变截面铁木辛柯梁振动特性快速计算方法

提出了一种快速计算变截面铁木辛柯梁横向振动特性的方法.基于铁木辛柯梁理论建立的变截面梁的横向振动方程,其梁的截面参数如有效剪切面积、密度、弯曲刚度、转动惯量等沿梁轴线连续或非连续变化；首先将变截面梁等效为多段均匀阶梯梁；然后基于相邻两段连接处的位移(位移、转角)和力(弯矩、剪力)连续条件,建立相邻两段模态函数间相互关系,并递推出首段段与末段模态函数相互关系,利用边界条件得到相应特征方程,使用Newton-Raphson方法计算其固有频率；最后针对梁常见边界条件,得到计算变截面铁木辛柯梁横向振动固有频率特征     

空间薄壁梁单元面向对象程序的实现

针对传统有限元分析软件主要面向过程设计,其可维护性和可扩展性等较差的问题,基于面向对象程序设计方法,建立具有内部节点的空间薄壁截面梁单元模型,给出线弹性空间薄壁梁单元的UML类图,介绍矩阵类、截面类、材料类、节点类、单元类和结构类等6种类成员的主要属性和方法.用C#编制相应的有限元程序,通过T形框架算例比较和验证其位移和弯曲转角计算值、理论解和ANSYS的BEAM 189梁单元的数值解,结果表明该程序精度良好,可用于空间薄壁结构的有限元分析.     

非理想矩形锚单元的节点分析法

为了在节点化设计方法中考虑非理想锚效应,采用铁木辛柯梁理论和加权余量法建立了非理想矩形锚单元的节点化模型,在Hspice中构建了相应的等效电路。结合已有单元模型,实现了静电执行器的系统级仿真,与有限元模拟结果吻合较好,可模拟出非理想矩形锚对系统静态和动态特性的影响。     

用Timoshenko修正理论研究有梯度界面层双材料梁的振动特性

采用Timoshenko梁修正理论研究了有梯度界面层双材料梁的振动问题,利用静力方程确定了有梯度界面层双材料梁的中性轴位置,在此基础上应用Timoshenko梁修正理论建立了有梯度界面层双材料梁的振动方程,求得其自振频率表达式及其在简谐荷载作用下强迫振动的解析解.讨论分析了梯度界面层高度等因素对有梯度界面层双材料梁的振动影响,并用有限元法验证了Timoshenko梁修正理论.通过实例计算,得到了梯度界面层高度等因素对有梯度界面层双材料梁振动特性有较大影响的结论.     

功能梯度双层悬臂梁的有限元建模分析

为考察不同建模形式和界面处理方式对由功能梯度材料构成的双层悬臂梁计算结果的影响,通过有限元计算结果与理论解的对比发现,对于功能梯度悬臂梁,选取八节点二次单元能更好地消除剪力自锁现象,比四节点线性单元的求解结果更加精确;对于双材料理想界面,采取强制位移约束条件比消除重合节点的约束条件更符合真实情况;梁端部附近应力场的有限元解比理论解更加合理.     

在裂纹尖端引入奇异单元的偶应力有限元法

针对在微观状态下结构力学行为会受尺度效应影响的问题,在偶应力理论中考虑微观结构的旋转梯度可以较好解释结构的尺度效应.建立基于一般偶应力理论的有限元法的基本方程,并在裂纹尖端引入奇异单元,计算受单向拉伸的中心斜裂纹板裂纹尖端场的应力强度因子(Stress Intensity Factor,SIF),分析特征长度变化对SIF的影响,对比偶应力理论下的结果与经典理论下的结果.结果表明：在裂纹尖端引入奇异单元可以提高计算精度和稳定性;偶应力使得裂纹尖端SIF比经典理论下的值小,并且SIF随着特征长度增大而减小.     

基于无网格法考虑热效应及剪切效应FGM梁的动力学建模与仿真

将无网格点插值法和无网格径向基点插值法用于温度场中旋转柔性功能梯度材料梁的动力学分析.在考虑剪切效应的基础上,在梁本构关系中计及热应变,采用4种离散方法描述梁的变形场,运用第二类Lagrange方程,推导出大范围运动功能梯度材料梁的一次近似刚柔耦合动力学方程,研究不同温度变化下梁的动力学响应.通过动力学仿真得出以下结论：温度场对沿横向对称分布的功能梯度材料梁的横向变形影响较小,对纵向变形的影响较大,且在计算温度荷载作用下的梁末端变形时不应忽略轴向变形影响.     

