A coupled bending-torsion model for electrostatically actuated torsional nano/micro-actuators with considering influence of van der Waals force

In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton’s second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of the bending stiffness to the torsion stiffness of the supporting torsion beams is relatively low, the dominant instability mode of the actuator would be the bending mode and otherwise the dominant instability mode would be the torsion mode. It is also observed that the presence of the vdW force can significantly reduce the pull-in angle and pull-in deflection of the nano/micro-actuator. The presented results also show that the vdW force can lead to considerable reduction in the pull-in voltage of the actuator. The equilibrium behavior of the actuator is studied, and it is observed that the vdW force and also bending of the supporting torsion beams greatly reduce the maximum allowable voltage which can be applied to the actuator. Results of this paper can be used for successful design of electrostatically actuated torsional nano/micro-actuators where the size of the actuator is sufficiently small, and as a result, the vdW force plays a major role in the system.     

Theory of thin-walled composite beams with single and double-cell sections

In the present work, a mixed beam approach that combines both the stiffness and the flexibility formulation in a unified manner has been performed to analyze the elastically-coupled composite beams with closed cross-sections. The analysis model includes the effects of elastic couplings, shell wall thickness, torsion warping, and constrained warping. The Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. The theory is validated against detailed finite element analysis results for coupled composite beams with single and double-celled box sections. Various layup cases of box beams with bending–torsion or extension–torsion couplings are considered to evaluate whether all the significant non-classical structural effects of composites are captured in the beam theory. Good correlation of the present theory with the finite element analysis is obtained over the different cases. Numerical results showing the accuracy of the approach are demonstrated in the framework of the analysis.     

《薄壁Timoshenko梁弯扭耦合振动的动态有限元法》

通过直接求解单对称均匀薄壁Timoshenko梁单元弯扭耦合振动的运动微分方程,推导了其精确的动态刚度矩阵。在本文研究中考虑了弯扭耦合、翘曲刚度、转动惯量和剪切变形的影响。针对某弯扭耦合的薄壁梁算例,应用本文推导的动态刚度矩阵,采用自动Muller法和结合频率扫描法的二分法求解频率特征方程,计算了该薄壁梁的固有特性,并讨论了翘曲刚度、剪切变形和转动惯量对该弯扭耦合薄壁梁的固有频率和模态形状的影响。数值结果验证了本文方法的精确性和有效性,并指出随着模态阶次的增加,剪切变形、转动惯量和翘曲刚度对薄壁梁的固有特性的影响更加显著。     

旋翼桨叶结构载荷计算方法比较研究

基于有限转角假设,建立了刚柔耦合旋翼动力学模型。该模型考虑了刚体转动与弹性变形之间的耦合效应,相较于基于小转角假设的传统有限元模型具有明显的优势。气动力以广义力形式与桨叶刚体转动及弹性变形耦合组建方程。在方程求解的单步上,分别采用力积分法、反力法以及曲率法计算桨叶剖面结构振动载荷。以BO105模型桨叶及SA349/2小铃羊直升机为仿真对象,比较研究了这三种载荷计算方法的预测精度与适用范围。对于不考虑气动力的纯结构振动载荷,三种计算方法具有相同的精度。在气弹瞬态计算中,力积分法对桨根载荷的预测精度不足。曲率法与反力法在桨叶有限元节点处得到了相近的结果。反力法预测精度取决于有限元建模精度,且只对节点处载荷有效。由于曲率法只计入弹性桨叶的弯曲曲率,该方法需要更高阶次的形函数以满足自由度二阶导数的连续性。此外,为加速收敛及减少累积误差,本文开发了基于外推法的数值积分算法。     

Study of warping torsion of thin‐walled beams with open cross‐section using macro‐elements

Thin‐walled beams with open cross‐section under torsion or complex load are studied based on the hypotheses of the classical theory (Vlasov). Different from previous techniques presented in the literature, the concept of a strip‐plate is introduced. This concept is used to accurately model the effect of bending induced by torsion and to define an alternate finite element called macro‐element. The macro‐elements are shown to model more accurately the thin‐walled beams under warping torsion or complex load therefore giving better results than the classical theory. Copyright © 1999 John Wiley & Sons, Ltd.     

Fracture and fatigue analysis of an agitator shaft with a circumferential notch

This paper is concerned with the fracture analysis of an agitator shaft of a large vessel and predicting its high cycle fatigue life. The agitator shaft has a circumferential notch around it and is subjected to remote bending and torque created by the mixing operation. The problem is comprised (i) the analyses of the bending force and torque acting on the agitator by using the analytical method, (ii) calculation of stress intensity factors under mode I and III loading conditions by using finite element method and, (iii) fatigue analysis of the agitator shaft failed in service.An agitator model is set up and data obtained from the agitator are processed to make more realistic approximations for bending forces, since they form a base for stress analysis, in which mode I stress intensity factors are evaluated. Mode I stress intensity factors obtained by finite element analysis are compared with the results provided by using the body force method.     

