求框架临界荷载的新方法

以往求框架结构临界荷载的方法,都是假定杆件轴力与外力成比例变化。但是当框架结构受有横向荷载作用时,由于P-△效应,轴力与外力不是成比例变化的。本文由此提出新的框架结构求临界荷载的方法,并和通常的方法做了比较,在理论上比较完善,也有实用意义。     

选取最大载荷为岩石KIC测试中临界载荷的合理性研究

本文对选取最大载荷为岩石 K_(IC)测试中临界载荷的合理性从理论上和实验上进行了研究,结果表明,选取最大载荷为岩石 K_(IC)测试中的临界载荷是合理的,正确的。     

Variational Derivative for Buckling Loads of Beams and Frames

The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative. By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained. The performance of this formulation is verified by comparison with numerical examples in the literature __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005.     

轴向冲击载荷作用下直杆弹性动态屈曲的研究

本文利用分叉的概念,从应力波理论出发,把轴向冲击载荷作用下直杆的弹性动态屈曲问题化为特征值问题,从而导出直杆动态屈曲的临界分叉准则。同时,本文对一端固支直杆受轴向冲击时的弹性屈曲问题进行了实验研究,测到的临界屈曲时间和理论预计值基本符合,证实了理论模型的合理性.理论和实验两方面的结果都表明,直杆受轴向冲击载荷作用时的屈曲现象发生在波动过程的前期,因此在处理这类问题时考虑波动效应是必要的。     

金属蜂窝材料的弹塑性屈曲临界应力值

本文参考Hexcel公司生产的各种规格的金属蜂窝芯,讨论了金属蜂窝芯夹层板承受单轴面外压力时的屈曲模式,发现大多数商用金属蜂窝夹层板受到面外压力作用时发生弹塑性屈曲。基于二维蜂窝结构的代表性单元,建立了金属蜂窝材料弹塑性屈曲的力学模型,进而推导出其临界应力显式公式。该公式反映了蜂窝材料的几何特征及其母材的力学性能,并通过单参数表征金属蜂窝材料的弹塑性屈曲特性。本文还探讨了相对密度和开度角对金属蜂窝材料弹塑性屈曲值的影响规律。最后,通过与已有理论结果和实验结果的比较证实：本文采用的屈曲模式合理,与实验测定值符合较好表明理论预测公式有一定应用价值。     

The Effect of Multiple Buckling Modes on the Postbuckling Behavior of Plane Elastic Frames. Part I. Symmetric Frames

The postbuckling behavior of a one-bay, two-storey frame with built-in edges and symmetric with respect to midspan is analyzed. Columns are assumed to be inextensible and shear-undeformable, and beams are rigid. Then two buckling modes are possible, that is, sidesway of the lower floor with rigid horizontal displacement of the top floor and sidesway of the top floor with the lower floor undergoing no displacement. Obviously, the two buckling modes occur simultaneously if the ratios EI/h⁷ (EI being the bending stiffness of a column and h its length) are properly selected. Within the framework of a Koiter-type energy approach a suitable perturbation formulation is derived from a “hybrid” functional which is obtained by adding to the potential energy certain extra terms which account for the nonlinear energy associated with the internal forces applied to the beam at the joints. Results show that the postbuckling behavior of a single buckling mode can be stable or unstable according to the value of the ratio h/l, where l is the frame span. In the case of simultaneous buckling modes the structural behavior in the postbuckling range never improves, but no severe changes are noticed in comparison with the preceding case.     

The Effect of Multiple Buckling Modes on the Postbuckling Behavior of Plane Elastic Frames. Part II. Asymmetric Frames

The postbuckling behavior of an asymmetric one-bay, two-storey frame with clamped edges is analyzed. Columns have different bending stiffnesses and are pairwise of the same length. By assuming columns to be inextensible and shear undeformable, and beams to be rigid, two buckling modes are possible which are described by the sidesway of the lower floor with a rigid horizontal displacement of the upper floor and a sidesway of the upper floor, the lower floor undergoing no displacement. By properly selecting the ratios EI/h² (EI being the bending stiffness of a column and h its length) the two buckling modes may occur simultaneously. A third buckling mode is also possible which is characterized by no displacement of the horizontal beams and local deflection of one or more columns in the shape of a beam with fixed edges. This third case will not be considered in this paper. The Koiter general nonlinear theory of elastic stability recast in a form convenient for the development of finite elment models along lines similar to the recent presentation by Budiansky has been employed in the analysis. Nonlinear constraints on the field variable φ (φ being the cross-section rotation) are accounted for by means of Lagrangian multipliers. Results show that the postbuckling behavior of a single buckling mode is always asymmetric unstable and depends both on the degree of asymmetry of the structure and on the ratio h/l, l being the frame span. The occurrence of simultaneous buckling modes exacerbates the imperfection sensitivity of the structure.     

纳米薄膜屈曲模式的实验研究

薄膜/基底系统在信息科学以及微电子机械系统中有着十分重要的地位.薄膜中常会有压或拉的残余应力,因此薄膜/基底结构通常是工作在残余应力以及外加应力的联合作用下.根据结构的功用不同,其载荷方式也有不同,从而也导致了不同的破坏模式.压缩载荷下的脱粘屈曲是薄膜基底结构主要的破坏形式之一.本文使用磁控溅射镀膜技术,制作了压缩薄膜...     

限制失稳模态方程及约束载荷计算

针对受压限制失稳结构,利用点接触、线接触屈曲模型,建立了杆在各种屈曲模态下的挠度曲线方程.通过求解曲线方程,可以得到发生限制失稳结构在各种屈曲模态下,与外部限制失稳构件之间的接触载荷大小,分析了受压结构与限制失稳构件之间的间隙对接触载荷的影响.通过对屈曲模态中各波形的形态进行调整,研究了同一屈曲模态,不同失稳波形下接触载荷的差异.     

