船体开孔薄板面内剪切屈曲特性研究

船体板材不可避免地存在不同形式的开孔,开孔破坏了结构的连续性,对结构的强度、稳定性具有重要影响,因此研究船体板开孔结构的屈曲特性对保证船舶安全十分重要。在面内载荷作用下,通过画框型剪切夹具、3D全场变形测量-分析系统等对两种不同形式的船体开孔薄板进行剪切屈曲试验,获得了圆形开孔板和方形开孔板的临界屈曲载荷、全场位移/应变信息和拉力-伸长率曲线等;考虑试验夹具的影响,基于Abaqus对不同形式的开孔板进行数值仿真,通过对开孔板进行特征值屈曲分析和非线性屈曲分析,获得了两种不同形式船用开孔薄板的屈曲、后屈曲力学响应信息。通过数值仿真与试验结果的对比研究,验证了数值仿真方法的有效性、准确性。在此基础上,重点剖析载荷-伸长率关系、典型时刻板面全场位移、临界屈曲载荷以及开孔边缘的应力分布响应特征,明确了面积等效情况下圆孔和倒圆角方孔对方形薄板剪切稳定性的影响。为船用薄板面内剪切稳定性的试验和仿真研究以及大型船体结构的设计优化、力学性能评估等提供有益参考。     

开孔薄板弹性波散射与动应力集中

本文采用边界无法对开孔无限大薄板弹性波的散射与动应力集中问题进行理论分析和数值计算。基于动力学功的互等定理建立了薄板弯曲波动问题的边界积分方程,应用Ｍａｔｈｅｍａｔｉｃａ软件首次推导了各影响系数的计算公式．最后,给出了圆孔附近的动应力集中系数的数值结果。     

三边简支一边固支矩形薄板动力屈曲解析解

根据板的动力平衡方程和压缩波前附加约束方程,基于双特征参数法和应力波理论,求解了三边简支一边固支矩形薄板在面内轴向冲击载荷作用下动力屈曲位移的解析解。揭示了矩形薄板动力屈曲过程中板的厚宽比、屈曲模态、冲击载荷大小和临界屈曲长度之间的关系。计算结果表明,由于横向惯性效应的存在,动力屈曲的临界载荷要比静力屈曲的大得多。     

薄板结构边界支承刚度的识别

本文用动态测试与边界元法数值计算相结合的方法来识别薄板结构的边界支承的刚度参数。薄板在给定的激励下,根据在薄板有限点上振动响应的测量值,利用结构边界积分方程的解析关系即可较准确地估算出边界支承的参数。在建立边界积分方程中,采用了近似基本解技术。通过算例,验证了方法的可行性和有效性,其识别精度对工程问题来说,是足够满意的。     

矩形薄板在面内撞击下动力屈曲的实验研究

利用Hopkinson压杆系统对矩形薄板在面内撞击下的动力屈曲进行了实验研究。结果表明矩形薄板存在屈曲后强度,在屈曲发生后面内载荷可以继续增加,通过记录屈曲发生的时间求得临界屈曲长度,并对实验模型进行了理论分析。对比分析结果表明,当压应力波向前传播一定距离后矩形薄板发生局部屈曲,得到的临界屈曲长度与理论计算结果吻合良好。     

弹性压应力波作用下矩形薄板动力屈曲解析解

根据板的非线性动力平衡方程和压缩波前附加约束方程,基于双特征参数法和应力波理论,求解了矩形薄板在面内轴向冲击载荷作用下动力屈曲位移的解析解。揭示了矩形薄板动力屈曲过程中板的厚宽比、屈曲模态、冲击载荷大小和临界屈曲长度之间的关系。求得的屈曲模态与之前文献中用差分解得出的结果吻合良好。     

弹性支承上边界转动约束矩形板屈曲分析

随着工程结构的轻型化、薄壁化,薄板结构稳定问题越来越受到重视,针对不同条件下薄板屈曲问题开展了大量研究。弹性支承上的薄板屈曲、边界弹性转动约束的薄板屈曲和刚性支承上边界转动约束的薄板屈曲问题已有相关文献,关于非加载边弹性转动约束、弹性支承上薄板屈曲问题的研究尚不充分。该文研究了非加载边弹性转动约束、均匀受压弹性支承矩形薄板弹性屈曲问题。由Ritz能量变分法得到了临界载荷计算公式,应用有限元分析证实了理论解的适用性。得到了屈曲半波数与板的纵横比、边界转动约束系数及支承刚度之间的关系式,支承刚度增加使屈曲半波数和屈曲系数增大。     

