重力对超静定结构受力的影响
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摘要
目前有关超静定结构的受力分析中几乎均未考虑分支重力的影响,针对此,提出了一种考虑分支重力情况下超静定结构受力分析的方法。首先基于分支的力矩平衡方程直接求解出在分支重力作用下产生的施加给动平台的垂直分支轴线方向的约束力分量,并将其视作施加给结构的广义外力;然后基于结构变形协调关系和受力平衡方程,获得超静定结构各分支沿其轴线方向的约束力分量的完整解析表达式以及存在制造误差时装配内力的解析表达式;最后讨论了分支重力对超静定结构受力的影响机理。以平面超静定结构3-RR和空间超静定结构7-SS为例进行了实例分析,并建立对应的刚柔混合模型,进行了仿真验证。
In view of the facts that the literatures about force analyses of the statically indeterminate structures almost had not considered limb's gravity at present,a method was proposed,which took it into account.Firstly,the constraint force components perpendicular to the axis of each limb which were caused by the corresponding limbs' gravity were solved based on single limb's torque equilibrium equations,and it was regarded as the generalized force imposed on the whole structure.Then,according to the force equilibrium equations and deformation compatibility conditions of the whole structure,the analytical expressions were derived including the limbs' axial constraint force components and the assembly internal forces brought by manufacturing errors.Finally,the influences of limbs' gravity on the force analysis of the statically indeterminate structures were discussed.Taking the planar mechanism 3-RR and the spatial mechanism 7-SS as examples,the constraint forces were analyzed and the rigid-flexible mixed models of the two mechanisms were established.Based on the models the theoretical results were verified.
In view of the facts that the literatures about force analyses of the statically indeterminate structures almost had not considered limb's gravity at present,a method was proposed,which took it into account.Firstly,the constraint force components perpendicular to the axis of each limb which were caused by the corresponding limbs' gravity were solved based on single limb's torque equilibrium equations,and it was regarded as the generalized force imposed on the whole structure.Then,according to the force equilibrium equations and deformation compatibility conditions of the whole structure,the analytical expressions were derived including the limbs' axial constraint force components and the assembly internal forces brought by manufacturing errors.Finally,the influences of limbs' gravity on the force analysis of the statically indeterminate structures were discussed.Taking the planar mechanism 3-RR and the spatial mechanism 7-SS as examples,the constraint forces were analyzed and the rigid-flexible mixed models of the two mechanisms were established.Based on the models the theoretical results were verified.
引文
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[19]KOWAL Z.Instruments of Probabilistic Optimization of Load Bearing Capacity and Reliability of Statically Indeterminate Complex Structures[J].Archives of Civil Engineering,2014,60(1):77-90.
[20]陈永林.广义逆矩阵的理论与方法[M].南京:南京师范大学出版社,2005:36.CHEN Yonglin.The Theory and Method of Generalized Inverse Matrix[M].Nanjing:Nanjing Normal University Press,2005:36.
[21]赵永生,刘文兰,许允斗,等.一种过约束并联机构受力的数值仿真分析方法[J].中国机械工程,2015,26(12):1576-1583.ZHAO Yongsheng,LIU Wenlan,XU Yundou,et al.A Numerical Simulation Method for Force Analysis of an Overconstrained PM[J].China Mechanical Engineering,2015,26(12):1576-1583.
[2]ROJAS A L.Method of Structural Analysis for Statically Indeterminate Rigid Frames[J].International Journal of Innovative Computing,Information and Control,2013,9(5):1951-1970.
[3]李银山,李彤,郭晓欢,等.索-梁耦合超静定结构的一种快速解析法[J].工程力学,2014,31(增刊1):11-16.LI Yinshan,LI Tong,GUO Xiaohuan,et al.A Fast Analytical Method for Statically Indeterminate Problems of Cable-beam Coupled Structures[J].Engineering Mechanics,2014,31(S1):11-16.
[4]边文凤,董正筑.超静定桁架变形协调方程的新方法[J].计算力学学报,2002,19(2):250-252.BIAN Wenfeng,DONG Zhengzhu.A New Method for Problem of Hyperstatic Truss[J].Chinese Journal of Computational Mechanics,2002,19(2):250-252.
[5]皮天祥,罗俊,张爱环,等.跨高比L/h≤1.5复合配筋连梁箍筋受力性能的拉杆-压杆模型分析[J].工程力学,2015,32(4):69-76.PI Tianxiang,LUO Jun,ZHANG Aihuan,et al.Strut and Tie Model Analysis of Shear Capacity for Stirrup in Compositely Reinforced Coupling Beams with Span-to-depth Ratio L/h≤1.5[J].Engineering Mechanics,2015,32(4):69-76.
