方板弹性突跳的数值模拟——第二部分:计算结果与实验结果的比较

本文的第一部分给出了分岔问题的计算方案和稳定性判据的数值方法,并对一个大型有限元程序进行了改进,本文的第二部分使用这一程序模拟方板在后屈曲过程中的弹性突跳(snap-through)现象。 对四边夹支(clamped support)边界条件下、受单向面内压力作用的方板在后屈曲过程中的力学行为进行了大范围数值追踪,确定了其中稳定的平衡状态,这些稳定的平衡状态可以模拟弹性突跳的整个过程,包括加载和卸载过程中的弹性突跳。可以解释卸载过程中第二屈曲形态跳回到第一屈曲形态后,横向挠度与加载过程中第一屈曲形态的横向挠度方向相反的现象[1]。计算结果和前人的实验结果[1]进行了比较。     

“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳分析

本文按非线性大挠度弹性屈曲理论对广泛应用于工程中的“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳现象进行了分析，并对典型算例用积分法与MWR－CM的伽辽金法相结合的方法进行了数值计算，结果表明了几何参数对弹性突跳的影响。本文工作可为工程应用设计提供一定的依据。     

“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳分析

本文按非线性大挠度弹性屈曲理论对广泛应用于工程中的“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳现象进行了分析，并对典型算例用积分法与MWR－CM的伽辽金法相结合的方法进行了数值计算，结果表明了几何参数对弹性突跳的影响。本文工作可为工程应用设计提供一定的依据。     

多跨弹性支承连续矩形薄板屈曲分析

针对钢箱梁和混凝土薄壁箱梁受压翼缘的稳定问题,基于状态-空间向量法,提出了一种用于弹性支承连续矩形薄板弹性屈曲分析的计算方法。与有限条法结果对比,验证了该方法的可靠性。分析了跨间弹性支承刚度和布置以及荷载参数对屈曲的影响,结果表明：跨间弹性支承对连续矩形薄板屈曲影响明显,屈曲系数随着弹性支承刚度的增大呈非线性增长;等间距、等刚度布置弹性支承有利于板的稳定性,弹性支承的刚度或间距差别越大,对板的稳定性越不利;不同荷载工况下,弹性支承刚度-屈曲系数关系曲线的变化规律基本相同,弹性支承刚度较小时,荷载参数对屈曲系数影响显著,单向受压的屈曲系数可达双向等值受压的两倍。     

弹性支持任意铺层加筋板的非线性稳定性分析

本文利用能量变分原理和广义傅里叶级数法对具有弹性支持的复合材料任意铺层加筋板在面内各种组合载荷作用下的非线性稳定性特性进行了研究.通过采用牛顿一梯度法数值求解,证明前屈曲压-弯耦合效应对弹性支持的复合材料加筋板的屈曲和后屈曲特性均产生了明显的影响,以致于在压、剪载荷作用的开始即产生了横向翘曲变形.只有当加筋板的四边为夹支时,这种前屈曲耦合效应才不明显.除此之外,还得到了一些与非加筋的层合板完全不同的屈曲和后屈曲特性.所得结果与文献上的相关计算或实验结果对比后均吻合很好,证明本文的理论分析和数值计算是正确有效的.     

数字图像相关技术在复合材料加筋曲板压缩试验中的应用

对复合材料自动铺丝和手工铺丝两种T型加筋曲板进行了单轴压缩试验，采用基于数字图像相关技术(Digital image correlation, DIC)的三维光学测量方法对该型加筋曲板的局部屈曲及后屈曲波形进行实时监测，并与传统应变、位移测量结果进行了对比分析。试验结果表明:DIC能够准确捕捉整个试验过程中的位移场，使用DIC设备观测到的屈曲模态与应变片数据反映的波形具有良好的一致性；不同于传统测量方法，DIC能够准确捕捉蒙皮在后屈曲阶段的屈曲模态转换的全过程；利用DIC技术能够对试验不同时间节点(即不同载荷水平)的屈曲模态进行清晰、直观的观测，因而能够较准确地获得结构的屈曲载荷，该载荷与由应变-载荷曲线确定的屈曲载荷相比，误差小于5%。采用ABAQUS有限元软件对试验过程进行了数值仿真分析，并通过与试验结果的对比表明了计算结果、DIC测量结果与传统方法测量结果三者具有良好的一致性。      