含孔复合材料点阵夹层结构数值计算方法及其影响因素

针对含孔复合材料点阵夹层结构在面内压缩载荷作用下的失效模式及其影响因素问题,通过实验对含孔复合材料点阵夹层结构失效模式进行了研究;基于3D Hashin准则和Chang-Chang刚度退化准则建立了含孔复合材料点阵夹层结构有限元渐进损伤失效分析模型,并将计算结果与实验结果进行了对比;基于有限元分析方法探讨了开孔形状、开孔率以及开孔位置对其极限承载力的影响。结果表明:当点阵夹层结构面板厚度较大时,含孔复合材料点阵夹层结构的主要失效模式为面板圧溃;通过对比有限元计算结果和实验结果,极限承载力的最大误差约为12%,失效位置与实验结果一致;当点阵夹层结构的对称面与载荷方向平行且孔的中心在对称面上时,面内压缩强度与开孔位置无关,主要受到开孔形状和开孔率的影响;当点阵夹层结构对称面与载荷方向垂直且孔的中心在对称面上时,边距大于一个胞元,面内压缩强度基本不变,边距小于一个胞元,面内压缩强度下降。     

弹性地基板的无界边界元—有限元耦合计算法

本文应用无界边界元－有限元耦合法对弹性地基上的薄板进行了计算。弹性薄板采用有限元离散，弹性半无限地基应用边界元离散，并应用无界边界元模拟半无限体表面的无限性，通过板与基础接触面位移和力的协调性（光滑接触），建立了弹性地基和板的综合算式。计算结果表明，本文方法具有工作量少、精度高等优点，非常适合于机场道面工程及其它基础工程。     

弹性圆薄板受迫振动的浑沌判据

本文用Ｍｅｌｎｉｋｏｖ－Ｈｏｌｍｅｓ方法研究了边界固定的弹性圆薄板可能发生浑沌振动的临界条件，文中提出了方法可以适用于具有各种边界条件和载荷工况的大量其它类似问题，也可以推广应用到圈底球扁壳的浑沌问题研究中去。     

复合材料层合板在非保守力作用下的动力稳定性

利用弹性非保守系统自激振动的拟固有频率变分原理,推导出复合材料矩形板受非保守随从力作用的变分方程,进而导出此问题的有限元基本方程及求解临界力和固有频率的特征方程。用载荷增量法计算了在多种边界条件下不同边长比的复合材料矩形板在面内受随从力作用的临界载荷,分析了不同角铺设方向及两种材料组合板的临界载荷。计算结果表明,边界条件对层合板的动力稳定性有较大影响,复合材料层合板的角铺设方向对临界载荷有较大影响。     

具有局部分层的对称铺设层合板在非保守力作用下的屈曲分析

利用弹性非保守系统自激振动的拟固有频率变分原理,推导出复合材料矩形板受非保守随从力作用的变分方程,进而导出复合材料层合板含分层损伤的有限元基本方程及求解临界荷载力和固有频率的特征方程。用载荷增量法计算了不同边长比的复合材料矩形板在面内受随从力作用且含有分层的临界载荷,分析了不同角铺设方向对临界载荷的影响。分析表明,分层对临界载荷有一定影响,复合材料层合板的角铺设方向对临界载荷有较大影响。     

Arbitrary loading problems of doubly symmetric regions containing a central crack

This paper presents a method of analysis of doubly symmetric plates with a central crack subjected to symmetric concentrated forces at points on the outer boundary. The problem is treated by using complex stress functions appropriate for the traction free crack and by means of a kind of boundary collocation method. The method is also valid for arbitrary loading problems, since the applied loads can be replaced by concentrated forces so far as the crack tip stress intensity factors are concerned.Numerical examples are given for elliptical and rectangular plates and plates of other configurations of practical importance. Results of rectangular plates give informations on experimental estimation of crack tip stress intensity factors in complex structures.     

