具任意脱层复合材料梁的非线性谐波响应

研究了具任意脱层复合材料梁的非线性谐波响应问题。基于弹性理论，建立了考虑剪切变形时的复合材料梁脱层的基本方程式。在空间上采用B样条函数和Galerkin积分法，在时间上采用增量谐波平衡法进行计算。通过实例计算，得出了简谐力作用下的非线性动力响应曲线。认为基谐波振动仍是非线性振动的主要部分。     

张力结构的非线性有限元分析

张力结构中的索结构分析通常采用非线性二节点直线或二次曲线单元，但是在大跨度结构，尤其是索弯顶结构的分析中，常用的单元已不能满足精度的要求，本文提出了考虑自重作用下有初始垂度的五结点非线性空间曲线元模型，放弃了一些特殊的假定，考虑了应变表达式中高阶量的影响，推导出了适合于弹性大位移几何非线性分析的Ｌａｇｒａｎｇｄ方程及其切线刚度矩阵，编制了相应的计算程序。     

非线性弹性基础上矩形板热后屈曲分析

给出非线性弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下的后屈曲分析。采用摄动——Ｇａｌｅｒｋｉｎ混合法给出完善和非完善矩形板热屈曲载荷和热后屈曲平衡路径。数值计算结果表明，非线性弹性基础上矩形板具有不稳定的热后屈曲平衡路径，且对初始几何缺陷是敏感的     

具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学行为研究

弹性梁结构作为一种基本单元被广泛于建筑、航空、航天、船舶等工程领域. 为有效降低弹性梁结构的振动水平, 深刻理解其振动特性、动力学行为显得尤为重要. 本文建立了具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学分析模型, 并采用伽辽金截断法预报梁结构的动力学响应. 在伽辽金截断法的求解过程中, 选取具有弹性边界约束的轴向载荷梁结构的模态振型函数作为伽辽金截断法的试函数与权函数. 首先, 研究截断数对伽辽金截断法稳定性的影响, 并采用谐波平衡法研究伽辽金截断法的可靠性. 在此基础上, 研究谐波激励扫频方向、非线性支撑参数对具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学响应的影响规律. 研究结果表明, 具有非线性支撑和弹性边界约束的轴向载荷梁结构的动力学响应具有初值敏感性且非线性支撑参数对梁结构动力学响应的影响显著. 相关非线性支撑参数使得梁结构出现复杂动力学行为. 合适的非线性支撑参数能够抑制具有非线性支撑和弹性边界约束的轴向载荷梁结构的复杂动力学行为并对梁结构边界处的减振具有有益效果.      

桁架结构几何大变形分析的精确方法

以往对桁架结构的大变形非线性分析,都是应用最小势能原理建立关于节点位移的非线性联立平衡方程,求解的工作量大,尤其对多自由度的大型复杂桁架更为突出.为了克服这个困难,本文采用两步交替迭代线性逐步逼近法,使平衡状态与变形状态协调统一,建立并求出变形后的平衡方程及其解.第一步,由已知杆件内力建立计算节点位移的连续方程并求解;第二步,由已知节点位移建立计算杆件内力的平衡方程并求解.通过多次迭代求得平衡状态与变形状态协调统一的非线性大变形分析的精确解.若干例题计算证明,本法是有效、精确的.尤其是对几何大变形桁架结构的优化设计,可将结构分析的迭代过程与优化过程相结合,省去了多次结构重分析的迭代过程,只在一次结构分析的迭代过程中即可完成优化设计,大大节省了时间.本法对扁桁架尤其有用.     

复杂结构热屈曲有限元分析

实现了机械载荷和温度载荷共同作用下复杂结构的弹性分歧热屈曲有限元分析，计算结果表明，局部温度场将使结构的屈曲强度大幅度降低。复杂结构的热屈曲研究具有理论和实际意义。本文研究成果表明，从计算结构力学角度出发，探讨强热源作用复杂结构引起宏观破坏机理研究的可行性。     

复杂结构热屈曲有限元分析

实现了机械载荷和温度载荷共同作用下复杂结构的弹性分歧热屈曲有限元分析，计算结果表明，局部温度场将使结构的屈曲强度大幅度降低。复杂结构的热屈曲研究具有理论和实际意义。本文研究成果表明，从计算结构力学角度出发，探讨强热源作用复杂结构引起宏观破坏机理研究的可行性     

桅杆结构静力分析简化计算方法

通过整体分析,推导出空间单索在任意荷载作用下的静力计算公式和空间索单元的非线性刚度方程,在此基础上,给出桅杆结构静力分析简化计算的非线性方程式。     

从刚体力学引出结构稳定性的几个基本概念

在材料力学、结构力学等课程的教学中,由于弹性力学理论本身过于复杂,压杆或结构的稳定性主要概念难以全面引入.本文通过刚体力学模型和能量法,引入了临界力、平衡路径分叉、非线性后屈曲平衡路径稳定性、临界点稳定性、缺陷结构稳定性等重要概念,由于模型简单导致了所有概念都可解析讨论,力学概念清晰,易于理解,供相关人员参考.     

