基于多弹簧模型的空间梁柱单元(II):参数分析

为模拟地震作用时杆件在变动轴力和双向弯曲的耦合特点,基于简化纤维模型的多弹簧单元模型近年被广泛应用。本文作者在相关论文中提出了考虑剪切变形弹塑性刚度影响的多弹簧模型空间梁柱单元,杆件的计算模拟精度除了取决于单元模型之外,还决定于两个重要参数:弹簧位置及个数布置、塑性区长度,本文将针对其进行参数分析并提出合理建议取值。本文最后还提出了模拟杆件残余应力的合理弹簧布置方式。     

板材多点成形过程的有限元分析

多点成形过程采用静力隐式格式进行数值模拟是比较合适的。本文建立了用于多点成形过程分析的静力隐式弹塑性大变形有限元方法 ,给出了对稳定迭代收敛过程效果较好的板壳有限单元模型、处理多点不连续接触边界的接触单元方法以及增量变形过程中应力及塑性应变计算的多步回映计算方法。基于这些方法编制了计算软件 ,应用该软件进行了矩形板的液压胀形过程及球形模具拉伸成形过程的有限元分析 ,数值计算结果与典型的实验结果及计算结果吻合很好。最后给出了球形、圆柱形目标形状的实际多点成形过程的数值模拟结果。     

基于多弹簧模型的空间梁柱单元(Ⅱ):参数分析

为模拟地震作用时杆件在变动轴力和双向弯曲的耦合特点,基于简化纤维模型的多弹簧单元模型近年被广泛应用.本文作者在相关论文中提出了考虑剪切变形弹塑性刚度影响的多弹簧模型空间梁柱单元,杆件的计算模拟精度除了取决于单元模型之外,还决定于两个重要参数:弹簧位置及个数布置、塑性区长度,本文将针对其进行参数分析并提出合理建议取值.本文最后还提出了模拟杆件残余应力的合理弹簧布置方式.     

钢筋混凝土桥墩弯剪数值分析模型

基于修正的压力场理论MCFT(The Modified Compression Field Theory)和纤维单元模型建立了钢筋混凝土桥墩的弯剪数值分析模型,以MCFT理论确定桥墩的剪切力-剪切位移关系,并与考虑桥墩弯曲变形的纤维单元模型组合,共同考虑桥墩的弯-剪-轴力耦合作用.通过与六个弯剪破坏控制的圆形截面钢筋混凝土桥墩拟静力试验结果的对比,对分析模型进行了验证.主要认识结论为基于MCFT理论可准确地计算弯剪破坏桥墩的屈服荷载、极限荷载和弹性阶段剪切刚度,剪切开裂是引起钢筋混凝土构件剪切力-剪切位移关系刚度突变的主要因素,而弯曲开裂与纵筋屈服对刚度的影响较小;分析模型对弯剪破坏桥墩的滞回曲线、弯曲与剪切变形成分均进行了较为准确的模拟分析.     

可计算厚度方向应力的壳单元

在板料成形数值模拟中通常使用壳单元,然而,传统的壳单元在计算“回弹”(弹性恢复)变形时精度很差,其原因之一是由于这些壳单元忽略了厚度方向的应力而代之为平面应力条件。为了改善这个缺陷,本文提出的壳单元,通过构造厚度方向的二次形函数引入厚度方向的变形,使得三维本构关系可以不经任何改变被直接使用,并且壳上、下表面的载荷对厚度方向应力的影响也能较好地表现出来。通过几个数值算例证明该壳单元对弹塑性大变形问题分析是有效的。     

厚钣金件压弯翻边与回弹的数值研究

在独立研制的板材冲压成形性分析软件KMAS中，组入可有效模拟厚钣金件压弯成形与回弹变形的三维退化曲壳单元模型，简述了考虑凹，凸模间隔可变的基于有限元网格双面接触算法以及回弹的处理技术，数值研究了铁路客车牵引架厚钣金件压弯翻边与回弹变形过程，并将压弯过程模拟结果与国外基于单面接触算法的商品化软件的模拟结果以有实验结果进行比较，最后，给出了该类问题回弹量的预示方法。     

