悬臂矩形板在对称边界荷载下的屈曲

本文用变分法对悬臂矩形板在对称边界荷载下的稳定性进行研究.我们将对在悬臂矩形板的一对相对的自由边作用有不同的对称边界荷载时,求出薄板的最小临界力.文中分别讨论了有一对集中力,均布荷载,局部均布荷载,三角形分布荷载及一对集中力偶作用之下悬臂矩形板发生屈曲时的最小临界荷载.     

悬臂板侧屈中的几个问题

本文用能量法研究悬臂矩形板侧向屈曲中的几个问题.文中分别讨论了有集中力,均布荷载,三角形分布荷载及集中力偶作用之下悬臂矩形板发生侧向屈曲时的最小临界荷载.     

矩形板不对称侧向屈曲中若干问题

本文用能量法研究了矩形板不对称侧向屈曲的几个问题,文中讨论了具有不对称支承的矩形板分别在有集中力,均布荷载及集中力偶作用之下发生不对称侧向屈曲时的最小的临界荷载.     

矩形板大挠度问题的样条函数解

本文以中心挠度为摄动参数,将矩形板大挠度问题的非线性偏微分方程缉转化为几个线性的偏微分方程组,然后分别用样条有限点法和样条有限元法求解,得到了在多种边界条件下具有任意长宽比的,受均布荷载的矩形板的解答,给出了板中面的位移、挠度的解析表达式;并编制了相关的计算机程序.计算的结果与现有的其他理论的结果作了比较,表明本文的结果是良好的.     

双向压缩简支矩形板后屈曲平衡路径的迭代算法*

本文从von Kármán板大挠度方程出发,在双重三角级数解的基础上,提出一种简单、快速和有效求解双向压缩简支矩形板后屈曲平衡路径的迭代算法.     

矩形板屈曲和后屈曲弹塑性分析

本文以摄动法给出了矩形板屈曲和后屈曲全过程的弹塑性分析. 本文同时讨论了初始几何缺陷对矩形板后屈曲性态的影响.计算结果表明,矩形板非弹性屈曲对初始缺陷是敏感的.计算结果与实验结果的比较表明二者相当一致.     

矩形板在横向压力和面内压缩共同作用下的后屈曲

本文从Kármán板大挠度方程出发,先用Galerkin法将横向载荷作用转化为初挠度影响,然后以挠度为摄动参数,采用直接摄动法研究简支矩形板在横向载荷与面内压缩共同作用下的后屈曲性态.本文讨论了两种面内边界条件,同时计及板初始几何缺陷的影响.计算结果与实验结果的比较表明二者是一致的.     

中厚板的弹性屈曲和后屈曲

本文采用Reissner假定考虑横向剪切变形的影响,导出弹性矩形板大挠度方程.本文讨论考虑横向剪切变形的矩形板的弹性屈曲和后屈曲.采用文[8]提供的摄动方法,给出了完善和非完善中厚板的后屈曲平衡路径,并与经典薄板理论结果进行了比较.     

简支夹层矩形板的非线性弯曲

本文应用变分法导出了具有软夹心的夹层矩形板的非线性弯曲理论的基本方程和边界条件.然后,使用摄动法研究了均布横向载荷作作用下简支夹层矩形板的非线性弯曲问题,得到了相当精确的解析解.     

一边固定及一角点支承的矩形板在均布荷载作用下的弯曲解

本文采用叠加法求出一边固定及一角点支承的矩形板在均布荷载作用下的弯曲解答,计算表明这种解法收敛速度快,计算精度高。     

Buckling and lateral buckling interaction in thin-walled beam-column elements with mono-symmetric cross sections

Effects of axial forces on beam lateral buckling strength are investigated here in the case of elements with mono-symmetric cross sections. A unique compact closed-form is established for the interaction of lateral buckling moment with axial forces. This new equation is derived from a non-linear stability model. It includes first order bending distribution, load height level and effect of mono-symmetry terms (Wagner’s coefficient and shear point position). Compared to the so-called three-factors (C₁–C₃) formula commonly employed in beam lateral buckling stability, another factor C₄ is added in presence of axial loads. Pre-buckling deflection effects are considered in the study and the case of doubly-symmetric cross sections is easily recovered. The proposed solutions are validated and compared to finite element simulations where 3D beam elements including warping are used. The agreement of the proposed solutions with bifurcations observed on the non-linear equilibrium paths is good. Dimensionless interaction curves are dressed for the beam lateral buckling strength and the applied axial load, where the flexural-torsional buckling axial force is a taken as reference.     

Optimal design of multi-purpose beam-columns

The paper deals with the optimal design of an elastic pinended member of given volume that is to serve as a beam for a part of its design life and as a column for the rest. The optimal design can be interpreted in two ways. Firstly, it is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection as a beam. Secondly, it is the design that has the least deflection as a beam under a midspan concentrated load, subject to a minimum permissible Euler buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.     

