an orthotropic shell element in the FE model and was validated by comparing the bending stiffness, maximum bending force, and failure formation from the experimental test. It was found in the experiment that the 90° sample had the highest bending stiffness with the lowest maximum bending force while the 0° sample had the opposite. An interesting finding was that the 30° and 45° samples improve the bending stiffness than does 0° without significantly affecting the maximum bending force. Both the FE model and analytical solution predicted the bending stiffness trend of the board from 0° to 90° with good agreement compared with experimental results. The maximum bending force in the FE model showed reasonable agreement with the experimental findings. The failure regions on the samples showed similar patterns in both experiments and the FE model. The accurate response in the FE model justify that it is a good tool to predict the bending behaviour of CFB.     

索穹顶结构非线性分析的杆索有限元法

索穹顶结构是大变形柔性组合结构，其受力分析属于几何非线性问题，求解较复杂。本文应用有限元法，结合索穹顶结构特征，提出三节点等参数索单元与两节点杆单元相结合的混合有限元模式。基于Lagrangian坐标描述法和虚功原理推导了空间拉索和杆单元的大位移刚度矩阵，并建立了索穹顶结构非线性分析的增量平衡方程，利用NewtonRaphson法进行了实例计算。结果表明，本文方法精度很高，适合于索穹顶结构的空间非线性分析。