Equivalent bending stiffness of simply supported preflex beam bridge with variable cross-section

In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.

Force Analysis of the Overconstrained Mechanisms Based on Equivalent Stiffness Considering Limb Axial Deformation

Overconstrained mechanism has the advantages of large bearing capacity and high motion reliability,but its force analysis is complex and difficult because the mechanism system contains overconstraints.Considering the limb axial deformation,taking typical 2SS+P and 7-SS passive overconstrained mechanisms,2SPS+P and 7-SPS active overconstrained mechanisms,and 2SPS+P and 7-SPS passive-input overconstrained mechanisms as examples,a new force analysis method based on the idea of equivalent stiffness is proposed.The equivalent stiffness matrix of passive overconstrained mechanism is derived by combining the force balance and deformation compatibility equations with consideration of axial elastic limb deformations.The relationship between the constraint wrench magnitudes and the external force,limb stiffness is established.The equivalent stiffness matrix of active overconstrained mechanism is derived by combining the force balance and displacement compatibility equations.Here,the relationship between the magnitudes of the actuated wrenches and the external force,limb stiffness is investigated.Combining with the equivalent stiffness of the passive overconstrained mechanism,an analytical relationship between the actuated forces of passive-input overconstrained mechanism and the output displacement,limb stiffness is explored.Finally,adaptability of the equivalent stiffness to overconstrained mechanisms is discussed,and the effect of the limb stiffness on overconstrained mechanisms force distribution is revealed.The research results provide a theoretical reference for the design,research and practical application of overconstrained mechanism.

Method to analyze wrinkled membranes with zero shear modulus and equivalent stiffness

To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.

AN EQUIVALENT CONTINUUM METHOD OF LATTICE STRUCTURES

An equivalent continuum method is developed to analyze the effective stiffness of three-dimensional stretching dominated lattice materials. The strength and three-dimensional plastic yield surfaces are calculated for the equivalent continuum. A yielding model is formulated and compared with the results of other models. The bedding-in effect is considered to include the compliance of the lattice joints. The predicted stiffness and strength are in good agreement with the experimental data, validating the present model in the prediction of the mechanical properties of stretching dominated lattice structures.

Improved Stiffness Modeling for An Exechon‑Like Parallel Kinematic Machine(PKM)and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.

Statistical Linearization on 2 DOFs Hydropneumatic Suspension with Asymmetric Non-linear Stiffness

Most references on hydropneumatic suspension analysis regard it as harden Duffing spring and take the white noise as the system input, which is quite different from real physical model. It will introduce considerable errors to the analytical result compared with the numerical simulation which makes it impossible to give a good depiction of the hydropneumatic suspension dynamics. In this paper, the dynamic response of the hydropneumatic suspension is worked out using statistical linearization based on 2 DOFs nonlinear suspension model. The damping of the suspension and the tire stiffness are both regarded as linear components and the real road roughness spectrum is used to work out the system input. The explicit analytical equivalent stiffness, dynamic mean value offset from statistic equilibrium position and the sprung acceleration varied with parameters of hydropneumatic spring, road roughness and vehicle velocity are worked out by substituting the nonlinear stiffness of hydropneumatic spring with its first three terms Tyler series at the static equilibrium position using James formula. The comparison of the numerical simulation and analytical result both on statistical parameters and distribution shows the validity of the analysis. The explicit form provides a concise and valid method on hydropneumatic suspension design and optimization.

Influence Predictions of Contact Effects on Mesh Stiffness of Face Gear Drives with Spur Gear

Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.

Equivalent Bar Conceptions for Computer Analysis of Pantographic Foldable Structures

An equivalent bar conception is firstly developed for the computer analysis of pantographic foldable structures. The uniplet of two three node beam elements is assumed as a six bar assembly with respect to least norm least square solution for the elastic strain energy equality. The equilibrium equation is developed for the equivalent models, and the internal forces formulated sequently for backup calculation. This procedure is proved practical for some engineering, and some interesting concepts proposed. Finally, three numerical tests are presented.