加劲钢板剪力墙弹性抗剪屈曲性能研究

系统地分析了三个主要参数(板高厚比λ、肋板刚度比η和柱刚度β)对钢板剪力墙弹性屈曲性能的影响;提出了钢板剪力墙的三种弹性屈曲形式(局部屈曲、整体屈曲和相关屈曲),指出肋板刚度比η=40时(相当于I s=3.7bt3)能保证十字加劲板发生小区格板的局部屈曲或整块板的相关屈曲;指出现行高层建筑钢结构规范用于纵横加劲板局部屈曲荷载的设计表达式仅适用于η≥40的条件,而在η<40范围内,其计算结果偏于不安全;研究了交叉加劲板的弹性屈曲荷载,并与非加劲板和十字加劲板的屈曲性能进行了比较;最终给出了柱刚度对弹性屈曲荷载的修正系数,提出了交叉加劲板弹性屈曲荷载的简化计算公式。     

基于弹性扭转约束边界的波形钢板整体剪切屈曲分析

波形钢板的整体剪切屈曲对波形钢腹板PC组合箱梁桥的竖向抗剪设计有重要意义。该文在正交各向异性薄板理论的基础上,利用势能驻值原理和瑞利-里兹法,推导了基于弹性扭转约束边界的波形钢板弹性整体剪切屈曲荷载的分析方法,并给出了几种特殊边界条件下的简化计算公式。计算结果表明:对于四边简支板和四边嵌固板,该方法与现有公式计算结果一致;波形钢板强抗弯刚度方向上的约束条件是影响其整体剪切屈曲的决定性因素,随着该方向上约束的增强,屈曲模式将从四边简支情况向四边嵌固情况过渡;弱抗弯刚度方向上约束条件的影响很小,可以忽略。最后给出了将波形钢板在实际梁结构中受到的边界约束等效为弹性扭转弹簧的方法。     

刚性基底上弹性约束矩形板的屈曲行为分析

对刚性基底上非加载边弹性约束矩形板在固支边均匀面内压力作用下的屈曲行为进行了分析研究。用里兹能量变分法建立确定板屈曲强度的本征值问题,利用满足边界条件的屈曲位移函数导出板屈曲系数计算公式。将该方法用于矩形钢管混凝土钢板局部屈曲的分析和计算,提出了目标板边界约束系数计算公式。试验结果表明,方形钢管混凝土柱钢板局部屈曲强度计算值与试验值吻合良好,钢板边界弹性约束的处理和约束系数的计算方法是有效的。     

轴向碰撞弹性直杆动力后屈曲有限元分析

利用显式动力学有限元方法对弹性直杆的动力后屈曲进行了分析;模拟了弹性直杆轴向碰撞动力屈曲的变形及发展过程。分析中将碰撞杆视为无初始缺陷的理想直杆,将弹性直杆动力屈曲双特征参数的解答作为非线性动力后屈曲求解的初始条件,实现了对无缺陷理想直杆的动力后屈曲分析。计算结果与文献中的实验数据获得了很好的一致。计算结果同时也揭示了直杆动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures

A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton–Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.     

盘绕式伸展臂收纳过程理论分析与数值模拟

盘绕式伸展臂在收纳过程中的力学行为决定其展开性能,收纳过程是否顺利是工程设计的关键问题,这取决于纵杆和三角框的刚度关系。盘绕臂收纳过程中纵杆和三角框均体现出大转动、大变形的特性,三角框还体现大挠度后屈曲特性。该文采用势能驻值原理及几何精确理论建立三角框的后屈曲列式,计算出三角框的后屈曲刚度,基于势能驻值原理推导出盘绕臂收纳过程中通长纵杆的平衡方程以及保证稳定平衡的最小三角框屈曲后刚度,并得出盘绕臂设计使用的参考公式;为验证参考公式的正确性以及对收纳全程进行精确计算,采用自适应弧长迭代,基于增量有限元法模拟了盘绕臂收纳全过程,得到收纳过程中结构应力-应变及能量变化;通过对解析解和数值解在平衡方程、自由端高度、最小三角框刚度、能量守恒等关键参数的计算结果进行对比来相互论证计算的正确性。该文推导的解析公式与增量有限元法的精确模拟可相互补充,共同服务于盘绕臂设计中的参数选定和收展控制。     

