Comparative perturbation studies of the elastica

Continuum, harmonic and finite-element perturbation studies of the elastica are presented and compared, each study yielding the first four post-buckling path derivatives from an exact non-linear energy formulation. In the exact continuum analysis the boundary conditions demand the “suppression of secular terms” and the four path derivatives are obtained in closed form. The discrete harmonic and finite-element modal analyses are based on a recently developed general branching theory and a concise and extended version of this is presented. In the harmonic analysis and corresponding to the form of the continuum solution the initial infinite series are found to be progressively truncated by certain orthogonality conditions and closed-form solutions agreeing with those of the continuum analysis are obtained. The solutions of the finite-element study are seen to converge rapidly to those exact values as the number of elements is increased. The exact post-buckling load derivatives are used to construct approximate series solutions for the post-buckling equilibrium path of the strut, and these are shown to converge to the complete solution for values of the lateral deflexion up to about one-quarter of the length of the strut. The continuum and discrete perturbation schemes are seen to have identical patterns and it is observed that the suppression of secular terms in the continuum theory plays precisely the same role as the contraction of the equilibrium equations in the discrete theory.     

碟形封头压力容器在内压作用下的弹塑性屈曲及后屈曲行为研究

基于ABAQUS对受内压碟形封头压力容器的弹塑性屈曲及后屈曲行为进行分析.通过非对称网格剖分技术诱发结构的屈曲行为,采用Riks算法捕捉完整的屈曲及后屈曲路径,分析屈曲载荷和后屈曲形态.计算结果表明,在内压作用下碟形封头压力容器过渡区域出现波状的分叉屈曲形态,随着加载的继续,过渡段将逐渐生成肉眼可视的褶皱,进入后屈曲阶段.后屈曲路径可以分为第一阶段与第二阶段.对引入初始厚度缺陷的结果分析可知,初始缺陷厚度的布置将对后屈曲路径产生影响,并降低结构的分叉屈曲载荷.     

Comparative study of thermal post-buckling analysis of uniform slender & shear flexible columns using rigorous finite element and intuitive formulations

Thermal post-buckling analysis of uniform, isotropic, slender and shear flexible columns is presented using a rigorous finite element formulation and a much simpler intuitive formulation. The ends of the columns are axially restrained to move and consequently any temperature rise above the stress free condition of the column produces an equivalent constant compressive mechanical load that causes the column to buckle at a critical temperature. Further increase in temperature beyond critical temperature results in the thermal post-buckling phenomenon. As a result of constraints imposed on the axial displacement at the ends of the column, the post-buckling phenomenon is governed by the von-Karman strain displacement relation applicable to one dimensional problems. Empirical formula for ratio of nonlinear axial load to critical load (equivalent constant mechanical load for a given temperature rise) as a function of the central deflection are obtained using both the rigorous finite element and intuitive formulations for various boundary conditions. The boundary conditions considered are the classical such as hinged-hinged, clamped-clamped and clamped-hinged conditions and nonclassical boundary conditions like the hinged-guided or the clamped-guided conditions. Post-buckling analysis results pertaining to nonclassical boundary conditions are meagre in the literature. It is observed that results obtained from both the formulations are in excellent agreement for all boundary conditions considered. Also the accuracy and simplicity of the intuitive formulation is aptly demonstrated to slender and shear flexible columns.     

A post-buckling analysis for isotropic prismatic plate assemblies under axial compression

This paper presents a post-buckling analysis for prismatic plate assemblies made of isotropic materials. The structures are assumed to consist of a series of long flat strips rigidly connected together at their edges, subjected to longitudinal in-plane compressive load. The buckling load and corresponding buckling mode of the structure are first obtained as the results of transcendental eigenvalue problems, which arise when exact solutions to the member differential equations are used to form the stiffness matrix of the plate assemblies. The other post-buckling field functions are also obtained analytically as exact solutions to the member differential equations. Results for the load end-shortening and load–deflection relationships for long prismatic plate assembly examples are obtained and compared with results obtained by other authors.     

