局部加强体对预压双稳态结构跳转力学特征的影响分析

基于轴向挤压后屈曲模态的双稳态结构,其跳转力、保持力和跳转行程等双稳态特征与预应力分布和后屈曲模态密切相关,使得难以通过仅调整预压缩量来实现特定双稳态指标的设计。本文提出引入局部加强体调控预压双稳态梁临界屈曲载荷、应力分布及跳转特征的方法,建立了具有对称局部加强体的预压双稳态梁跳转分析模型,分析了预应力、加强体尺寸参数和位置对屈曲临界载荷、跳转力和行程的影响规律。结果表明:局部加强体不影响原结构跳转力和保持力相等的特征;与尺寸参数相比加强体位置参数对跳转力有较大影响,随着位置的变化,跳转力存在由大变小再变大的变化过程,且调控同行程双稳态梁跳转力的幅度可达17.04%;跳转行程主要依赖于局部加强体的刚度和所承受的预应力。     

小方坯连铸机振动装置支撑梁的设计与分析

采用钢结构梁作为振动装置支撑梁,不仅结构简单,而且方便实用.文中根据连铸机振动装置支撑梁的设计,采用有限元方法对其强度、刚度进行计算,并分析了支撑梁的模态,得到结构合理的振动装置支撑梁.     

电除尘器壳体的整体承载性能分析

研究电除尘器壳体结构的空间整体承载性能。用有限元方法进行壳体结构的特征值屈曲分析。根据壳体的施工和使用过程,考虑加载路径的影响,分三步施加荷载,进行完善壳体的承载能力非线性分析。将特征值屈曲模态和完善壳体结构的非线性极值点变形模态作为初始缺陷模态,进行带缺陷壳体的承载力非线性分析。特征值屈曲分析表明,结构的前60阶屈曲模态均为发生在立柱连接腹板、墙板和顶板的局部屈曲。完善壳体的非线性分析表明,结构的破坏主要由隔宽柱的弹塑性局部屈曲引起。带缺陷壳体的非线性分析表明,壳体对中间隔宽柱连接腹板上多处局部初始几何缺陷最为敏感,可使其承载力严重降低。电除尘器壳体的空间整体刚度较大,不会出现整体失稳破坏。壳体的失效是源于单个构件的破坏。单个构件失效后,壳体内不会发生内力重分布。工程中现行的平面分析设计方法是合理可行的。     

用渐进摄动法对具有二次非线性项的多自由度系统摄动分析

考虑大挠度几何非线性和剪切变形的影响,工程中机械柔性板壳结构的非线性动力学运动控制方程经常被转化为二阶模态的、包含有二次和三次非线性项和外激励的非线性常微分方程,由于二次非线性项的存在,常用的多尺度法进行摄动分析时,需要复杂的运算才能将其包含进来。相比之下,基于傅里叶扩展和时间尺度的渐进摄动法可以较容易地将非线性动力学微分方程中的平方项考虑进来。通过引进适当的尺度变换,利用渐进摄动法对该系统在二阶模态之间发生1:2内共振、主参数共振、1/2亚谐共振时进行摄动分析,得到自治系统下的平均方程。数值结果发现4自由度自治系统存在复杂的周期运动、倍周期运动、概周期运动。该非线性系统为量纲一后的结果,对于与该系统类似的多自由度非线性机械系统可以直接用此平均方程进行全局分叉和混沌动力学研究。     

超起拉索非保向力作用下伸缩臂几何非线性分析

为获得超起拉索非保向力作用下伸缩臂结构几何非线性变形的理论解,将具有超起装置的伸缩臂受力模型等效为弹性支撑条件下的多级伸缩臂模型.基于小变形理论建立空间对称双拉索多级伸缩臂的静力平衡方程,推导计及轴力二阶效应的多级伸缩臂结构臂端挠度的递推表达式.以具有超起装置的伸缩臂结构为例,分析其在轴力、侧向力和弯矩作用下的几何非线性变形,获得任意多级伸缩臂臂端挠度,并与ANSYS仿真结果对比,给出不同弹性支撑刚度的伸缩臂几何非线性变形.分析结果表明:推导的任意多级伸缩臂挠度递推表达式是正确的和合理的,能有效地满足工程实际应用.     