Deformation-based longitudinal equivalent stiffness beam model for shield tunnel and its application in seismic deformation method

In the longitudinal seismic deformation method for shield tunnels,one of the most commonly used is the longitudinal equivalent stiffness beam model(LES)for simulating the mechanical behavior of the lining.In this model,axial deformation and bending deformation are independent,so the equivalent stiffness is a constant value.However,the actual situation is that axial deformation and bending deformation occur simultaneously,which is not considered in LES.At present,we are not clear about the effect on the calculation results when axial deformation and bending deformation occur simultaneously.Therefore,in this paper,we improve the traditional LES by taking the relative deformation as a load and considering the coordinated deformation of axial and bending degrees of freedom.This improved model is called DNLES,and its neutral axis equations are an explicit expression.Then,we propose an iterative algorithm to solve the calculation model of the DNLES-based longitudinal seismic deformation method.Through a calculation example,we find that the internal forces based on LES are notably underestimated than those of DNLES in the compression bending zone,while are overestimated in the tension bending zone.When considering the combined effect,the maximum bending moment reached 13.7 times that of the LES model,and the axial pressure and tension were about 1.14 and 0.96 times,respectively.Further analysis reveals the coordinated deformation process in the axial and bending directions of the shield tunnel,which leads to a consequent change in equivalent stiffness.This explains why,in the longitudinal seismic deformation method,the traditional LES may result in unreasonable calculation results.

不同内固定系统治疗股骨转子间骨折的力学稳定性

背景:股骨转子间骨折的骨折类型和固定方式多样,各固定系统间的力学稳定性相差较大。使用有限元分析方法对各固定系统开展生物力学研究具有科学的临床意义。目的:通过有限元方法对比分析多种内固定应用于股骨A031-A2.1型转子间骨折的力学稳定性。方法:在已验证有效性的股骨有限元模型基础上,对模型进行必要的切割,造模成股骨A031-A2.1型转子间骨折,模拟临床手术方法置入不同的内固定系统,分别建立股骨近端防旋髓内钉、动力髋螺钉、经皮加压钢板和股骨近端锁定钢板固定模型。约束4组模型股骨远端下所有节点,在股骨头上施加700,1400和2100N的压缩载荷,通过计算分析,观察各组模型的等效应力分布和压缩刚度,比较各组模型之间的力学稳定性。结果与结论:①通过计算分析,对比各组模型的变形量计算压缩刚度后,在各级载荷作用下,各组模型上压缩刚度呈现的趋势:生理组>股骨近端防旋髓内钉组>股骨近端锁定钢板组>经皮加压钢板组>动力髋螺钉组;完整的生理组模型的压缩刚度明显高于所有的手术组模型;②观察应力指标,因存在应力遮挡效应,致使各固定组的应力峰值均高于生理组,最大峰值均集中分布于各内固定上;其中股骨近端防旋髓内钉固定组应力峰值最小,动力髋螺钉固定组应力最高,应力分布趋势呈现:生理组<股骨近端防旋髓内钉固定组<经皮加压钢板固定组<股骨近端锁定钢板固定组<动力髋螺钉固定组;③分布于骨质模型的应力,因内固定置入位置不同呈现不同的分布结果;④提示对于股骨转子间骨折,各种内固定均能起到有效的固定,结合有限元分析结果得出股骨近端防旋髓内钉组是较好的一种内固定选择,呈现变形量小、应力峰值低,应力分布均匀的特性;经皮加压钢板组和股骨近端锁定钢板组的力学效果优良,固定效果接近股骨近端防旋髓内钉固定;动力髋螺钉固定效果欠佳,同比于其他内固定,其力学稳定性较差。

不同因素导致的差异沉降对盾构隧道受力特性影响研究

盾构隧道在下卧地层软硬突变、局部堆载等因素影响下易产生不均匀沉降,可能诱发管片环间错台、螺栓断裂和接缝渗水等病害,危及隧道安全。然而,现有试验研究在隧道模型上多将纵向接头简化处理,难以反映盾构隧道纵向受力变形特性,对于隧道下卧软硬突变地层等工况的模拟也较为缺乏。为此,提出一种可同时模拟抗拉、抗弯刚度的“弹簧+螺栓型”接头,并以此接头制作可满足纵向力学性能相似的隧道模型,对盾构隧道进行下卧软硬突变、局部堆载等工况下的模型试验,进一步探明不同因素导致的差异沉降对盾构隧道的影响机理,并采用数值模拟验证了试验的可行性。研究结果表明:1)较单一地层而言,隧道下卧软硬突变时纵向沉降曲线呈现明显的非线性,其隧道沉降及差异沉降最值显著增大,软土侧隧道沉降较硬土侧更为显著,最大沉降、沉降差均出现在突变区软土侧衬砌处;2)下卧地层突变导致隧道横向收敛变形在纵向上分布不均,使软土侧衬砌收敛变形减小,硬土侧衬砌收敛变形显著增大;3)局部堆载对管片弯矩分布影响较小,对弯矩最值影响较大;4)下卧软土区隧道结构内力分布明显变异,隧道衬砌正弯矩区域显著增大,负弯矩区域略有减小,且弯矩最值提升显著。因此针对软硬突变地层,必要时在硬土侧隧道可采用粘钢法等方法提升衬砌横向刚度,以控制其收敛变形;软土侧隧道建议对管片进行螺栓复紧,并加强接缝防水,以减小下卧地层弱化对隧道结构产生的不利影响。