非线性弹性地基梁在随动载荷作用下的屈曲和振动

基于可伸长梁的几何非线性理论,建立了非线性弹性地基上梁在随动载荷作用下的屈曲问题和振动问题控制方程,分别采用打靶法分析了弹性地基梁的后屈曲行为以及后屈曲构形上的振动问题。给出了不同非线性弹性地基系数下,梁在随动载荷作用下的过屈曲平衡路径曲线以及过屈曲附近前三阶频率随载荷变化的曲线。研究表明:立方刚度系数K_2对梁的屈曲和振动影响较小,而线性刚度系数K_1对梁的过屈曲性态和固有频率都有影响。     

支座位移非线性迭代法确定软管平衡形态

在海洋工程计算领域软管空间形态的非线性分析是特别复杂的课题,更加困难与令人易于受挫的研究方向是寻求软管在各种外荷载作用下软管的平衡形态。本文通过支座位移非线性迭代法结合空间梁结构非线性有限元分析理论加Newton-Raphson荷载增量法成功地解决了这一问题,并进行了相关的实验研究。边界条件考虑了固端约束与铰支约束,浮力既可分布作用也可集中作用在软管的任意位置。计算结果表示本文理论的正确性,在工程应用上具有重要的意义。     

受热复合材料层合板的非线性静动态响应分析

基于高阶剪切变形理论，突出考虑横向正应变和横向剪切应变的影响，对受热和外力联合作用下复合材料层合板的非线性静、动态响应进行分析。动态分析时计及了转动惯量的影响，给出了Ｃ°类有限元公式。文中数值算例同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性。文中还对层合反的边界条件、纵厚比及铺设角度对非线性动态响应的影响进行了分析。     

On an inverse problem of bending of a physically nonlinear inhomogeneous plate

An elastic plate with a physically nonlinear inclusion of an arbitrary shape is considered. This plate is subjected to pure bending under the action of transverse forces and bending moments applied at the external boundary of the plate. There are no loads distributed over the surface. The problem of finding external actions that provide a necessary uniform moment state in the inclusion, i.e., prescribed constant moments and curvatures, is formulated and solved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 104–107, September–October, 2007.     

半圆环截面细环壳的屈曲

本文由Sanders非线性平衡方程和Koiter小应变协调方程推导出细环壳的非线性微分方程和稳定方程。用伽辽金法求解了静水压或边界载荷作用下的半园环截面细环壳的稳定方程。对于不同的边界条件及一系列几何参数,计算得到了临界载荷及屈曲模态。     

Supercritical vibration of nonlinear coupled moving beams based on discrete Fourier transform

Natural frequencies of nonlinear coupled planar vibration are investigated for axially moving beams in the supercritical transport speed ranges. The straight equilibrium configuration bifurcates in multiple equilibrium positions in the supercritical regime. The finite difference scheme is developed to calculate the non-trivial static equilibrium. The equations are cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for non-trivial equilibrium configuration. Under fixed boundary conditions, time series are calculated via the finite difference method. Based on the time series, the natural frequencies of nonlinear planar vibration, which are determined via discrete Fourier transform (DFT), are compared with the results of the Galerkin method for the corresponding governing equations without nonlinear parts. The effects of material parameters and vibration amplitude on the natural frequencies are investigated through parametric studies. The model of coupled planar vibration can reduce to two nonlinear models of transverse vibration. For the transverse integro-partial-differential equation, the equilibrium solutions are performed analytically under the fixed boundary conditions. Numerical examples indicate that the integro-partial-differential equation yields natural frequencies closer to those of the coupled planar equation.     

Supercritical forced response of coupled motion of a nonlinear transporting beam

Steady-state periodic responses of nonlinear coupled planar motions are investigated for transporting beams in the supercritical transport speed ranges. The straight equilibrium configuration bifurcates into multiple equilibrium positions in the supercritical regime. The finite-difference schemes are developed to calculate the non-trivial static equilibrium and the steady-state response under simply supported or clamped boundary conditions. The forced vibration is assumed to be spatially uniform and temporally simple harmonic. Based on the long time series, the steady-state transversal amplitudes of nonlinear planar motions are recorded with changing load frequencies. A?resonance exists if the external load frequency approaches the fundamental frequency. The effects of material parameters and vibration amplitude on the resonance responses are investigated. The coupled planar model can be reduced to two nonlinear models on transversal vibrations, an integro-partial?Cdifferential equation and a partial?Cdifferential one. Numerical examples are displayed for the pros and cons between the two transversal models. It is also revealed that the increased axial speed converts the hardening-type behavior into the softening-type one.     

Bifurcation and chaos of the circular plates on the nonlinear elastic foundation

According to the large amplitude equation of the circular plate on nonlinear elastic foundation , elastic resisting force has linear item , cubic nonlinear item and resisting bend elastic item. A nonlinear vibration equation is obtained with the method of Galerkin under the condition of fixed boundary. Floquet exponent at equilibrium point is obtained without external excitation. Its stability and condition of possible bifurcation is analysed. Possible chaotic vibration is analysed and studied with the method of Melnikov with external excitation . The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.     

Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads

In the present study, the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analysed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a relatively large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Axisymmetric modes are included; indeed, they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetric deflection due to axial loads. A finite length, simply supported shell is considered; the boundary conditions are satisfied, including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid is investigated. The linear dynamic stability and nonlinear response are analysed by using continuation techniques and direct simulations.     

Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The nonlinear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge–Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance (10⁻⁵). The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.     

Direct method for analysis of flexible cantilever beam subjected to two follower forces

The static analysis of the flexible non-uniform cantilever beams under a tip-concentrated and intermediate follower forces is considered. The angles of inclination of the concentrated forces with respect to the deformed axis of the beam remain unchanged during deformation. The governing non-linear boundary-value problem is reduced to an initial-value problem by change of variables. The resulting problem can be solved without iterations. It is shown that there are no critical loads in the Euler sense (divergence) for any flexural-stiffness distribution and angles of inclination of the follower forces. In particular, if the follower forces are tangential, the rectilinear shape of the non-uniform cantilever beam is the only possible equilibrium configuration. In this paper some equilibrium configurations of the uniform cantilever under normal or tangential follower forces are presented using direct method.