The Effects of Initial Curvature and Other Parameters on the Nonlinear Buckling of Simple Frames*

In this investigation a nonlinear variational analysis is performed on a simple two-bar frame with initially crooked bars that is subjected to an eccentrically applied load at its joint. The influence of crookedness may be detrimental or beneficial, depending on the manner of design of the frame. It is also found that for some critical value of crookedness, the frame does not buckle elastically. Moreover, it is shown that for some characteristic values of the length ratio and moment of inertia ratio of the two bars, the load-carrying capacity of the frame becomes maximum. Finally, the combined effect of the aforementioned parameters is discussed     

An Algorithm for Computing Critical Buckling Loads of Elastic Structures

The algorithm presented enables one to calculate the number of critical buckling loads of an elastic structure which lie below any specified total load, and hence to converge on all required buckling loads with ease and certainly. The algorithm is always valid when the total load is applied proportionally, it is also valid for nonproportional loading, subject to a single restriction.

The algorithm applies to continuous structures, as well as to structures with a finite number of degrees of freedom. It is based on a stiffness matrix analysis and substructures can be used.     

Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures

Localization phenomena in one-dimensional imperfect continuous structures are analyzed, both in dynamics and buckling. By using simple models, fundamental concepts about localization are introduced and similarities between dynamics and buckling localization are highlighted. In particular, it is shown that strong localization of the normal modes is due to turning points in which purely imaginary characteristic exponents assume a non zero real part; in contrast, if turning points do not occur, only weak localization can exist. The possibility of a disturbance propagating along the structure is also discussed. A perturbation method is then illustrated, which generalizes the classical WKB method; this allows the differential problem to be transformed into a sequence of algebraic problems in which the spatial variable appears as a parameter. Applications of the method are worked out for beams and strings on elastic soil. All these structures are found to have nearly-defective system matrices, so their characteristic exponents are highly sensitive to imperfections.     

加筋板的非线性相关屈曲研究

本文将线性样条有限条理论推广到大挠度弹塑性范围,建立了样条有限条非线性分析方法,成功地分析了纵向加筋板结构局部与整体稳定相关作用对其极限承载能力的影响.采用弧长法和Newton-Raphson迭代求解非线性刚度方程,可获得包括峰值点在内的一条完整的荷载—挠度曲线.分析中考虑了加筋板结构的初曲和残余应力的影响,使得计算结果更具实用价值.     

柱状电极屈曲或裂纹扩展的临界力学参数研究

柱形结构电极是近年来使用最为广泛的锂电池电极结构之一.本文以硅材料细长柱形电极为例,研究了充电电流大小、电极长径比、初始裂纹长度以及断裂韧性对于电极的屈曲现象和裂纹扩展现象发生时间的影响.计算结果表明,屈曲与裂纹扩展现象出现的先后顺序与充电电流大小无关;具有小的长径比,大的初始裂纹长度以及较小断裂韧性的电极,裂纹扩展比屈曲现象更早发生.对于硅材料,不同长径比的电极具有不同临界断裂韧性值,当材料的断裂韧性小于该临界值,在锂化过程中裂纹扩展会先于屈曲现象发生;该临界断裂韧性值随初始裂纹长度的增加而增加.本文的结论对于电极的结构设计以及材料选取具有一定指导意义.     

多级载荷下疲劳寿命的可靠性研究

本文利用断裂力学，疲劳及可靠性分析方法，讨论了剩余强度的概率分布。假定裂纹萌生阶段已结束，在裂纹扩展阶段。剩余强度R与裂纹长度α满足R=αK，α^-1/2，裂纹扩展速率可用Paris公式da/dN=c(△K）^n描述，在以上两个公式的基础上，我们推导出了疲劳载荷过程中剩余强度，循环应力，疲劳寿命及失效概率间的关系。选用变速箱齿轮12Cr2Ni4钢制成的试样，我们在Amsier HFP5100高频疲劳试验机上，两级循环应力水平下进行了9组试验，得出了12Cr2Ni4钢的P-R-S-N曲线。利用该曲线估算了12Cr2Ni4钢多级载荷下的疲劳寿命。同Mine准则计算的结晶相比更接近真实值，本文的方法具有较强的工程实用性，对承受疲劳载荷零构件的选材及设计具有重要的参考价值。     

轴向瞬间阶梯载荷下圆柱壳动力屈曲的双特征参数分析

对于轴向瞬间阶梯载荷下圆柱壳的弹性非轴对称动力屈曲问题，将临界应力和屈曲惯性项指数参数作为双特征参数求解。由能量转换和守恒准则，导出压缩波阵面上的屈曲变形附加约束条件。失稳控制方程、边界条件和波阵面上的连续条件，连同此附加约束条件构成求解两个特征参数和动力失稳模态的完备定解条件。由伽辽金法得出求解双特征参数问题的数值方法。     

考虑剪切效应时压杆临界载荷的新数值方法

熟知,计入剪切效应时压杆临界载荷的求解归为某些常微分方程的特征值问题,本文提出一种求解该种问题的新数值方法.此种方法的思想是基于将特征值问题转化为同一方程的初值问题,要点为:(1)首先在积分始端取一个补充的初值,(2)又取一个暂设的特征值,(3)数值求解此微分方程的一个初值问题,(4)多次试凑和改变暂设特征值,让终端条件得到满足.数值算例已在文中给出.