Synthesis methodology of a compliant exact long dwell mechanism using elastica theory

Compliant exact dwell mechanism design and its synthesis methodology are investigated. This class of compliant dwell mechanisms incorporates the buckling motion of an initially straight fixed–fixed flexible member as a follower. The initially straight flexible beam is modeled using nonlinear exact inextensible Elastica theory. The output response of a compliant long dwell mechanism is obtained using design charts for a mechanism that complies with the desired dwell time, maximum rise height and mechanism space requirements.     

柔顺停歇机构伪刚体模型的运动学和动力学分析

针对柔顺停歇机构的柔性构件在运动中产生的大变形、大挠度等几何非线性行为,采用伪刚体模型法来分析该类非线性大变形系统.首先,基于大挠度理论对大变形柔性梁进行屈曲分析,运用第一、第二类椭圆积分模拟初始状态为直梁的柔性梁,用多项式拟合得到其载荷—位移关系式.结合边界条件与受力特性,得到柔性梁的等效非线性弹簧伪刚体模型.在此基...     

On approximate solutions for the deformation of plane anisotropic beams

Plane deformation of anisotropic beams with narrow rectangular cross sections exhibits coupling of stretching, bending and transverse shearing. For anisotropic cantilever beams with a stiff end-cap under end forces and an end couple, assessments were made for approximate solutions by comparing these with numerically exact finite element (FE) solutions. Specific attention is given to point-wise or approximate satisfaction of the end-fixity conditions. As approximate methodologies, (i) the elementary polynomial form of Airy's stress function for the plane stress problem in a rectangular region, (ii) a Timoshenko-type beam theory, and (iii) the Bernoulli-Euler beam theory were selected. Among these, only the polynomial form of Airy's stress function violates the point-wise end-fixity conditions. Both the polynomial Airy stress function and the Timoshenko-type beam theory successfully model the effects of transverse shear deformation and the coupling of stretching and transverse deflection. Analytical solutions demonstrate that the normal shear coupling effect increases linearly with the thickness-to-span ratios in axial normal stress and axial displacement, while the coupling manifests quadratically in transverse displacement. The comparison of end displacements with the numerically exact FE solutions indicates that the polynomial form of Airy's stress function is no better than the Timoshenko-type beam theory. Similar conclusions were reached for the problem of uniformly loaded cantilever beams. It has been found that the accurate prediction of the deformation of thick anisotropic beams with significant normal-shear coupling requires the use of higher order theories.     

Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection

This research is concerned with the analysis of post-buckling of a nano-composite beam reinforced by graphene plateletes (GPLs) having geometrical imperfection. GPLs are uniformly and nonuniformly distributed thorough the thickness direction. Different porosity distributions are considered. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The postbuckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin's method needless of any iteration process. New results show the importance of porosity coefficient, porosity distribution, GPL distribution, GPL weight fraction, geometrical imperfection, and foundation parameters on nonlinear buckling behavior of porous nanoscale beams. Specially, porosities and GPL reinforcement have a great impact on postbuckling configuration of both ideal and imperfect nanocomposite beams.     

Bending Analysis of Curved Sandwich Beams with Functionally Graded Core

In this article, bending analysis of curved sandwich beams with transversely and functionally graded (FG) core is studied. The Euler–Bernoulli beam theory is used to model the thin face-sheets and high-order shear theory is used to analyze the core. Equilibrium/field equations, compatibility and boundary conditions are used to derive the set of governing equations. The numerical solution of the governing nonlinear differential equations is based on the series Fourier–Galerkin method. Finally, the effect of geometric properties on radial deflection of core and the effect of core radius and Young's modulus on radial deflection, circumferential displacement, and stresses are investigated.     

Inverse finite element method for large‐displacement beams

A finite element model for the inverse analysis of large‐displacement beams in the elastic range is presented. The model permits determining the initial shape of a beam such that it attains the given design shape under the effect of service loads. This formulation has immediate applications in various fields such as compliant mechanism design where flexible links can be modeled as large‐displacement beams. Numerical tests for validation purposes are given, together with two design applications of flexible mechanisms with distributed compliance: a flexible gripper and a flexible S‐type clutch. Copyright © 2010 John Wiley & Sons, Ltd.     

