复合受载下简支矩形板屈曲分析的微分求积法

为了精确求解复合受载下简支矩形板屈曲失稳的问题。推导简支矩形板无量纲屈曲微分方程,给出简支矩形板屈曲分析的微分求积计算格式。以单(双)向轴压作用下的简支矩形板为例,通过与解析解、有限元解对比验证微分求积法求解简支矩形板屈曲失稳问题的精确性。以轴压和剪应力作用下的简支矩形板为例,通过同解析解对比分析表明,当边长比r=1～5时,解析解与数值解间的差别较小;当边长比r=1/5～1时,解析解随方程数N的增大而逐步逼近数值解。     

Timoshenko梁单元的有限元屈曲分析程序解

为提高欧拉梁理论在梁类结构屈曲失稳载荷求解的适用性,提出了一种基于Timoshenko梁单元的数值求解方法。首先根据最小势能原理推导出了梁单元的弹性刚度矩阵与几何刚度矩阵,建立了有限元屈曲失稳求解方程,并采用Matlab软件对其进行数值求解程序的开发。通过将数值解与欧拉公式解进行对比分析验证表明,当梁柔度系数较大时,两者之间较小的相对误差验证了本文有限元程序解的精确性;当梁柔度系数较小时,两者之间相对误差较大。同时,从梁单元有限元理论角度,给出了两者相对误差产生的理论原因。最后,以欧拉公式解相对程序解的误差小于5%为基准,给出了不同边界条件下对应柔度系数的推荐值。     

局部矩形板剪切屈曲的数值仿真分析

针对剪应力作用下局部矩形板,屈曲失稳系数的数值解、解析解编程繁琐的问题,以简支边界条件为例,从力学基本原理出发,系统研究局部矩形板有限元屈曲分析时,限制刚性位移的约束边界条件及等效节点载荷的施加方式;同时,给出能量变分法解析求解剪应力作用下矩形板屈曲失稳系数的方程式。通过对比分析解析解、有限元数值解和其他数值解表明,当解析解方程数N增加时,解析解与其他数值解逐步逼近;当解析解方程数N不变、边长比r增加时,解析解与其他数值解间相对误差逐步增大,有限元数值解与其他数值解间相对误差较小。     

轴向运动粘弹性Rayleigh梁的参激振动稳定性

研究了轴向运动粘弹性Rayleigh梁参激振动的稳定性。根据广义哈密顿原理建立轴向运动Rayleigh梁横向振动的控制方程,同时考虑轴力的变化。采用多尺度方法直接求解控制方程,推导出主共振和组合共振的可解性条件;利用Routh-Hurwitz稳定性判据导出了稳定性边界方程;进而确定梁两端简支和固支边界条件下,因共振而产生的失稳区域。数值算例给出了两端简支和固支边界条件下弯曲刚度,支撑刚度,粘弹性系数以及平均速度对前两阶主共振及组合共振稳定性区域的影响。     

周期性弧形凸起凹凸板等效刚度的研究

根据构造正交各向异性周期性凸起结构凹凸板,研究了弧形凸起凹凸板的等效刚度。利用经典弹性薄板理论和板结构在宏观上周期性均匀化分布特性,推导出弧形凸起凹凸板等效刚度的解析公式。通过有限元数值分析模拟出集中载荷下四边简支弧形凸起凹凸板的数值结果,再与解析方法所求的计算结果对比,验证了等效刚度的合理性和精确性。然后利用本文解析方法计算出四边简支下弧形凸起凹凸板的固有频率,计算结果与有限元模拟结果一致,再次验证了刚度等效解析方法的正确性。提出的新方法能够较精确的计算出此类周期性凸起结构板的等效刚度,并具有直观简洁的优点,可以根据典型单元的几何参数直接计算,提高了求解效率。研究结果对其他类型周期性凸起凹凸板的静动力学进一步研究以及实际工程应用奠定了基础。     

有限元法在扭转杆计算中的应用

使用弹性力学解决扭转问题实际上就是求解偏微分方程组,很难得到解析解,有时甚至得不到解析解.为了克服弹性力学解决扭转问题的缺陷,采用有限元法来解决扭转问题,首先以三节点的三角形单元划分网格,并对应力函数进行插值,构造了可用于描述各个子域的场函数.然后利用最小余能原理推导出了扭转问题的泛函,通过求解泛函极值,得到了单元刚度矩阵,最后用Matlab编写了对应的程序用于模拟有限元计算过程.数值算例表明,随着网格的细化,数值解越来越精确,只要网格划分得当,有限元的解能够较好地逼近解析解.     