基于垂直扭转梳齿驱动结构的硅微机械扭转微镜的设计加工与表征

为了改善扭转微镜的机电耦合特性和光学特性,提出了一种新的基于SOI硅片的垂直扭转梳齿静电驱动结构．通过有限元与边界元方法,对不同厚度扭转梁的机电耦合特性进行了数值模拟,得到了相应的阈值电压和吸合电压,并提出了几种新的折叠梁结构,以进一步改善器件的机电耦合特性;通过力学分析,从理论上推导了垂直扭转梳齿静电驱动方式微镜的最大扭转角度、阈值电压、扭转刚度以及固有频率,获得了结构参数对器件机电耦合特性的影响机制;最后,利用比例散射理论讨论了表面粗糙度、入射光束波长和入射角度等参数对微镜表面光学反射性能的影响,并利用原子力显微镜测量了微镜的表面粗糙度,理论模拟与实验研究表明,基于SOI硅片和垂直扭转梳齿结构的硅微机械扭转微镜可显著降低器件的驱动电压,提高器件的机电耦合特性和微镜表面的光学反射特性．     

单层和双层足尺度海底管道抗冲击性能分析

海底管道在服役过程中除了受到常规荷载作用外,还会受到各种意外的冲击载荷作用而失效.为了研究承受横向冲击载荷作用下海底管道的动态特性,对三个单层和一个双层的足尺度管道进行了落锤冲击试验,获得了横向冲击作用下管道的破坏形态、冲击力时程曲线、位移时程曲线及应变时程曲线.建立了分析冲击荷载作用下海底管道失效过程的有限元模型,并...     

罕遇地震下曲线钢-混凝土组合梁桥的墩柱扭转效应

为了研究曲线钢-混凝土组合梁桥在罕遇地震下的墩柱扭转效应,基于考虑扭转效应的钢管混凝土纤维梁模型,建立了曲线组合梁桥的杆系有限元分析模型。对不同输入方向的三条地震波作用下是否考虑墩柱扭转效应的纤维梁模型的计算结果进行了对比,包括墩顶位移、墩柱扭转角和墩柱内力等。在此基础上,对曲线组合梁桥在罕遇地震作用下的扭转效应的关键影响参数进行了分析。结果表明：采用考虑扭转效应的纤维梁模型分析曲线组合梁桥在地震作用下的受力反应,可有效的反映罕遇地震下曲线钢-混凝土组合梁桥的墩柱扭转效应。另外,曲率半径和墩高是影响曲线组合梁桥在纵向地震作用下墩柱扭转效应的主要因素。     

考虑扭转作用的钢管混凝土纤维梁模型

通过引入纤维梁截面的正应变平截面假定和剪应变线性分布假定, 根据美国学者Hsu 提出的转角软化桁架模型中的混凝土材料二维本构关系, 从基本的材料力学原理出发, 推导了可考虑扭转作用的钢管混凝土纤维梁单元的本构关系求解流程。基于大型通用有限元程序ABAQUS 提供的用户自定义子程序UEL, 采用FORTRAN语言开发了可考虑扭转作用的钢管混凝土纤维梁模型, 能够模拟钢管混凝土柱在轴力-弯矩-扭矩复合受力下的全过程力学行为, 并可考虑任意加载路径。该文所开发的纤维梁模型具有较高的精度和求解效率。     

任意截面预应力混凝土细长柱的非线性分析

提出了轴力和双向弯曲作用下任意截面混凝土和预应力混凝土细长柱的非线性有限元计算模型.分析时既考虑了由单元变形和轴力二次矩引起的几何非线性效应,也考虑了由材料非线性应力应变关系和截面刚度矩阵引起的材料非线性效应.推导了非线性全过程分析的标准有限元公式,得到的单元刚度矩阵可分割成三个子矩阵,分别反映了材料非线性、材料非线性和单元大位移的耦合、轴力二次矩等三种不同的非线性作用效应.计算分析结果和试验结果吻合较好.     

考虑弯曲效应的弯管高精确度模态分析

基于塑性理论和有限元软件ANSYS,考虑弯曲效应对各种不同材料参数、不同直径、不同弯曲半径和弯曲角度的弯管固有频率和振型的影响,建立了高精度弯管有限元模型进行模态分析,并利用实验结果进行验证.研究表明,考虑弯曲效应后的有限元模型计算结果更接近实验结果,特别是第一阶固有频率和振型的精度得到了提高,说明应用该模型可以得到高精度的弯管模态.     

Non-linear pre-buckling behavior of shear deformable thin-walled composite beams with open cross-section

A kinematic model is presented for thin-walled composite beams able to account for axial force, bending, torsion and warping. Shear deformations on the mid-surface are considered and modeled by means of a polynomial approximation. For this scope appropriate shape functions on the curvilinear abscissa along the cross-section mid-line are introduced.Small strains and moderate rotations are considered over the pre-buckling range.The model allows to predict the static non-linear behavior and the critical loads of composite pultruded beams.A finite element approximation is derived from a variational approach. Some numerical results are also presented revealing the importance of the shear terms on the mechanical response and their effect on the stability of pultruded composite members.     