柔性双稳态结构分岔跳跃模式的探讨

针对柔性双稳态结构跳跃路径不唯一及其力位移曲线存在不连续点(即尖点)的问题,基于有限元大变形理论建立了双稳态柔性结构的跳跃控制方程,采用多步位移载荷循环加载/卸载的方法数值模拟了跳跃过程中存在的可能屈曲模态及其变换方式,得到了其对称跳跃分岔的完整解。分析了双稳态结构参数对跳跃不连续点(尖点)和跳跃路径的影响关系,提出将结构品质因数作为双稳态跳跃"尖点"判据的方法,得到了具有稳定单一跳跃路径的双稳态结构。采用热成型方法研制了类余弦梁双稳态结构,考虑残余应力、夹持边界条件及载荷加载方式的影响,仿真预测的屈曲模态转换过程与实验结果基本一致,为双稳态跳跃特征的精确设计与控制提供理论依据。     

复合材料加筋板在剪切载荷下的屈曲特性研究

通过对复合材料薄壁加筋板结构进行剪切载荷下的屈曲试验研究,得到结构的屈曲模态、屈曲失稳载荷以及破坏形式,并通过有限元方法对结构的屈曲进行数值分析,分析得到的复合材料薄壁加筋板结构的屈曲模态和试验结果一致,屈曲载荷与试验结果吻合较好.试验还发现复合材料薄壁加筋板结构有较高的后屈曲承载能力,后屈曲过程中由于桁条脱胶会造成屈曲模态的变化.还分析了筋条的连续性对屈曲载荷的影响.     

简支双层叠合梁的变形计算

考虑小变形假设,利用梁挠度近似微分方程、积分方程理论和数值方法,研究简支双层光滑接触叠合梁的变形计算问题。通过上、下梁变形的协调条件,给出双层梁之间相互作用分布力系满足的第一类沃尔特拉积分方程及其精确解,直接利用上、下梁之间分布力满足的积分方程和梁挠度近似微分方程,推出上、下梁截面转角函数的解析表示式,对梁的变形和应力计算提出简明的求解方法。算例结果说明方法的可行性,其结论可为复合梁的强度设计和刚度校核提供理论参考。     

具有不对称弹性梁的梳状微加速度计的结构变形分析

通常情况,梳状微加速度计具有对称结构.但是加工工艺的缺陷可能导致梳状微加速度计的弹性梁不对称,引起结构发生扭转运动.对于双端固定梁式结构,分析了弹性梁的不对称性对结构等效刚度的影响.在假设弹性梁长度相等,但弯曲刚度不相等的前提下,推导出了结构的等效刚度计算公式,并将其推广到任意不对称情况.最后用有限元仿真实例验证了理论...     

复合材料薄壁箱梁的非线性自由振动分析

根据复合材料特性、梁的几何非线性和哈密尔顿原理,建立了复合材料薄壁梁的模型及非线性平衡方程。基于悬臂梁的边界条件,对非线性自治系统进行有限差分离散处理,得到了系统的质量和刚度矩阵。运用MATLAB振动工具箱进行模态分析,求得CUS和CAS架构下薄壁箱梁的前三阶固有频率与铺层角的变化关系,并对两种架构下的结果进行对比分析。在有限差分离散的基础上建立非线性薄壁梁的状态空间,运用时间离散和MATLAB振动工具箱对非线性自治系统进行仿真,求得CUS架构下不同铺层角度时的时间位移曲线和非线性振动幅度与铺层角之间的变化关系。     

Differential quadrature application in post-buckling analysis of a hinged-fixed elastica under terminal forces and self-weight

Based on geometrically non-linear theory for extensible elastic rods, governing equations of statically post-buckling of a beam with one end hinged and the other fixed, and subjected to a terminal force and a self-weight, are established. The formulation is derived from geometrical compatibility, equilibrium of forces and moments, and constitutive relations, which characterize a complex two-point boundary value problem. By using differential quadrature method (DQM), the non-linear governing equations are solved numerically and the post-buckled configurations of the deformed column are presented. Results are plotted in non-dimensional graphs for a range of density and terminal force, and are in good agreement with available references.     