In-plane and out-of-plane dynamics and buckling of functionally graded circular curved beams

In this paper the dynamic and buckling features of slender structures with curved axis are addressed. A survey on the literature concerning mechanics of beams constructed with non-homogeneous materials or with functionally graded materials reveals only a few papers devoted to the dynamics and buckling of curved beams constructed with such materials. This problem was tackled mainly through 2D or 3D numerical formulations, but comprehensive beam theories on the matter are scarce. In the present paper a model of non-homogeneous and/or FGM curved beams is developed. The model is deduced by adopting a consistent displacement field which incorporates second order rotational terms based on the semi-tangential rule. The model also incorporates the shear flexibility due to bending and warping due to twisting effects. Arbitrary initial stresses and initial off-axis loads are taken into account in the linearized principle of virtual works. The finite element method is employed to discretize the motion equations with the objective to solve problems of dynamics, statics and buckling. The model contains, as particular cases, several straight beam theories as well as curved beam theories. Some comparisons with the available experimental data of the open literature are performed in order to illustrate the predictive features of the model, and comparisons with 2D and 3D finite element approaches are also performed.     

含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析

该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实现裂纹大小(深度)、位置、数目的模拟.引入变截面Euler-Bernoulli梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁弹性屈曲问题,得到优化的网格和满足预设误差限的高精度屈曲荷载和屈曲模态解答.数值算例表明该算法中网格非均匀加密可适应裂纹损伤引起的屈曲模态...     

初始缺陷对三向张弦梁结构整体稳定性影响研究

三向张弦梁结构是新广州站工程采用的一种新型张弦梁结构,因此有必要对三向张弦梁结构的整体稳定性能进行深入的研究。该文首先对随机缺陷模态法进行了改进,使其更适用于网壳与张弦梁混合结构的缺陷稳定性分析。然后分别采用改进的随机缺陷模态法和一致缺陷模态法对三向张弦梁结构的缺陷稳定性进行了研究。分析结果表明:改进后的随机缺陷模态法更适用于网壳和拱梁混合结构形式的缺陷稳定性分析;缺陷越大,该三向张弦梁结构对缺陷越敏感,整体稳定性能受缺陷的影响越大;与理想结构破坏模式最接近的特征值屈曲模态为最不利的特征值屈曲模态,按此模态施加初始缺陷后的结构承载力最低;按非线性屈曲模态对结构施加缺陷得到的结构极限承载力小于按特征值屈曲模态施加缺陷的情况,与随机缺陷模态法的结果最为接近。     

Free vibration of functionally graded spatial curved beams

A formulation for the free vibration analysis of functionally graded (FG) spatial curved beams is presented by taking into account the effects of thickness-curvature. The governing equation is based on the first-order shear deformation theory (FSDT) and Ritz method is employed to obtain the natural frequencies. The curved beams presented are in the form of the cylindrical helical spring. The material distribution is in the direction of the curvature of the curved beam. The results for isotropic planar curved beams are validated with the known data in the literature. The effects of helix pitch angle, number of turns and boundary conditions on frequency parameters of spatial curved beams are investigated.     

曲梁弯扭屈曲分析

本文基于有限变形理论导出了薄壁曲梁位移和应变的一般表达式。从探讨薄壁曲梁弯扭屈曲的变形模态出发,考虑其弯矩作用平面内变形的影响,利用变分原理导出了曲梁稳定分析的基本微分方程。稳定分析表明,即使绕弱轴弯曲,曲梁也可能发生弯扭屈曲。对于曲率甚小的情况,本文把曲梁看作为具有初曲率的直梁,较精确地分析了初曲率对直梁弯扭屈曲临界弯矩的影响。此外,本文给出的闭合解与Timoshenko,Vlasov及Chai Hong Yoo等人的结果进行了比较,指出了其间差异的根源所在。     

任意开口薄壁截面圆弧曲梁的通用线性理论

在曲梁精确的翘曲位移基础上,根据变分原理,提出了对任意开口薄壁截面圆弧曲梁通用的线性理论,给出平衡微分方程和相应的边界条件。定义了两个新的变量vH和qH,借助它们可以很方便地计算曲梁中的剪力和扭矩。最后就该理论在常见截面形式(工字形,槽形及无对称轴H形)水平曲梁中的应用进行说明,并与已有理论进行比较。     

单级柔顺正交位移放大机构非线性建模与优化

同时实现操作的灵活性与稳定性是精密工程领域的研究热点。单级柔顺正交位移放大机构可通过正交位移转换实现平行夹持,并通过位移放大提高操作的灵活性,但该机构的传统建模方法主要基于小变形假定并忽略剪切作用,导致模型精度较低。为此,对典型的单力输入单级柔顺正交位移放大机构进行精确的非线性建模与优化。考虑到剪切作用与几何非线性因素,对单级柔顺正交位移放大机构输出位移进行两步法半解析建模,以实现非线性结果的快速预测。第1步,基于能量法与欧拉-伯努利梁理论,建立该机构输出位移的线弹性解析模型,并结合小变形静力学有限元分析,拟合剪切非线性修正系数;第2步,结合几何非线性静力学有限元分析与数值拟合,建立该机构输出位移的几何非线性修正系数模型。为最大化输出位移并抑制几何非线性作用,提出机构平面尺寸和厚度综合优化策略,并利用ANSYS Workbench有限元仿真验证了机构输出位移非线性模型与优化结果的有效性。仿真结果显示,机构输出位移非线性模型的误差小于5%,且可依据不同优化策略显著增大输出位移或将几何非线性程度约束于指定范围内。研究表明利用所提出的方法对单级柔顺正交位移放大机构进行非线性建模与优化,可有效提高压电驱动柔顺微夹钳的位移输出性能与开环控制的精度和实时性,有利于实现稳定灵活的微操作。     