Vibrational analyses of stiffened and unstiffened composite plates subjected to in-plane loads

Situations occur in which stiffened and unstiffened composite plates are required to withstand vibrational forces as well as in-plane stresses, consequently, to achieve good structural performance and an economical design, the plates must have high specific strength and stiffness. It is, therefore, necessary to undertake vibration and stability analyses and to design the system accordingly. The paper discusses the dynamic response of rectangular composite plates subjected to static in-plane compressive loads. To undertake the analyses, a finite element package was used to predict the dynamic behaviour and critical buckling loads of in-plane loaded plates; the latter had different aspect ratios. To verify the dynamic analytical analysis an experimental technique was used, however, the plates were not loaded to their critical load values. Relationships between the fundamental and six harmonic modes and the in-plane compressive loads for rectangular stiffened and unstiffened plates have been presented. The critical load values of the composite plates have been estimated from the stability and vibrational analyses.     

解Reissner板弯曲问题的一个新的边界元法

本文从虚功原理出发,以胡海昌导出的E、Reissner板弯曲理论归结为求解两个位移函数作为中间变量,推导出三个广义位移和三个广义力表示的边界积分方程。本文提出的方法适用于任意边界,任意载荷的薄板,中厚板弯曲。文未给出了固支。简支和自由三类边界的算例,均得到满意的结果。     

The critical velocities of a load moving on a floating ice plate that is subjected to in-plane forces

The critical velocities of moving loads over floating ice plates were determined by several authors. In all of these analyses it was assumed that the in-plane force field in the ice cover is zero. However, due to constrained thermal strains, in-plane forces do occur in the field. The purpose of the present paper is to determine its effect upon the critical velocities of the moving loads. It is shown that a uniform compression force field reduces the critical velocity whereas a tension force field has the opposite effect. Graphs are presented to show these findings.     

Buckling behavior of a central cracked thin plate under tension

The buckling characteristics of cracked plates subject to uniaxial tensile loads are analysed by the aid of the finite element method. Owing to the fact that crack buckling behavior is affected by the in-plane stress distribution around a crack, to get more accurate results, pre-buckling in-plane stress fields are analysed by the finite element method. For the critical loads calculation, the finite element approach adopted is based on Von Karman's linearize theory for buckling of plates subjected to pre-buckling state of plane stress. Several singular elements based on the Willian series are used in this plate bending approach. In this study, the effect of crack length, the effect of boundary condition, the effect of Poison's ratio and the effect of biaxial force on critical loads are analysed and discussed. Furthermore, the effect of initial imperfection is also discussed. There is a good agreement between other researcher's work and present results.     

Experimental study of dynamic buckling of plates under fluid–solid slamming

This paper describes the experimental investigation of the elastic–plastic dynamic buckling properties of rectangular plates under in-plane fluid–solid slamming. Based on the observation of elastic–plastic dynamic response characteristics of the plates, a dynamic buckling criterion and a dynamic yielding criterion are defined. The corresponding critical impulse are determined from the experimental results for each tested plate. The effect of different boundary conditions on the elastic–plastic dynamic buckling properties of plates is also examined. The results indicate that dynamic buckling always takes place elastically for the types of rectangular plates tested under fluid–solid slamming. The dynamic buckling modes of the plates are governed by the plate fundamental transverse free vibration mode. It is also found that boundary conditions strongly affect the dynamic buckling properties of plates subjected to fluid–solid slamming loads. Strengthening plate boundary constraint is a very effective way to enhance the plates’ ability to resist dynamic buckling.     

纤维增强复合材料层合板屈曲性态分析的边界元法

本文用边界元法分析了纤维增强复合材料正交各向异性层合板的屈曲性态。为了克服在用边界元法求解正交各向异性层合板屈曲时寻求相应的基本解的困维,本文采用了双重傅立叶级数和引用等效荷载的概念,建立了层合板屈曲临界荷载的特征方程。算例说明了本文方法的可行性和有效性。      

A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates

A new inverse trigonometric shear deformation theory is proposed for the static, buckling and free vibration analyses of isotropic and functionally graded (FG) sandwich plates. It accounts for a inverse trigonometric distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion obtained here are solved for three types of FG plates: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Closed-form solutions are obtained to predict the deflections, stresses, critical buckling loads and natural frequencies of simply supported plates. A good agreement between the obtained predictions and the available solutions of existing shear deformation theories is found to demonstrate the accuracy of the proposed theory.