Y形横梁六维力/力矩传感器的应变分析

设计电阻应变式六维力/力矩传感器的前提是预知其弹性结构的应变分布,而传统的基于几何建模的有限元分析设计方法存在耗时长、效率低等问题。针对Y形横梁六维力/力矩传感器的弹性结构,提出一种高效、精确的解析分析方法。详细考察了该六维力/力矩传感器弹性横梁在各轴力/力矩载荷作用下的变形特征,基于铁木辛柯梁理论建立简化的力学模型,从而解析地得到各轴力/力矩载荷作用下弹性横梁中应变的显式表达式,与有限元模拟进行对比。结果表明:解析模型给出的预测结果与有限元数值解基本吻合,说明了该解析模型的正确性和有效性,从而为Y形横梁六维力/力矩传感器的设计提供了高效、精确的解析手段。     

变截面格构式结构轴压临界力的高效分析方法

变截面格构式结构为工程实际中常见的复杂杆系结构,为高效、准确地分析其轴压稳定性问题,利用三次样条函数建立变截面格构式梁单元的位移场,基于有限元插值理论推导变截面梁单元的切线刚度矩阵.通过静力凝聚法消除单元节点的曲率自由度,获得一种全新的两节点变截面格构式梁单元.基于该新型变截面格构式梁单元,采用有限单元法研究悬臂变截面格构式结构和中间等截面两端变截面的组合格构式结构在典型约束下的失稳临界力,并将计算结果与Timoshenko精确解进行对比.结果 表明,推导的变截面格构式梁单元是正确的和有效的,该新型梁单元可高效的应用于变截面格构式结构轴压临界力分析.     

基于空载侧隙与周向啮合刚度的谐波减速器啮合力研究

谐波减速器啮合力分布对其承载能力、传动效率、传动精度以及使用寿命有着重要的影响.为了更准确地描述负载状态下柔轮与刚轮之间的啮合状况,提出了一种基于空载侧隙和周向啮合刚度的解析模型.利用几何法计算出装配状态下的空载侧隙;建立并分析了负载条件下柔轮力学模型,得到了周向啮合刚度矩阵.根据空载侧隙和周向啮合刚度矩阵,迭代求解得到不同负载条件下啮合力的分布.建立有限元模型验证了解析模型的准确性,结果基本吻合.     

杆件轴力的一种识别方法

针对杆系结构中的轴力杆或索缆结构中的短索,提出了一种解析方法识别边界不确定杆件的绝对轴力,重点探讨了杆件抗弯刚度的影响.基于振动测试提取杆件的固有频率、位移模态或应变模态,以此构建特征方程进而识别其绝对轴力.数值算例分析表明,本方法在采用不同阶次的模态参数以及不同的杆件边界条件下都可取得相对误差3％以下的高精度识别结果,且在不测量杆件两端节点的有效长度、仅已知传感器之间的相对位置时即可实施.试验证实,基于加速度测量得到的前5阶模态参数都可基本准确地识别不同加载工况下杆件的绝对轴力,除小荷载外的多数工况都取得了相对误差10％以下的良好识别效果.     

Elastic lateral-torsional buckling of circular arches subjected to a central concentrated load

An arch under an in-plane central concentrated radial load is subjected to combined axial compressive and bending actions. When these combined axial compressive and bending actions reach a certain value, the arch may suddenly deflect laterally and twist out of its plane of loading and fail in a lateral-torsional buckling mode. This paper derives analytical solutions for the elastic lateral-torsional buckling load of pin-ended circular arches that are subjected to a central concentrated load, using the principle of stationary potential energy in conjunction with the Rayleigh-Ritz method. Analytical solutions of the buckling load for in-plane fixed and out-of-plane pin-ended arches and for the case of the load acting above or below the shear centre are also derived. The analytical solutions are compared with results of a commercial finite element package ANSYS and a finite element code developed by authors elsewhere for arches with different slendernesses, included angles, and cross-sections. The agreement between the analytical solutions and the finite element results is very good.     

Generalized buckling analysis of laminated plates with random material properties using stochastic finite elements

A generalized layer-wise stochastic finite element formulation is developed for the buckling analysis of both homogeneous and laminated plates with random material properties. The pre-buckled stresses are considered in the derivation of geometric stiffness matrix and the effect of variation in these stresses on the mean and coefficient of variation of buckling strength is studied. The mean buckling strength of plates under uniform stress assumption exactly matches with those reported in the literature. However, it is shown that the actual mean buckling strength of plates can be significantly different based on the pre-buckled stress analysis which depends on boundary constraints, principal material directions, aspect and thickness ratios of plates. The statistics of buckling strength is determined using a Taylor series expansion based mean centered first order perturbation technique. The stochastic finite element solutions obtained using layer-wise plate theory is also validated with analytical solutions presented in this paper. Parametric studies are conducted for different aspect ratios, ply orientations and boundary conditions.     