A non-linear thin-walled beam theory

A non-linear thin-walled beam theory for elastic beams of open section is presented. The theory takes into account geometric non-linearities and longitudinal deformations caused by large cross-sectional rotation of the beam. The non-linear differential equations are derived by the minimum potential energy principle. The boundary conditions associated with the differential equations are obtained. It is shown that the set of equations reduces to the linear theory of Vlasov if non-linear terms are neglected. Also, the set of equations admits a simple solution in the special cases of large uniform torsion of thin-walled members of open cross-section. The torque-rotation relationship and axial strain-rotation relationship thus obtained are identical to the results obtained by Cullimore and Gregory.     

A critical review of the heavy elastica

The heavy elastica models thin or slender elements with non-negligible density. The non-linear governing equation depends on a non-dimensional parameter representing the relative importance of density and length to rigidity. Buckling, post-buckling and large deformation cases are discussed. Almost all relevant literature are included.     

多墙翼面结构后屈曲强度试验和数值研究

采用静态试验和有限元分析相结合的方法研究了复合材料中厚蒙皮多墙翼面结构的后屈曲性态、强度和破坏过程。有限元分析取得的载荷-位移曲线和试验结果的一致性说明了有限元模型的正确性。在此模型基础上,采用非线性弧长法追踪外载-位移路径,研究了盒段在压缩和集中力两种不同载荷下的后屈曲行为。给出了屈曲临界载荷和屈曲变形性态,分析了后屈曲强度和破坏过程。     

Laterally restrained beam columns with uniform biaxial loading

The analytical and experimental results for sixteen beam columns with uniform biaxial loading and an enforced axis of rotation are presented. The theoretical behaviour is predicted using a finite beam column element computer program which allows for non-linear elastic effects and the formation of complex plastic hinges. The iteration procedure increases the external loads incrementally, thus allowing the complete load-deflexion behaviour up to failure to be examined. A theoretical investigation is made of the effect of flange plates at the beam column ends, the number of lateral supports and geometrical imperfections.     

The dynamics of symmetric post-buckling

This work examines the relationship between natural frequency and compressive load for a conservative elastic mechanical system characterised by symmetric buckling. Application of some general theory shows that for a perfect system, exhibiting a stable-symmetric point of bifurcation, the initial post-buckling curve of compressive load against the square of the natural frequency is linear and has a slope of that of the pre-buckling curve. Simple link models and discretised continuous systems are analysed to illustrate the results of the general theory. These models are also used to show that the initial post-buckling curve is independent of axial inertia. The influence of initial imperfections is then considered and compared with experimental evidence.     

The extensible elastica of a prestressed beam with arbitrary boundary conditions

An axially prestressed elastic beam with arbitrary boundary conditions is considered. The solution of the problem is sought within the non-linear bending theory derived under the assumptions of finite deflections and small strains. The extensibility of the beam axis is taken into account, while the influence of shear force is neglected. A set of transcendental equations with incomplete elliptic integrals is obtained as the general solution. For small deflections, a linear solution of the problem is given too. Several numerical results for the case of prestressed bolt in a joint are discussed and presented in the form of appropriate diagrams.     

梁结构边界条件识别的行波法

基于Euler-Bernoulli梁模型，研究了梁结构的波动动力学方程以及结点散射关系，在此基础上提出了行波法识别梁结构边界条件的新方法。以系统固有频率值为已知量，从行波观点出发，建立起系统的特征方程，由特征方程反解识别得到结构的边界参数。通过对附加弹性支撑的悬臂梁进行振动实验，利用所测的低阶固有频率值，辨识出边界的横向和扭转刚度。实验结果表明，该方法具有良好的识别精度，是一种极有潜力的参数辨识方法。     

Large deformations of thin curved plane beam of constant initial curvature

A theory for the large deformations of a thin curved plane beam of constant initial curvature is presented, based on the hypothesis that only the longitudinal component of the strain tensor exists in the beam. In this case, five of the six compatibility equations are identically satisfied, while the remaining one requires the axial strain to vary parabolically over the cross-section of the curved beam. The non-linear strain-displacement relations are then solved for two in-plane displacement components in terms of two arbitrary functions of the longitudinal co-ordinate, angle . It is shown that, as a consequence of our hypothesis, the displacements vary linearly over the cross-sections of the beam. The obtained functional form of the displacement components leads to equilibrium equations of a beam on a deformed configuration expressed in terms of deformation functions. For the special case of a linearly elastic material and circular cantilever beam subjected to conservative and non-conservative point loads these equations have been numerically integrated. A number of numerical examples, including the bending of a C-shaped spring, are presented.