具有单元分裂功能的间断有限元方法

介绍一种能够模拟材料开裂过程的有限元方法,该方法引入单元分裂和界面分离技术,结合具体的破坏准则,模拟材料变形中的破坏,同时还可以方便地处理材料中任意分布的界面结构．以三点弯曲实验为例,通过数值模拟结果和实验数据的比较,验证了该方法的适用性．     

应变硬化薄板夹持型滚弯成形过程分析

现存文献对薄板的连续滚弯成形过程的数学模拟多限于讨论三辊轮解锥型弯板过程,且基于较多的假定和板的小变形情况。而开发有更多的功能和更高的生产效率的四辊轮连续弯板机需研究夹持型滚弯成形过程。本文将「１」的工作,理想塑性材料平面应变薄板的夹持型连续滚弯成形过程的弹塑性大变形弯曲的力学分析,推广至一般应变硬化材料的情形。得出了控制微分方程的解析解。采用固支边界条件模拟刚度很大的平持系统对板的夹持。通过对线     

一种考虑横向剪切变形的三角形板弯曲单元

本文从部分协调的三角形薄板弯曲单元出发,并假设横向剪切应变在单元内线性变化,提出了一种考虑横向剪切变形的具有15个自由度的三角平板弯曲单元。该单元应用于薄板和中等厚度板分析均有较高的精度,计算效率高,可用于工程中具有复杂形状的薄板和中等厚度板结构的分析。     

金属板材冲压成型过程的有限单元法模拟

用有限单元法模拟了金属板材的冲压成型过程。在模拟过程中，应用了同时考虑了薄膜力和弯矩的板壳大变形理论，考虑了板材在塑性阶段各向异性的强化性质，考虑了模具和工件的接触和摩擦条件，分析了金属板在冲压过程中的屈曲现象，建立了增量形式的变分原理。弹塑性薄壳单元被引入，它的位移模式在变分的意义上满足单元边界上一阶导数连续的条件，并有足够的秩来适应单元的有限拉伸、转动和弯曲，计算中采用了罚函数方法，即在模具和工件的接触面上，模具的表面被假设为文克尔地基，采用了修正的库伦摩擦定律，迭代法被用来决定模具与工件的接触条件和金属板的塑性行为。本文最后提供了一个算例。     

Elastic-plastic secondary indeterminate problem for thin-walled pipe through the inner-wall loading by three-point bending

The inner-wall loading by three-point bending about thin-walled pipe is an elastic-plastic secondary indeterminate problem in the symmetrical three-roller setting round process. In this study, the shifting of the tangent point between the pipe and lower roller is ignored. The bilinear hardening material model is adopted, and the static equilibrium condition, physical relationship of elastic-plastic deformation, and deformation compatibility condition are taken into account. Based on the geometrical discrete idea, a semi-circular pipe is meshed equably into N micro-pipe-wall elements with same geometric parameters along the circumferential direction. Deformation characteristics of each element are calculated, and then the deformation history response of the whole pipe is resolved by the load increment method. The finite element model of static bending in three-roller setting round process is established by using the software package ABAQUS. The theoretical and simulated results show that the cross section of pipe has two positive bending regions and two reverse bending regions; the maximum bending curvature appears in the bottom section of pipe, the minimum bending curvature appears in the section corresponding to the tangent point of the pipe and lower roller. The quantitative relationships between the upper roller load, maximum(minimum) bending curvature and reduction are given. Finally, the reliability of theoretical calculation is proved by numerical simulation.     