水平井中钻柱屈曲的非线性有限元分析

建立了直井中钻柱屈曲的平衡方程及对应的泛函表达式,使用有限元法对不同约束下水平井中钻柱从稳定到非线性屈曲的整个过程进行了分析。力学模型中考虑了重力和扭矩对屈曲的影响。分析结果表明:钻柱的屈曲是一个从局部屈曲到总体屈曲的过程,屈曲段的井壁约束力、钻柱弯矩和屈曲位移呈周期性变化;重力在水平井中对屈曲有较强的抑制作用;边界约束对屈曲的影响不可忽略;扭矩对屈曲的影响很小,可以忽略。     

Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods

In this paper, the buckling analysis of laminated composite plates reinforced by single-walled carbon nanotubes (SWCNTs) is carried out using an analytical approach as well as the finite element method. The developed model is based on the classical laminated plate theory (CLPT) and the third-order shear deformation theory for moderately thick laminated plates. The critical buckling loads for the symmetrical layup are determined for different support edges. The Mori-Tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight nanotubes. The effect of the agglomeration of the randomly oriented straight nanotubes on the critical buckling load is also analyzed. The results of analytical solution are compared and verified with the FEM calculations The critical buckling loads obtained by the finite element and the analytical methods for different layup and boundary conditions are in good agreement with each other. In this article, the effects of the carbon nanotubes (CNTs) orientation angle, the edge conditions, and the aspect ratio on the critical buckling load are also demonstrated using both the analytical and finite element methods.     

Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method

The buckling of thin rectangular plates with nonlinearly distributed loadings along two opposite plate edges is analyzed by using the differential quadrature (DQ) method. The problem is considerably more complicated since it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses, and then the buckling problem be solved. Thus, very few analytical solutions (the only one available in the literature is for rectangular plates with all edges simply supported) have been available in the literature thus far. Detailed formulations and solution procedures are given herein. Nine combinations of boundary conditions and various aspect ratios are considered. Comparisons are made with a few existing analytical and/or finite element data. It has been found that a fast convergent rate can be achieved by the DQ method with non-uniform grids and very accurate results are obtained for the first time. It has also been found that the DQ results, verified by the finite element method with NASTRAN, are not quite close to the newly reported analytical solution. A possible reason is given to explain the difference.     

Improved flexural–torsional stability analysis of thin-walled composite beam and exact stiffness matrix

A simple but efficient method to evaluate the exact element stiffness matrix is newly presented in order to perform the spatially coupled stability analysis of thin-walled composite beams with symmetric and arbitrary laminations subjected to a compressive force. For this, the general bifurcation-type buckling theory of thin-walled composite beam is developed based on the energy functional, which is consistently obtained corresponding to semitangential rotations and semitangential moments. A numerical procedure is proposed by deriving a generalized eigenvalue problem associated with 14 displacement parameters, which produces both complex eigenvalues and multiple zero eigenvalues. Then the exact displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently exact element stiffness matrices are evaluated by applying member force–displacement relationships to these displacement functions. As a special case, the analytical solutions for buckling loads of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, the numerical, analytical, and the finite element solutions using the Hermitian beam elements are presented and compared with those from ABAQUS's shell elements. The effects of fiber orientation and the Wagner effect on the coupled buckling loads are also investigated intensively.     

Application d'un modèle de flambement conditionné à la pose des câbles à fibres optiques

Application of a conditioned buckling solution to the laying of optical cables. Mechanical behaviour of cables submitted to an axial compressive load is subjected to buckling instabilities due to their length compared with their diameter. In some cases rigid walls modify the boundary conditions during the loading or the buckling phenomenon, it will be called conditioned buckling. This paper presents the buckling of a homogeneous cable in a horizontal circular rigid duct subjected to its own weight and an axial compressive load. Buckling load and pitch associated to sinusoidal and helical buckling are determined as transmission of axial load during buckling. A finite element simulation is computed and comparisons are made with the analytical solution. A direct application to the optical fibre cable laying in underground duct is made and experimentation is conducted with a life-sized bench designed at the LM ² S of the ENSAM of Paris and located at the CNET Lannion. Comparisons between experimental and analytical results are presented.     

Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM

The critical compressive load in the buckling of circular and annular composite plates reinforced with carbon nanotubes (CNTs) is calculated using finite element method. The developed model is based on the third-order shear deformation theory for moderately thick laminated plates. Effects of CNTs orientation angles and thickness-to-inner radius ratio on the buckling of composite plates are discussed. The results are compared with those obtained by analytical method based on classical plate theory. The finite element method shows lower values for critical buckling load because of the elimination of shear strain in the classical plate theory.     

Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations

The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.     

基于有限单元法的渐开线斜齿轮静力学特性分析

基于ANSYS建立渐开线斜齿轮有限元模型,确定斜齿轮静力学有限元分析的边界条件,讨论了主动轮在不同周向力矩作用下主动轮和从动轮的静力学特性。结果表明运用有限单元法可以准确地分析斜齿轮的静力学特性,对准确地掌握齿轮应力的分布特点和变化规律具有重要的意义。