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Analysis of plane strain bending of a strain hardening curved beam based on unified yield criterion

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Journal of Southeast University(English Edition) 2016年第3期32卷 339-345页

作者：傅军庞苗宋广远张永强杨博浙江理工大学建筑工程学院杭州310018 浙江大学建筑工程学院杭州310058

The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. The solutions for the mechanical properties of plane strain bending are derived, which are adapted for various kinds of non-strength differential materials and can be degenerated to those based on the Tresca, von Mises, and twin-shear yield criteria. The dependences of the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane on different yield criteria and Poisson’s ratios are discussed. The results show that the influences of different yield criteria and Poisson’s ratio on the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane of the curved beam are significant. Once the value of bis obtained by experiments, the yield criterion and the corresponding solution for the materials of interest are then determined.

关键词： curved beam plane strain strain hardening elastic-plastic bending unified yield criterion

Non-uniform rational B-spline based free vibration analysis of axially functionally graded tapered Timoshenko curved beams

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Applied Mathematics and Mechanics(English Edition) 2020年第4期41卷 567-586页

作者： Zhiwei ZHOU Meixia CHEN Kun XIE School of Naval Architecture and Ocean Engineering Huazhong University of Science and Technology College of Engineering Huazhong Agricultural University

The free vibration of axially functionally graded(FG) tapered Timoshenko curved beams is studied with the numerical approach. By using the non-uniform rational B-spline(NURBS) basis functions, the exact geometry and the generalized displacement?eld are formulated. Variable geometric parameters and material properties, including the curvature, cross-sectional area, area moment of inertia, mass density, and Young’s modulus, are expanded as functions of the coordinate in a parametric domain. Based on Hamilton’s principle, the weak formulation is derived by applying a re?ned constitutive relation which considers the thickness e?ect. Natural frequencies and mode shapes are obtained from the eigenvalue equation. Circular, elliptic, and parabolic curved beams are considered in numerical examples. The obtained results are in good agreement with those in the existing studies and those calculated by the ?nite element software ***, the e?ects of the material gradient, taper ratio, slenderness ratio, and heightspan ratio on vibration behaviors are discussed.

关键词： free vibration functionally graded(FG) material non-uniform crosssection curved beam variable curvature thickness effect

Exact solution for warping of spatial curved beams in natural coordinates

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Applied Mathematics and Mechanics(English Edition) 2008年第7期29卷 933-941页

作者：朱莉莉赵颖华 Institute of Road and Bridge Engineering Dalian Maritime University School of Mechanical Engineering Dalian Jiaotong UniversityDalian 116028Liaoning ProvinceP.R.China

The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present theory are demonstrated by comparing its numerical results with Heins＇ solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

关键词： curved beam multiple loads warping natural coordinate analytical solution

Explicit Analytical Solutions for the Shearingand Radial Stresses in curved beams

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 151-156页

作者： Aiming YU+ Xiangrong LI+++ (Tongji University, Shanghai 200092, China)++ (Shanghai University, Shanghai 200072, China) Tongji University Shanghai 200092 China Shanghai University Shanghai 200072 China

The shearing stresses in curved beams can be solved explicitly from anintegral equation, which is obtained by differentiation & integral manipulations. Twonovel formulae for shearing & radial stresses are also presented in the paper. The resultsof an example reveal that the shearing & radial stresses arrive at their maximum valuesslightly below the centroid of the section.