开洞钢板剪力墙的抗侧刚度分析

钢板剪力墙作为一种新型抗侧力结构体系,墙板开洞对钢板剪力墙结构体系的抗侧力行为具有重要影响。抗侧刚度和抗侧承载力是设计中最为关心的两项基本性能,该文重点研究墙板开洞对抗侧刚度的影响。首先介绍了3个钢板剪力墙试件的低周往复荷载试验,试验表明钢板剪力墙试件抗震性能优越,开洞会影响试件的抗侧刚度和抗侧承载力。随后,建立了钢板剪力墙结构的壳-实体精细有限元单层模型,研究了影响抗侧刚度的关键因素。在此基础上,通过大量数值计算和参数分析,提出了用于计算开洞墙板厚度折减率的简化计算公式,建议结构体系建模时以折减厚度的不开洞墙板代替实际厚度的开洞墙板,计算公式和精细有限元计算结果进行充分对比,具有良好的精度。最后,采用考虑剪切变形的悬臂梁理论和该文建议的厚度折减率简化计算公式对国内外一些不开洞与开洞钢板剪力墙试验进行验证,理论结果与试验结果吻合良好,该文建议的开洞墙板厚度折减率公式与抗侧刚度理论计算模型具有较高的精度,可供工程设计参考。     

Artificial neural network model of the strength of thin rectangular plates with weld induced initial imperfections

Probabilistic assessment of post-buckling strength of thin plate is a difficult problem because of computational effort needed to evaluate single collapse load. The difficulties arise from the nonlinear behaviour of an in-plane loaded plate showing up multiple equilibrium states with possible bifurcations, snap-through or smooth transitions of states. The plate strength depends heavily on the shape of geometrical imperfection of the plate mid-surface. In this paper, an artificial neural network (ANN) is employed to approximate the collapse strength of plates as a function of the geometrical imperfections. For the training set, mainly theoretical imperfections with the corresponding collapse loads of plate calculated by FEM are considered. The ANN validation is based on the measured imperfections of ship plating and FEM strength.     

Boundary elements with equilibrium satisfaction: a consistent formulation for plate bending analysis considering Reissner’s theory

The present paper presents a self-equilibrated boundary element formulation for elastostatic analysis of Reissner’s plate bending problems. In this formulation, rigid body movements are introduced to the generalized displacement fundamental solution, resulting in modified boundary element matrices with inherent equilibrium satisfaction. The procedure is quite general and easy to implement into existing boundary element codes. In the end of the paper, numerical examples are presented, illustrating the benefits of the proposed formulation.     

Numerical and experimental study on morphing bi-stable composite laminates actuated by a heating method

This paper presents a new heating actuation method to induce the snap-through phenomenon of bi-stable laminates by manipulating the residual stress in laminates. The mechanism of the heating actuation method is analyzed, and the snap-through process is simulated by the finite element method. The heating actuation experiments on two types of laminates with different stacking sequences are performed. Good agreement is obtained between the experimental data and the finite element analysis (FEA). Subsequently, the heating actuation method is applied to several different bi-stable laminates and investigated by FEA. The FEA results show that this heating actuation method is an effective way to induce the snap-through phenomenon of bi-stable laminates of different thicknesses, sizes and shapes.     

A study on the effect of stiffeners on quasi-static crushing of stiffened square tube with non-linear finite element method

During ship collision and grounding, the crushing collapse of a thin-walled structure subjected to compressive loads is one of the important failure mechanisms. Non-linear finite element method (FEM) is a powerful tool for analyzing large deformation plasticity problems. In this paper, the effects of longitudinal and transverse stiffeners on the quasi-static crushing of stiffened square tubes, which have relatively light stiffeners, are studied with non-linear FE program LS-DYNA. Based on the experimental data and numerical simulation results, new formulas for equivalent plate thickness and the mean crushing load are developed. The prediction of the mean crushing load is in good agreement with the experimental data.     

General case of multiple crack problems in an infinite plate

General case of multiple crack problems in an infinite plate is a case that the tractions applied on two edges of each crack are arbitrary, generally, are not in equilibrium. Two elementary solutions are present to solve the proposed problem. The first (second) elementary solution is defined as a solution that two pairs of normal and tangential concentrated forces are applied at a point of both edges of a single crack in an infinite isotropic elastic medium, with same magnitude and opposite direction (with same magnitude and same direction). Using the two elementary solutions and the principle of superposition, we found the proposed problem can be converted into a system of Fredholm integral equations. Finally, the system is solved numerically and SIF values at the crack tips can be easily calculated. In order to explain our study, one numerical example is given in this paper.     

波浪与弹性板作用的数值模拟

该文采用高阶有限元和边界元联合的方法求解波浪与弹性板的相互作用。其中流场采用边界元法求解,结构弹性响应方程采用基于Mindlin板理论的有限元方法求解,通过模态叠加技术实现了弹性板变形与流场相互作用的解耦。通过对一矩形板的计算,验证了该文方法与他人试验结果和数值模拟结果都吻合良好。利用这一模型进一步分析了波浪与弹性圆形板的作用问题,并对圆形板运动响应的收敛性进行了分析。