基于梯度向量的交互式CT图像分割

首先采用旋转模板对图像进行平滑去噪处理，同时得到各像素点的梯度值方向，然后根据梯度值方向采用Are Weights方法计算各点的梯度值，这些方法的结合可以有效的降低噪声对灰度值计算的影响，得到了较好的梯度值图像。根据改进后的边缘检测方法，对边缘梯度信息进行最优化计算，选择最优的边缘点，最后将这些边缘点进行曲线拟合。实验结果显示该方法能有效地分割出胆囊图像。     

基于压电薄膜驱动的微定位平台建模与分析

设计了一种基于压电薄膜驱动梁和柔性铰链结构的3维微定位平台,并且为了准确评估平台性能提出了一种理论建模分析方法.首先,根据力平衡条件下的欧拉-伯努利梁理论和压电本构方程,得到压电薄膜梁的输出模型;然后,根据柔度矩阵方法,推导得到微定位平台的整体柔度模型;最后,综合压电薄膜梁模型和平台柔度模型得到平台的整体输出模型.通过有限元仿真分析微定位平台的输出位移和转角,并与理论计算结果进行对比验证.结果显示,仅有1个驱动器作用时,输出位移和转角理论计算结果与有限元分析结果的相对误差分别为5.4%和5.5%;3个驱动器共同作用时,输出位移理论结果与有限元分析结果的相对误差为11.6%.     

带边角裂纹悬臂Mindlin 板的振动特性研究

本文基于Mindlin板理论,应用Ritz法研究带边角裂纹Mindlin板的振动特性,分析了不同裂纹参数如裂纹位置,裂纹长度,裂纹角度对悬臂Mindlin板的固有频率和模态的影响.利用Ritz法求解固有频率和模态函数,本文构造了一个特殊的模态函数,其模态函数由两部分构成,一部分是用梁函数组合法得到的无裂纹理想完整矩形板的振型,另一部分是利用裂纹尖端奇异性理论,构造描述裂纹附近位移和转角不连续的角函数.通过高精度的数值计算软件Maple得出结果,并与有限元软件ANSYS分析的结果进行对比,验证本文计算结果的准确性.     

带裂纹石墨烯增强金属泡沫梁的振动特性研究

分析了带裂纹功能梯度石墨烯增强金属泡沫梁的自由振动.采用Timoshenko梁理论进行建模,裂纹由无质量扭转弹簧模拟,利用Halpin Tsai微观力学模型预测材料的有效性能.通过哈密顿原理,得到了带裂纹功能梯度石墨烯增强金属泡沫(FG GPLRMF)梁的运动方程及其边界条件.采用微分变换法分析带裂纹FG GPLRMF梁的自由振动.结果表明,带裂纹FG GPLRMF梁的振动特性受到石墨烯几何尺寸、孔隙类型和石墨烯分布的影响显著.     

Consistent curved beam element

Curved beam finite elements with shear deformation have required the use of reduced integration to provide improved results for thin beams and arches due to the presence of a spurious shear strain mode. It has been found that the spurious shear strain mode results from an inconsistency in the displacement fields used in the formulation of these elements. A new curved beam element has been formulated. By providing a cubic polynomial for approximation of displacements, and a quadratic polynomial for approximation of rotations a consistent formulation is ensured thereby eliminating the spurious mode. A rotational degree of freedom which varies quadratically through the thickness of the element is included. This allows for a parabolic variation of the shear strain and hence eliminates the need for use of the shear correction factor k as required by the Timoshenko beam theory. This rotational degree of freedom also provides a cubic variation of displacements through the depth of the element. Thus, the normal to the centroidal axis is neither straight nor normal after shearing and bending allowing for warping of the cross section. Material nonlinearities are also incorporated, along with the modified Newton-Raphson method for nonlinear analysis. Comparisons are made with the available elasticity solutions and those predicted by the quadratic isoparametric beam element. The results indicate that the consistent beam element provides excellent predictions of the displacements, stresses and plastic zones for both thin and thick beams and arches.     