集中载荷作用下开顶扁球壳的非线性稳定问题

本文使用修正迭代法研究了具有硬中心的边缘固定的开顶扁球壳在中心集中载荷作用下的轴对称非线性稳定问题,得到了决定上、下临界载荷的二次近似解析公式.     

Comparison of classical Winter's bracing requirements of compressed truss chord with stability analysis of 3D truss-model

Most code requirements concerning bracing are based on principles developed by Winter. The present research is devoted to study a lateral buckling of truss with linear elastic side supports. The classical Winter's model of truss chord in the case of out of the truss plane buckling is compared with nonlinear analysis of 3D truss model. Full bracing condition, that permits the truss chord to support load level corresponding to an unbraced length equal to the distance between braces is calculated. Then an approximate buckling load with less than full bracing is developed and the model is modified to account for unequal normal force distribution in compressed chord. The coefficient of buckling length related to side support distance in function of bracing stiffness is also calculated. The results are compared to design code requirements. It is shown that buckling length of truss chord with side supports considered as elastic elements is larger than assumed in design codes. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analytical approach for postbuckling of eccentrically or concentrically stiffened composite double curved panel on nonlinear elastic foundation

This paper presents a detailed analytical investigation on the buckling and postbuckling behavior of laminated composite double curved panels with eccentrically and/or concentrically ortho-grid stiffeners subjected to in-plane compression, lateral pressure, thermal environment, and combined loads. The panels are surrounded by three parameter elastic foundations. Different types of simple-supported boundary conditions are considered. The equilibrium and compatibility equations of panel are derived based on Kirchhoff assumptions incorporating nonlinear von-Karman relations. The stress function and Galerkin method are applied to obtain explicit expressions of the buckling load and load-deflection relations. New results are presented to show effects of the combined loads, position of stiffener, and elastic foundation. As a key finding of these results, the buckling load and the postbuckling curves of concentrically stiffened panels are higher than eccentrically stiffened panels.     

Exploration of the encased nanocomposites functionally graded porous arches: Nonlinear analysis and stability behavior

This paper explores the nonlinear stability mechanism of the functionally graded porous (FGP) arch reinforced by graphene nanocomposites. Both the pores and the nanocomposites are distributed symmetrically to the mid-surface of the arch but not uniformly in the cross-section so that the bending stiffness can be best improved. The arch is confined in an elastic medium with a radially-pointed concentrated load at the crown position. The confinement of the medium results in a symmetrical deformed shape of the arch, which can be described by an admissible displacement function. Associated with the thin-walled arch theory and the principle of minimum potential energy, analytical predictions are obtained to express the critical buckling load, as well as the hoop force and bending moment. Subsequently, a numerical model is developed to simulate the medium and the arch in ABAQUS software. By introducing the modified arc-length method, the equilibrium paths of the encased arch are traced. After comparison in terms of the critical buckling load and the equilibrium paths, it is found the numerical results are in good accordance with the analytical solutions. Finally, particular attention is paid to the parameters that may impact the buckling load, such as the porosity coefficient, the weight fraction, the central angle, the geometry of the Graphene platelets (GPLs) et al.     

非均质材料梯度多墙结构非线性屈曲特性

非均质、各向异性材料梯度多墙结构充分利用了材料性质连续、渐进、变化的物理力学性能,现已广泛应用于飞行机翼结构和汽车轻量化结构．在层合板屈曲理论的基础上,针对梯度多墙结构这一具体结构形式,采用当量刚度方法,建立了相应的本构关系和非线性屈曲控制方程,求解得到不同复杂边界条件及组合载荷下的屈曲临界载荷,通过试验分析验证,计算结果可以较好地满足工程设计．研究结果表明:梯度材料能有效地减小界面中的应力集中,减弱材料中初始缺陷的作用,从而不同程度地提高了材料的强度和韧性．     

Stability and vibration analysis of axially-loaded shear beam-columns carrying elastically restrained mass

Classical shear beams only consider the deflection resulting from sliding of parallel cross-sections, and do not consider the effect of rotation of cross-sections. Adopting the Kausel beam theory where cross-sectional rotation is considered, this article studies stability and free vibration of axially-loaded shear beams using Engesser’s and Haringx’s approaches. For attached mass at elastically supported ends, we present a unified analytical approach for obtaining a characteristic equation. By setting natural frequencies to be zero in this equation, critical buckling load can be determined. The resulting frequency equation reduces to the classical one when cross-sections do not rotate. The mode shapes at free vibration and buckling are given. The frequency equations for shear beam-columns with special free/pinned/clamped ends and carrying concentrated mass at the end can be obtained from the present. The influences of elastic restraint coefficients, axial loads and moment of inertia on the natural frequencies and buckling loads are expounded. It is found that the Engesser theory is superior to the Haringx theory.