Post-buckling behavior of poroelastic columns

The post-buckling behavior of poroelastic columns subjected to axial compressive forces is investigated. The fluid-saturated poroelastic columns are permeable in the longitudinal direction and impermeable in the transverse directions as a result of the microgeometry of the material. The time-dependent behavior of the columns is governed by three coupled equations, obtained using the large deflection theory. These equations are transformed into a single one, enabling the analytical derivation of the initial and the final responses. It is shown that unlike the quasi-static response obtained by using the small deflection theory, the long time response derived here is bounded. The imperfection sensitivity of these columns is also investigated.     

Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical shells with temperature-dependent material properties under thermo-electro-mechanical loads

Only static buckling of the hybrid functionally graded material (FGM) cylindrical shells has been investigated so far. In the present paper, dynamic buckling of imperfect FGM cylindrical shells with integrated surface-bonded sensor and actuator layers subjected to some complex combinations of thermo-electro-mechanical loads is investigated. The general form of Green's strain tensor in curvilinear coordinates and a high-order shell theory proposed earlier by the author are used. The complicated nonlinear governing equations are solved using the finite-element method. Buckling load is detected by a modified Budiansky's criterion proposed earlier by the author. Effects of temperature dependency of material properties, volume fraction index, load combination, and initial geometric imperfections on thermo-electro-mechanical post-buckling behavior are evaluated. Results reveal that the volume fraction index, temperature gradient, layer sequence, and the adaptive feedback control somewhat may affect the buckling load.     

基于ANSYS的管子车床主轴动力学分析

借助有限元分析软件ANSYS,对一种具有径向进给功能的管子车床主轴系统进行三维建模,然后选择六面体单元Solid95进行网格划分和模态求解,计算出主轴系统的前五阶固有频率及其振型,验证了主轴系统的固有频率远高于发生共振的临界频率。通过加减谐载荷,在模态分析的基础上进行谐响应分析,计算出主轴系统在激振力作用下的响应位移与响应应力,得到系统的动力响应与系统振动频率的曲线,即幅频曲线,验证了该主轴结构能经受住不同频率的各种正弦载荷。经过以上动态特性的研究,获得了机床主轴组件的动态参数,为机床主轴组件设计和结构改进提供了重要依据。     

Optimum shape for buckling and post-buckling behavior of a laminated composite panel with I-type stiffeners

A shape optimization of stiffener was conducted to increase buckling load or failure load with stiffened laminated composite panel of I-type under compression loading. Design variables are cap length, web length, and/or thickness under the constraint of volume constancy. The objective function is buckling load and failure load of post-buckling based on Tsai-Hill theory using ABAQLJS 5.8 for analysis and Optimizer on Broydon-Fletcher Goldfarb-Sharno Method and Augmented Lagrange Multiplier Method. The effects of relative length of a web and a cap of stiffener on buckling load and failure load of post-buckling were investigated with the results of optimum design.     

Effect of compressive axial load on forced transverse vibrations of a double-beam system

Based on Bernoulli–Euler beam theory, the forced transverse vibrations of an elastically connected simply supported double-beam system under compressive axial load are investigated. It is assumed that the two beams of the system are continuously joined by a Winkler elastic layer. The dynamic responses of the system caused by arbitrarily distributed continuous loads are obtained. The effects of compressive axial load on the forced vibrations of the double-beam system are discussed for two cases of particular excitation loadings. The properties of the forced transverse vibrations of the system are found to be significantly dependent on the compressive axial load.     

大挠度后屈曲倾斜梁结构的非线性力学特性

基于弹性梁的几何非线性大挠度屈曲理论,建立两端固定对称倾斜支撑梁结构的大挠度后屈曲控制微分方程,采用几何非线性隐式变形协调关系来表达强非线性超静定边值问题,得到描述倾斜梁大挠度后屈曲行为的精确解析解.采用数值方法求解含有第一、二类椭圆积分的强非线性微分方程,给出不同倾角梁结构从初始屈曲到后屈曲并发生两态跳转过程中的位形曲线及非线性刚度.根据最小能量原理和挠曲线拐点个数,分析对称屈曲模态与非对称屈曲模态之间相互跳转的内在联系及其对结构非线性刚度突变的影响,得到了屈曲模态之间的转换条件.跳转过程的数值仿真表明,倾斜支撑梁结构发生大挠度后屈曲时具有明显的双稳态特性且只出现低阶(1、2阶)屈曲模态,仿真计算结果与试验结果相一致.     