The wavelet-based theory of spatial naturally curved and twisted linear beams

The paper presents the wavelet-based discretization of the linearized finite-strain beam theory which assumes small displacements, rotations and strains but is capable of considering an arbitrary initial geometry and material behaviour. In the numerical solution algorithm, we base our derivations on the vector of strain measures as the only unknown functions in a finite element. In such a way the determination of the beam quantities does not require the differentiation. This is an important advantage which allows a wider range of shape functions. In the present paper, the classical polynomial interpolation is compared to scaling and wavelet function interpolations. The computational efficiency of the method is demonstrated by analyzing initially curved and twisted beams.     

Thermal Postbuckling Analysis of Imperfect Reissner-Mindlin Plates on Softening Nonlinear Elastic Foundations

A thermal postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to uniform or nonuniform tent-like temperature loading and resting on a softening nonlinear elastic foundation. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first-order shear-deformation effect, and including plate-foundation interaction and thermal effects. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick plates resting on softening nonlinear elastic foundations. The effects played by foundation stiffness, transverse shear deformation, plate aspect ratio, thermal load ratio and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form and exhibit interesting imperfection sensitivity.     

Analysis of shear-deformable composite beams in postbuckling

The nonlinear response of composite beams modeled according to higher-order shear deformation theories in postbuckling is investigated. The beam ends are restrained from axial movement, and as a result the contribution of the midplane stretching is considered. The equations of motion and the boundary conditions are derived using Hamilton’s principle. The shear deformation effect on the critical buckling load and static postbuckling response is introduced using classical, first-order, and higher-order shear deformation theories. This paper presents an exact solution for the static postbuckling response of a symmetrically laminated simply supported shear-deformable composite beam. The shear effect is shown to have a significant contribution to both the buckling and postbuckling behaviors. Results of this analysis show that classical and first-order theories underestimate the amplitude of buckling while all higher-order theories, considered in this study, yield very close results for the static postbuckling response.     

Application of the homotopy method for the analytic approach of the nonlinear free vibration analysis of the simple end beams using four engineering theories

In this paper, nonlinear vibration analyses of Euler–Bernoulli, Rayleigh, Shear and Timoshenko beams with simple end conditions are presented using homotopy analysis method (HAM). Closed form solutions for natural frequencies, beam deflection, post-buckling load–deflection relation, and critical buckling load are presented. The calculated natural frequencies for all four cases were verified against some available results in the literature and very good agreement observed. Furthermore, obtained results for deflection, buckling, and post-buckling of each beam are presented and the effects of some parameters, such as slenderness ratio, the rotary inertia, and the shear deformation are examined.     

基于整体-局部弯曲模型的钢-混凝土组合梁界面滑移及其效应分析

提出了具有界面滑移的钢-混凝土组合梁截面弯矩由不考虑滑移的整体梁承担整体弯矩和自由滑移的叠合梁承担局部弯矩的整体-局部弯曲模型。基于Bernoulli梁理论和抗剪连接件线性剪力-滑移模型,建立了截面弯矩及剪力分配的计算方法,得到了整体-局部弯曲模型计算界面滑移及考虑界面滑移的截面应力和梁弯曲挠度的公式,并给出了集中荷载作用下简支组合梁的栓钉剪力及界面滑移计算公式。     

A firefly algorithm for optimum design of new-generation beams

This research addresses the minimum weight design of new-generation steel beams with sinusoidal openings using a metaheuristic search technique, namely the firefly method. The proposed algorithm is also used to compare the optimum design results of sinusoidal web-expanded beams with steel castellated and cellular beams. Optimum design problems of all beams are formulated according to the design limitations stipulated by the Steel Construction Institute. The design methods adopted in these publications are consistent with BS 5950 specifications. The formulation of the design problem considering the above-mentioned limitations turns out to be a discrete programming problem. The design algorithms based on the technique select the optimum universal beam sections, dimensional properties of sinusoidal, hexagonal and circular holes, and the total number of openings along the beam as design variables. Furthermore, this selection is also carried out such that the behavioural limitations are satisfied. Numerical examples are presented, where the suggested algorithm is implemented to achieve the minimum weight design of these beams subjected to loading combinations.