滚动轴承局部故障时变刚度系统动力学分析

针对滚动轴承局部故障动力学建模问题,通过分析各滚动体在进入、退出载荷区和陷入故障时的变化情况,基于Hertz接触理论,定义了接触变形保留因子,提出了滚动轴承等效时变刚度函数,建立了局部故障滚动轴承单自由度时变刚度动力学模型,并进行了理论分析和试验研究。研究结果表明:当滚动体进入或退出载荷区时,载荷区中承载滚动体数量增加或减少,引起系统等效时变刚度的小幅增加或减小;当滚动体陷入故障时,因接触变形保留因子的不同使得其有效接触刚度不同程度降低而导致系统等效时变刚度的减小。系统等效时变刚度的变化引起载荷区中其他滚动体的接触变形和接触力产生不同幅度的变化,从而平衡外部径向载荷,对载荷区中心附近的滚动体的影响较为明显,但不影响各滚动体的有效接触刚度。系统等效时变刚度发生突变,导致系统振动。当外环故障时,等效时变刚度等幅变化;当内环故障时,等效时变刚度的变化受到内环旋转的调制而幅值不同。提出的单自由度时变刚度动力学模型与实际更加吻合。

波浪荷载作用下车辆-轨道-悬浮隧道动力响应研究

为实现波浪荷载作用下车辆-轨道-悬浮隧道系统耦合动力学行为模拟和分析,基于车辆-轨道耦合动力学理论,引入轮轨非线性时变单元矩阵法和结构单元多尺度耦合法,采用弹簧-阻尼单元模拟锚索系统,建立车辆-轨道-悬浮隧道动力相互作用模型;根据线性波浪理论和Morison方程,确定波浪荷载计算方法;最后,基于所建立的车辆-轨道-悬浮隧道动力相互作用模型开展数值仿真模拟,研究波浪荷载作用下锚索等效刚度、波浪高度、行车速度等参数变化时系统振动响应特性及传播规律。研究结果表明:锚索等效刚度变化对轨道-悬浮隧道系统结构位移的影响显著,提高锚索等效刚度能够有效抑制结构位移增大,且考虑部分锚索失效后系统结构位移变化较大,位移增幅均大于43%,不利于结构稳定;轨道-悬浮隧道系统结构的横向位移主要由波浪荷载引起,随着波浪高度增加,轨道-悬浮隧道系统结构位移整体上呈增大趋势;在工程设计过程中,应充分调研场地水环境,并合理设置轨道-悬浮隧道系统的结构参数,以确保系统的安全性和稳定性。

CR连接件弹性抗剪刚度计算方法研究

当前对于钢混组合梁桥中CR连接件的研究主要集中于承载力,对其抗剪刚度研究较少,没有较为通用的理论计算公式。为建立合理的CR连接件抗剪刚度计算公式,笔者基于现有试验建立有限元模型并加以验证,模拟不同结构参数的剪力连接件弹性阶段的荷载-位移曲线,揭示不同参数下的连接件弹性抗剪刚度变化规律。利用等效弹簧模型和等效杆系弹簧模型,笔者分别研究了剪力键、混凝土榫以及混凝土榫内贯穿钢筋的抗剪刚度,结合弹性阶段刚度叠加关系,建立了CR连接件弹性抗剪刚度理论计算公式。理论计算与有限元拟合结果对比表明:连接件弹性抗剪刚度理论计算值与拟合值的误差在7.7%以内,结果吻合性较好,可作为结构设计的依据。

高度修正实现刚度等效的梁结构有限元建模方法

民用飞机中对于梁结构的有限元建模,一般采用刚度等效方法将梁建成杆单元与剪切板单元的组合形式,这种有限元简化方法仅能保证截面刚度与真实截面刚度近似等效,但有限元中的截面面积与实际面积却相差较大,致使有限元分析的结果不能准确反映结构严重部位的应力情况。针对传统刚度等效有限元建模方法的不足,提出一种采用高度修正的刚度等效有限元建模方法;将该方法的计算结果与传统建模方法的计算结果、理论计算结果、试验测量结果进行对比。结果表明:本文提出的高度修正的有限元建模方法比传统杆板系建模方法更准确,与试验结果更接近;将该方法用于民用飞机结构有限元建模,能够对真实结构进行更准确地模拟,分析结果也更精确。