Linear free flexural vibration of cracked functionally graded plates in thermal environment

In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are assumed to be temperature dependent and graded in the thickness direction. The effective material properties are estimated using the Mori–Tanaka homogenization scheme. The formulation is developed based on first-order shear deformation theory. The shear correction factors are evaluated employing the energy equivalence principle. The variation of the plates natural frequency is studied considering various parameters such as the crack length, plate aspect ratio, skew angle, temperature, thickness and boundary conditions. The results obtained here reveal that the natural frequency of the plate decreases with increase in temperature gradient, crack length and gradient index.     

Vibrations of moderately thick rectangular plates in terms of a set of static Timoshenko beam functions

In this paper, a set of static Timoshenko beam functions is developed as the admissible functions to study the free vibrations of moderately thick rectangular plates using the Rayleigh–Ritz method. This set of beam functions is made up of the static solutions of a Timoshenko beam under a series of sinusoidal distributed loads. The beam is considered to be a unit width strip taken from the rectangular plate in a direction parallel to the edges of the plate. In addition, the geometric boundary conditions of the plate are exactly satisfied in this set of beam functions, and the effect of the shear correction factor on the admissible functions of the plate is also taken into account. It can be seen that the method is sound in theory and no complicated mathematical knowledge is needed. Each of the beam functions is only a third-order polynomial plus a sine function or a cosine function. Furthermore, a change of the boundary conditions of the plate only results in a change of the coefficients of the polynomial. The method is very simple and a unified computational program can be given for the plates with arbitrary boundary conditions and thickness. Comparison and convergency studies demonstrate the correctness and the accuracy of the method. It can be shown that using a small number of terms of the static Timoshenko beam functions can give rather accurate results for all cases. Finally, the effect of thickness–span ratio on the eigenfrequency parameters of Mindlin rectangular plates is studied in detail.     

A corotational procedure that handles large rotations of spatial beam structures

A practical motion process of the three dimensional beam element is presented to remove the restriction of small rotations between two successive increments for large displacement and large rotation analysis of space frames using incremental-iterative methods. In order to improve convergence properties of the equilibrium iteration, an n-cycle iteration scheme is introduced.

The nonlinear formulation is based on the corotational formulation. The transformation of the element coordinate system is assumed to be accomplished by a translation and two successive rigid body rotations: a transverse rotation followed by an axial rotation. The element formulation is derived based on the small deflection beam theory with the inclusion of the effect of axial force in the element coordinate system. The membrane strain along the deformed beam axis obtained from the elongation of the arc length of the beam element is assumed to be constant. The element internal nodal forces are calculated using the total deformational nodal rotations. Two methods, referred to as direct method and incremental method, are proposed in this paper to calculate the total deformational rotations.

An incremental-iterative method based on the Newton-Raphson method combined with arc length control is adopted. Numerical studies are presented to demonstrate the accuracy and efficiency of the present method.     

Timoshenko beam finite element with four dof and convergence of O(h)

In situations where transverse shear deformations and rotary inertia in beams are important, elements based on the Timoshenko beam theory are useful. Among the two-noded, four DOF elements derived from the minimum total potential energy principle, the HTK. element proposed by Hughes et al. using linear displacement functions for both w and θ and the T1CC4 element proposed by Tessler et al. using quadratic displacement function for w and linear displacement function for θ are well known in the literature. The convergence of the HTK element in the thin beam situation has been too poor due to shear locking but by using selective integration this element can be shown to be equivalent to the T1CC4 element which has a rate of convergence of O(h²). In this paper a five DOF element with w and θ at the end nodes and θ at the middle node and based on the cubic displacement function for w and the quadratic displacement function for θ is first developed. Statically condensing the middle rotational DOF, the well-known (4 × 4) stiffness matrix using the φ-factor defined as φ = 12EI/kGAL² and hitherto obtained only through a flexibility approach or closed-form solution of the governing equations of the Timoshenko beam theory is derived. This element based on cubic displacement function for w has rate of convergence of O(h⁴), is completely free of shear locking and performs equally well in thin as well as thick beam situations.