[6]ABBAS A A,MOHSIN S M S,CPTSOVOS D M.Non-linear Analysis of Statically Indeterminate SFRC Columns[J].Structural Concrete,2014,15(1):94-105.
[7]ABBAS A,MOHSIN S,COTSOVOS D,et al.Statically-indeterminate SFRC Columns under Cyclic Loads[J].Advances in Structural Engineering,2014,17(10):1403-1417.
[8]吴晓,黄志刚,杨立军.用拉格朗日乘子法求解双模量静不定结构[J].力学与实践,2013,35(6):79-81.WU Xiao,HUANG Zhigang,YANG Lijun.Force Analysis of the Statically Indeterminate Structures with Double Modulus by Lagrange Multiplier Method[J].Mechanics in Engineering,2013,35(6):79-81.
[9]隋允康,邵建义.自适应超静定桁架结构强度控制的研究[J].固体力学学报,2001,22(2):136-142.SUI Yunkang,SHAO Jianyi.Research on Strength Control for Adaptive Structure of Statically Indeterminate Truss[J].Acta Mechanica Solida Sinica,2001,22(2):136-142.
[10]QIN Y D,SHIRINZADEH B J,ZHANG D W,et al.Compliance Modeling and Analysis of Statically Indeterminate Symmetric Flexure Structures[J].Precision Engineering,2013,37:415-424.
[11]XU Y D,YAO J T,ZHAO Y S.Inverse Dynamics and Internal Forces of the Redundantly Actuated Parallel Manipulators[J].Mechanism and Machine Theory,2012,51:172-184.
[12]FATEMI S,SHEIKH A,ALI M.Development and Application of an Analytical Model for Horizontally Curved Bridge Decks[J].Advances in Structural Engineering,2015,18(1):107-117.
[13]YAO J T,HOU Y L,CHEN J,et al.Theoretical Analysis and Experiment Research of a Statically Indeterminate Pre-stressed Six-axis Force Sensor[J].Sensors and Actuators A:Physical,2009,150:1-11.
[14]姚建涛,李立建,许允斗,等.超静定六维力传感器静定测量模型及标定方法[J].仪器仪表学报,2013,34(9):1927-1933.YAO Jiantao,LI Lijian,XU Yundou,et al.Statically Determinate Measurement Model and Calibration Method of Statically Indeterminate Six-axis Force Sensor[J].Chinese Journal of Scientific Instrument.2013,34(9):1927-1933.
[15]姚建涛,李立建,许允斗,等.冗余并联结构六维力传感器及其超静定静力映射解析分析[J].工程力学,2014,31(10):205-211.YAO Jiantao,LI Lijian,XU Yundou,et al.Redundant-parallel Structure Six-axis Force Sensor and Hyperstatic Static Mapping Analytical Analysis[J].Engineering Mechanics,2014,31(10):205-211.
[16]韩先国,陈五一.基于运动约束解过约束并联机构变形协调方程[J].力学与实践,2005,27(3):65-68.HAN Xianguo,CHEN Wuyi.The Method to Solve the Compatibility Equation of Distortion of Over constraint Parallel Manipulator Based on Kinematic Constraint[J].Mechanics in Engineering,2005,27(3):65-68.
[17]JIA Z Y,LIN S,LIU W.Measurement Method of Six-axis Load Sharing Based on the Stewart Platform[J].Measurement,2010,43(3):329-335.
[18]YANG D X,CHEN G H,DU Z L.Direct Kinematic Method for Exactly Constructing Influence Lines of Forces of Statically Indeterminate Structures[J].Structural Engineering and Mechanics,2015,54(4):793-807.
[19]KOWAL Z.Instruments of Probabilistic Optimization of Load Bearing Capacity and Reliability of Statically Indeterminate Complex Structures[J].Archives of Civil Engineering,2014,60(1):77-90.
[20]陈永林.广义逆矩阵的理论与方法[M].南京:南京师范大学出版社,2005:36.CHEN Yonglin.The Theory and Method of Generalized Inverse Matrix[M].Nanjing:Nanjing Normal University Press,2005:36.
[21]赵永生,刘文兰,许允斗,等.一种过约束并联机构受力的数值仿真分析方法[J].中国机械工程,2015,26(12):1576-1583.ZHAO Yongsheng,LIU Wenlan,XU Yundou,et al.A Numerical Simulation Method for Force Analysis of an Overconstrained PM[J].China Mechanical Engineering,2015,26(12):1576-1583.