Development of specimen and test method for strength analysis of MEMS micromirror

Specimens and fracture test methods for strength analysis of MEMS micromirrors were proposed. Bending and combined loading tests were performed, and torsion strength was estimated from those results. Two-parameter Weibull distribution was used to evaluate the fracture stresses estimated from the FEM model. The resulting scale and shape parameters were 787 MPa and 7.77 for the bending test and 517 MPa and 5.28 for the combined loading test. There was a difference in strength between the results of the bending and combined loading tests. From the load factor analysis, it was found that both geometry and stress distribution have to be considered to estimate the strength of MEMS since flaws are non-uniformly distributed. It was also found that torsional strength can be estimated on the safe side using the results of the combined loading test.     

Locking-free finite elements for shear deformable orthotropic thin-walled beams

Numerical models for finite element analyses of assemblages of thin-walled open-section profiles are presented. The assumed kinematical model is based on Timoshenko–Reissner theory so as to take shear strain effects of non-uniform bending and torsion into account. Hence, strain elastic-energy coupling terms arise between bending in the two principal planes and between bending and torsion. The adopted model holds for both isotropic and orthotropic beams. Several displacement interpolation fields are compared with the available numerical examples. In particular, some shape functions are obtained from ‘modified’ Hermitian polynomials that produce a locking-free Timoshenko beam element. Analogously, numerical interpolation for torsional rotation and cross-section warping are proposed resorting to one Hermitian and six Lagrangian formulation. Analyses of beams with mono-symmetric and non-symmetric cross-sections are performed to verify convergence rate and accuracy of the proposed formulations, especially in the presence of coupling terms due to shear deformations, pointing out the decay length of end effects. Profiles made of both isotropic and fibre-reinforced plastic materials are considered. The presented beam models are compared with results given by plate-shell models. Copyright © 2007 John Wiley & Sons, Ltd.     

Bending deformation of honeycomb consisting of regular hexagonal cells

In this study, the flexural rigidity of a honeycomb consisting of regular hexagonal cells is investigated. It is found that the bending deformation of the honeycomb cannot be evaluated by using the equivalent elastic moduli obtained from the in-plane deformation since the moments acting on inclined walls of honeycomb cell are different for the in-plane deformation and bending deformation. Based on the fact that the inclined wall of the honeycomb is twisted under the condition that the rotation angle in both connection edges is zero in bending deformation, a theoretical technique for calculating the honeycomb flexural rigidity is proposed. In the theoretical analysis, a torsion problem of a thin plate was solved by using the generalized variational principle. The validity of the present analysis is demonstrated by numerical results obtained by the finite element method.     

Determination of structural stress for fatigue analysis of welded aluminium components subjected to bending

The results of extrapolation procedures for the determination of structural stresses are often questionable due to the fact that the stresses at extrapolation points obtained with finite element analyses can be strongly dependent on the mesh size of finite element model and loading mode. Also, existing design S–N curves are derived mostly on the basis of fatigue testing of joints loaded axially. In the present paper the influence of the finite element mesh size on the structural stress value determined by a linear extrapolation method is analysed. Also, the paper examines the possibility of using existing design S–N curves for cases of bending induced by a force on the welded stiffener. Fatigue test results from aluminium welded components with longitudinal or round pad stiffeners subjected to bending loads have been assessed using a structural stress range approach, and compared with the structural stress design S–N curve FAT 40 (IIW) and the structural stress design S–N curve FAT 44 (Eurocode 9). It is concluded that the more precise estimation of fatigue life of aluminium components subjected to bending can be achieved with structural stress design S–N curve proposed by Eurocode 9. The conclusions also include recommendations for regarding component finite element modelling for the determination of structural stresses in case of bending.     

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three‐noded C¹ beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three‐dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three‐dimensional solu‐tions available for laminates under bending, and the elasticity three‐dimensional solution deduced from the de Saint‐Venant solution including both torsion with warping and bending. In addition, three‐dimensional solid finite elements using 27 noded‐brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length‐to‐thickness ratio, shear modular ratio, boundary conditions, free (de Saint‐Venant) and constrained torsion. Copyright © 1999 John Wiley & Sons, Ltd.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

反复水平荷载作用下偏心常轴压箱形钢柱抗震性能的数值分析

建立考虑材料非线性、几何非线性、几何初始缺陷、残余应力影响的有限元模型,对反复水平荷载作用下偏心常轴压箱形钢柱的受力性能进行模拟分析。通过与相关试验结果的比较,验证了有限元模型的正确性。在此基础上,对85个箱形构件进行数值分析,研究反复水平荷载作用下常偏压箱形钢柱的抗震性能。研究结果表明,腹板宽厚比是影响构件抗震性能的最主要因素,腹板宽厚比越大,构件的刚度、承载力退化越严重,延性越差。对于中等长细比的构件,当轴压比较小时,构件的抗震性能受整体失稳、局部屈曲和塑性变形的相互影响;但当轴压比较大时,整体失稳将起控制作用。柱顶弯矩使构件的骨架曲线发生平移,但柱顶弯矩对构件抗震性能的影响相对较小。根据有限元计算结果,回归出反复荷载作用下偏心常轴压箱形钢柱可承受的最大柱顶剪力和位移延性系数的拟合公式。