纤维增强FGM梁的自由振动和临界屈曲载荷分析

基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法（DTM）对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

裂纹扩展过程中电磁谐振疲劳试验系统动态特性分析*

电磁谐振疲劳裂纹扩展试验系统是一种工作在谐振状态下测试金属材料断裂特性的试验装置,要求在裂纹扩展过程中精确跟踪系统的固有频率和控制试验载荷,为达到这一目的,需要对裂纹扩展过程中系统的动态特性进行精确的分析。据此,建立3自由度有阻尼电磁谐振疲劳试验振动系统的数学模型,采用ANSYS有限元法计算CT紧凑拉伸试件的刚度,研究不同材料试件刚度、系统固有频率,试验载荷幅频曲线、共振振幅在裂纹扩展过程中的变化规律,并进行相关试验,试验结果表明：系统固有频率计算值与试验测量值之间的最大偏差为1.9 Hz;系统动态特性仿真结果与试验结果能够较好地吻合。该研究结果为电磁谐振式疲劳试验载荷的高精度控制提供了理论依据。     

Cross-sectional deformations of rectangular hollow sections in bending: Part II — analytical models

In this part, analytical models to predict the deflection of cross-sectional members such as flanges and webs are developed. The models are based on the deformation theory of plasticity along with the energy method, using appropriate shape functions capable of including the restraining effect of adjacent members. The present method provides explicit solutions of cross-sectional deformations prior to buckling, onset of buckling, as well as post-buckling deformations at different stages of bending. The predictions show that the suck-in of the tensile flange is closely related to geometry parameters, particularly the flange width. Plastic anisotropy appears to be the most significant material parameter. The width-to-thickness ratio tends to be the governing parameter with respect to buckling of the inner (compressive) flange. Also, the strain hardening of the material has a major effect on onset of buckling as well as post buckling deformations. Upon continued bending after buckling, the wavy deformation of the inner flange develops more rapidly than the more uniform deformation of the outer (tensile) flange. For relatively compact sections, however, the deformation mode of the compressive flange resembles that of the tensile flange without any typical buckling waves. There are also obvious interactions between deformations of different members. Comparing the theoretical predictions with the experimental results presented in Part I, a reasonably good agreement was found.     

Vibration reliability sensitivity analysis of general system with correlation failure modes

The vibration problem of the general system is the main object of research. The material properties and geometry of general system are random parameters because of the manufacturing environment, technical conditions, manufacturing and installation errors, multiphase materials, features and other factors. According to the relation criterion that the difference between the natural frequency and the driving frequency of general systems is not beyond a specific value, the vibration reliability mode and vibration reliability of general systems are defined considering the correlation of the multi-order natural frequency and the random characteristics of structure size and material, and the vibration reliability analysis method for avoiding the resonant is carried out. The second-order joint failure probability is obtained by using the numerical integration method. Based on the reliability design theory and sensitivity analysis method, the vibration reliability sensitivity of the general system with correlation failure modes is extensively discussed and a numerical method for vibration reliability sensitivity design is presented. The variation regularities of vibration reliability sensitivity are obtained and the effects of random parameters on vibration reliability of the general system are studied. The presented method provided the theoretic basis for the reliability design of the general system. A numerical example demonstrated that the proposed method is effective.     

力载荷下液体静压导轨的主动振动分析

以力载荷下的液体静压导轨为对象,建立了闭式导轨、开式导轨的主动振动模型,推导了系统的油膜刚度、阻尼系数的计算公式,计算了简谐、非简谐周期载荷下导轨系统的固有频率、幅值及相角,从理论上分析了设计参数对导轨系统的固有频率、幅值的影响。以闭式液体静压导轨为例,对导轨系统的固有频率、幅值放大系数进行了分析,结果表明：调整油腔压力、油膜厚度均可改变导轨系统的固有频率;力载荷作用下导轨的幅值放大系数基本上不受油腔压力的影响,而随油膜厚度的增大、油液温度的升高、载荷频率的降低而增大。详细地分析了力载荷下液体静压导轨的主动振动,为工程实际中减少导轨振动、提高加工精度提供了参考依据。     