基于稳态响应规律的双线性滞回模型等效参数研究

为了研究等效线性化方法的位移估算精度,以双线性滞回模型为分析模型,分析了非线性单自由度体系的自由振动过程,指出采用割线刚度法(R-H法)计算的等效参数与实际结果偏差较大,进而提出了一种简谐力作用下的等效参数计算方法。考虑了简谐激励的激励周期以及结构振动的位移峰值对计算结果的影响,通过数值分析对不同参数对应下的非线性体系进行等效线性化分析,验证了所提出的等效参数计算方法的有效性与准确性。结果表明,采用R-H法计算的等效刚度偏大,而改进方法能够合理估算非线性时程位移结果,其计算精度优于R-H法。

螺纹连接对引信过载信号粘连的影响因素

侵彻引信多采用螺纹结构与战斗部连接装配。弹体侵彻目标过程中,作用于弹体的冲击载荷将通过螺纹结构传递给引信,使得引信过载较弹体更为复杂,特别是当弹体高速侵彻多层硬目标时,引信过载信号易产生粘连混叠,针对这一问题,基于螺纹连接刚度理论模型,并根据弹引结构特点及其系统等效模型,以某弹引结构为例,对螺纹结构参数影响引信过载信号粘连的情况进行了分析。结果表明,螺距减少,螺纹连接刚度增加,与引信座与战斗部相比,引信与引信座之间螺距的改变对引信处过载影响更大,引信处螺距的增大有利于降低信号的粘连程度。

纵向槽钢和轴力共同作用的盾构隧道等效刚度解析解

为准确快速地预测纵向槽钢加固技术对盾构隧道等效刚度的影响,开展了纵向槽钢加固技术的理论研究。解析地提出了纵向槽钢和纵向轴力耦合作用的盾构隧道等效刚度理论解,并与经典理论、模型试验和数值模拟对比验证了本方法的可靠性。结果表明盾构隧道的中性轴φ随槽钢、纵向轴压力的增加而减小,其大小直接改变了隧道管片间的接触状态,从而影响了隧道的等效刚度;盾构隧道的等效刚度与纵向轴压力呈S曲线正相关,与弯矩呈非线性反相关,与隧道管片宽度、槽钢截面面积、数量、弹性模量呈线性正比关系;盾构隧道的等效刚度贡献大小顺序依次为纵向槽钢数量、截面面积、弹性模量。从理论上诠释了纵向槽钢等敏感性参数对隧道等效刚度的影响机理,可准确快速地预测纵向槽钢加固效果。

基于等效刚度法优化的风力机叶片刚度计算

风力机叶片刚度由于非线性且截面变化程度大的特点,针对叶片建模初期刚度的评估问题通常采用刚度展项分布图体现叶片刚度,存在评估叶片刚度的参考参数不够直接、宏观的问题。基于变刚度梁挠度计算的等效刚度法,将叶片等效成变截面悬臂梁,根据叶片特征合理选取边界条件,以叶片建模的截面数据特点为基础,优化原始等效刚度法的计算方式,使该方法更加贴合叶片模型,从而适用于叶片,达到方法优化的目的。利用ANSYS有限元软件进行叶片的预应力模拟实验,得出叶片的挠度模拟数值,以该模拟计算的挠度值为参考,验证优化后方法的有效性。结果表明:优化后的等效刚度法得到的刚度值,在低均布载荷值22.5 Pa下理论计算的挠度值与试验挠度值的误差达到9.68%,减小原始方法计算的误差贴近叶片模型,可用于叶片刚度估算,为叶片的刚度计算提供新方法。

弹簧蓄能密封圈中蓄能弹簧的有限元计算及等效建模研究

弹簧蓄能密封圈是一种性能优良的密封装置,其中的蓄能弹簧可以为密封圈提供初始密封压力,起到辅助密封的作用。但目前对弹簧蓄能密封圈的研究多是在有限元软件中建立二维轴对称模型进行仿真实验,对蓄能弹簧的力学特性和建模计算方法的认识尚有不足。为实现不同结构的弹簧蓄能密封圈的参数化仿真设计,推导环形蓄能弹簧的空间曲线参数方程,建立双层螺旋蓄能弹簧的三维有限元模型,并仿真分析其力学特性。定义蓄能弹簧的内侧刚度和外侧刚度,研究弹簧不同结构参数对其刚度的影响。结果表明,弹簧的厚度和弹簧截面外径对刚度的影响较大,而弹簧中径和匝数对刚度影响可忽略不计。提出轴对称等效模型的建立原则,建立轴对称等效模型的经验公式,为弹簧蓄能密封圈的参数化仿真设计提供了参考。