关键词： curved beam shearing stress radial stress integral equation

A bio-inspired spider-like structure isolator for low-frequency vibration

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Applied Mathematics and Mechanics(English Edition) 2023年第8期44卷 1263-1286页

作者： Guangdong SUI Shuai HOU Xiaofan ZHANG Xiaobiao SHAN Chengwei HOU Henan SONG Weijie HOU Jianming LI State Key Laboratory of Robotics and System Harbin Institute of TechnologyHarbin 150001China School of Astronautics Harbin Institute of TechnologyHarbin 150001China Yangtze River Delta HIT Robot Technology Research Institute Wuhu 241000Anhui ProvinceChina Tianjin Key Laboratory of Microgravity and Hypogravity Environment Simulation Technology Tianjin 300301China

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating *** curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS *** finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS *** harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental *** experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear *** frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 *** proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

关键词： bionic isolation structure curved beam nonlinear stiffness quasi-zero stiffness(QzS) low-frequency vibration isolator

Dynamic Performance of Straddle Monorail curved Girder Bridge

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Computer Modeling in Engineering & Sciences 2022年第3期130卷 1669-1682页

作者： Yan Zhou Kai Zhang Feng Miao Pengfei Yang Tianjin Key Laboratory of Civil Structure Protection and Reinforcement Tianjin Chengjian UniversityTianjin300384China Tianjin Municipal Engineering Design&Research Institute Co. Ltd.Tianjin300051China Dalian University Dalian116622China

In this work,a monorail vehicle-bridge coupling(VBC)model capable of accurately considering curve alignment and superelevation is established based on curvilinear moving coordinate system,to study the VBC vibration of straddlemonorail curved girder bridge and the relevant factors influencing *** taking Chongqing Jiao Xin line as an example,the VBC program is compiled using Fortran,where the reliability of algorithm and program is verified by the results of Chongqing monorail ***,the effects of curve radius,vehicle speed,and track irregularity on the corresponding vehicle and bridge vibrations are compared and *** is observed that the test results of lateral vibration acceleration(LVA)and vertical vibration acceleration(VVA)of track beam,and LVA of vehicle,are consistent with the simulation *** to the track irregularity,vibration of track beam and vehicle increases ***,an increase in vehicle speed gradually increases the vibration of track beam and *** the curve radius(R)≤200 m,lateral and vertical vibrations of the track beam and vehicle decrease significantly with an increasing curve ***,when 200 mbeamand vehicle decreases slowly with an increasing curve radius,while the relevant vertical vibration remains ***,when R≥600 m,the lateral and vertical vibrations of the track beam and vehicle tend to be ***,the results presented here can provide a strong reference for the design,construction,and safety assessment of existing bridges.

关键词： Straddle monorail curved beam curve radius track irregularity vehicle-bridge coupling vibration

Geometric nonlinear formulation for curved beams with varying curvature

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Theoretical & Applied Mechanics Letters 2012年第6期2卷 43-48页

作者： Keqi Pan Jinyang Liu School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

Based on exact Green strain of spatial curved beam, the relation for plane curved beam with varying curvature is derived nonlinear strain-displacement Instead of using the previous straight beam elements, curved beam elements are used to approximate the curved beam with varying curvature. Based on virtual work principle, rigid-flexible coupling dynamic equations are obtained. Physical experiments were carried out to capture the large overall motion and the strain of curved beam to verify the present rigid-flexible coupling formulation for curved beam based on curved beam element. Numerical results obtained from simulations were compared with those results from the physical experiments. In order to illustrate the effectiveness of the curved beam element methodology, the simulation results of present curved beam elements are compared with those obtained by previous straight beam elements. The dynamic behavior of a slider-crank mechanism with an initially curved elastic connecting rod is investigated. The advantage of employing generalized-or method is pointed out and the special nonlinear dynamic characteristics of the curved beam are concluded.

关键词： curved beam rigid-flexible coupling dynamics geometric nonlinear experiment

Large deflection of curved elastic beams made of Ludwick type material

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Applied Mathematics and Mechanics(English Edition) 2017年第7期38卷 909-920页

作者： Hua LIU Yi HAN Jialing YANG School of Aeronautic Science and Engineering Beihang University Beijing 100191 China

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlin- earities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

关键词： large deflection curved beam Ludwick type material nonlinearity

Free Vibration Analysis of Spatial curved beams with Variable Curvature and Torsion

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Free Vibration Analysis of Spatial Curved Beams with Variabl...