Post-buckling and delamination propagation behavior of composite laminates with embedded delamination

Delamination occurred due to poor manufacturing process or in-service actions significantly affects the mechanical and failure behavior of laminated composite structures. In this study, the buckling and post-buckling delamination behavior of laminated composite with an embedded initial delamination under in-plane compression was studied experimentally and numerically. First, compression tests for laminated composite specimens with embeded initial delamination were performed and the buckling and delamination responses were obtained. Then the experimental test was numerically simulated using finite element methods with the progressive failure accounted for by using cohesive zone modeling. The load-displacement curve, strain behavior and delamination shapes of experimental specimens obtained from load cells, strain gages installed at different locations, and C scan images, respectively, were compared with the FEM results, and good agreements were attained. The effect of the buckling modes, laminate stacking sequence and shape of initial delamination on the buckling load and propagation behavior was studied by considering different ply stacking and shapes of initial delaminations. It was found that the buckling mode determined the growth direction of the delamination propagation, and the stacking sequence influenced the extent of the propagation area, while the orientation of the delamination affected the buckling loads.     

Eigensolution of a BTA deep-hole drilling shaft system

A numerical investigation is conducted to obtain the eigensolution of a deep-hole drilling shaft system. The rotating drilling shaft is modeled as a Rayleigh beam that conveys cutting fluid and is subjected to torque, compressive axial force, and support constraints. The governing equation of the drilling shaft system for lateral vibration is obtained by considering fluid-structure interaction, rotational inertia, gyroscopic effect, effect of motion constraints, and frictional damping generated by the surrounding fluid. The influence of cutting fluid flow velocity, rotational angular velocity, torque, compressive axial force, and support constraints on the natural frequency and stability of the drilling shaft system is examined. Cutting fluid flow velocity, compressive axial force, and torque decrease the natural frequency of the system, whereas rotational angular velocity and support constraints improve system stability.     

Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings

This paper describes the underlying theory, and a general-purpose computer program, VIPASA, for determining the critical buckling stresses or natural frequencies of vibration of thin prismatic structures, consisting of a series of plates rigidly connected together along longitudinal edges. Each plate may be either isotropic or anisotropic and may carry a basic stress system consisting of longitudinal and transverse direct stress combined with shear. The structure is assumed to be subjected to a “dead load” system which does not cause buckling; in addition a “live load” system, defined in magnitude by a single load factor, may be applied and the value of the load factor at buckling is determined. Alternatively the natural frequencies of vibration of the structure when subjected to the dead load system are determined. Any number of critical load factors or natural frequencies can be obtained. The theory is based upon the assumption that all modes are sinusoidal, in the sense that all three components of displacement vary sinusoidally along any longitudinal line, but phase differences are incorporated to allow for the effects of anisotropy and shear. Apart from this assumption no further approximations are made other than those inherent in thin plate theory.     

Nonlinear bending of Reissner–Mindlin plates with free edges under transverse and in-plane loads and resting on elastic foundations

A nonlinear bending analysis is presented for a rectangular Reissner–Mindlin plate with free edges subjected to combined transverse partially distributed load and compressive edge loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner–Mindlin plate theory considering the first-order shear deformation effect, and including the plate-foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the load–deflection curves and load–bending moment curves. Numerical examples are presented that relate to the performances of moderately thick rectangular plates with free edges subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, transverse shear deformation, loaded area, the plate aspect ratio and initial compressive load are studied. Typical results are presented in dimensionless graphical form.     

基于ANSYS/LS - DYNA的齿轮传动冲击特性仿真分析

以连续介质波动理论为基础,使用ANSYS/LS- DYNA有限元动力学仿真软件,建立了一对齿轮传动的冲击特性仿真模型,得到了在不同加载、初始条件下,参与啮合的每个轮齿齿面动载荷和齿轮啮合力随时间变化的曲线,以及被动齿轮的转速动态响应曲线,从而为齿轮的强度分析提供了可靠依据.