金属板条在圆柱形模中弯曲成形的大变形有限元分析

本文采用大变形弹塑性有限元法对金属板条在柱形模中的压弯成形过程进行了数值模拟,并与实验进行了比较。首先给出了纠正的拉格朗日有限元公式和基于弹塑性乘法分解的超弹性塑性本构关系。对接触摩擦问题的处理采用了罚函数法。通过对数值结果的分析得出了一些对弯曲工艺的设计有指导价值的结论。     

具有压电材料薄板弯曲控制的有限元法

考虑一均匀各向同性薄板结构,在其上下表面离散分布状压电执行元件,在横向外载和电压共同作用下,分析板的弯曲变形,并通过变化作用于执行元件上的电压对板的变形进行控制,根据逆压电效应将电压转换成作用于板上的等效作用量,用Ｈａｍｉｌｔｏｎ原理导出压电结构板弯曲变形的有限元公式,并对环形板情况进行数值计算。     

A new type of plate bending element

Based on a two-field generalized variational principle, a new type of arbitrary quadrilateral plate bending element, with four nodes and with the effect of transverse shear deformation taken into account, is proposed. The element is applicable to a wide range of plate thickness and an explicit expression of stiffness matrix can be obtained. Therefore, it possesses the distinguished features of general applicability, high precision and less computer time.     

A crack bridging model for bonded plates subjected to tension and bending

A crack bridging model is presented for analysing the tensile stretching and bending of a cracked plate with a patch bonded on one side, accounting for the effect of out-of-plane bending induced by load-path eccentricity inherent to one-sided repairs. The model is formulated using both Kirchhoff–Poisson plate bending theory and Reissners shear deformation theory, within the frameworks of geometrically linear and nonlinear elasticity. The bonded patch is represented as distributed springs bridging the crack faces. The springs have both tension and bending resistances ; their stiffness constants are determined from a one-dimensional analysis for a single strap joint, representative of the load transfer from the cracked plate to the bonded patch. The resulting coupled integral equations are solved using a Galerkin method, and the results are compared with three-dimensional finite element solutions. It is found that the formulation based on Reissners plate theory provides better agreement with finite element results than the classical plate theory.     

Non-axisymmetric bending of thin annular plates due to circumferentially distributed moments

The non-linear deformation of a thin annular plate subjected to circumferentially distributed bending moments is studied. A von Kármán plate model is adopted to formulate the equations of motion. Free–free boundary conditions have been applied at both inner and outer edges. The matrix formulation of the Differential Quadrature Method is used to discretise and solve the governing equations. Linear analysis predicts that the annular disk deforms axisymmetrically into a spherical dome. However, the proposed non-linear analysis shows that a symmetry breaking bifurcation may occur after which the linear solution becomes unstable and the plate transitions into a non-axisymmetric cylindrical deformation. This is the case when at least one of two parameters reaches a critical value. These parameters are the non-dimensionalised ratio between applied moment and bending stiffness and the ratio between inner and outer radius. Furthermore, it is noted that free-free boundary conditions and circumferentially distributed bending moments do not break the circular symmetry of the annular disk. Hence, the principal axes of curvature in the deformed configuration do not have a preferred orientation. Therefore, the present work describes a shell possessing infinite identical equilibria, having different yet no favoured direction and, hence, links to previous researches on neutrally stable structures.     

板弯曲与平面弹性有限元的同一性

本文建立平面弹性与板弯曲的相似理论，并用于将平面弹性的单元移植到板弯曲元，从而其分片试验，收敛性等性质也同时移植到板弯曲元，使两者处于同一水平上，同时又将此基于力法的板弯曲元入位移法的轨道，找出共相应的位移系统，并证明其适定性，从而为将此类单元装入位移法通用程序系统创造了条件。     

Rational finite element method for elastic bending of reissner plates

IntroductionAsawell-establishedandsophisticatednumericalanalysistechniqueforthedifferentialequahons,thefiniteelementmethodwasoriginatedindependentlybythedomesticandtheforeignmechanicalinvestigatorstheyyearsago.ItfoundforthefirsttimewideapplicationsintheelasticstfUctolproblemsandwiththedevelopmentofcomputerextendedinvaryingdegreestOalmostalltheengineeringdisciplinesandmanyscientificandtechnologicalfields.Thisleadstoadramaticbreakthroughforthecurrentcomputationalmathematics.Themathematicalbasis…