计及二阶效应的一种桁架臂几何非线性方法
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摘要
基于二阶效应,运用微分方程法建立承受横向均布载荷压杆在变形位置后的微分方程,将微分方程分解为均承受轴向压力的正弦曲线和二次抛物线曲线的叠加,把变形方程变换成以待定几何参数表达的形式,根据边界条件和平衡条件求解承受横向均布载荷的压杆挠度计算公式;采用该方法对等截面空间桁架臂进行挠度变形分析,并将所求结果与有限元软件ANSYS和ABAQUS非线性分析结果进行对比分析,对比结果验证了所提出方法的可行性与实用性。
Based on the second-order effect, a differential equation of the compressing bars bearing laterally uniformly distributed loads was established under the deformation positions using the differential equation method. Then the differential equation was decomposed into the superposition of sinusoidal and quadratic parabolic curves, which were both under axial pressures. The equation was expressed in the form of undetermined geometric parameters, the deformation equation was obtained by analyzing the boundary conditions and equilibrium conditions. The deformations of the equal cross section space truss booms were analyzed by using this method, comparisons with the results of nonlinear analysis of ANSYS and ABAQUS indicate the proposed method's feasibility and practicability.
Based on the second-order effect, a differential equation of the compressing bars bearing laterally uniformly distributed loads was established under the deformation positions using the differential equation method. Then the differential equation was decomposed into the superposition of sinusoidal and quadratic parabolic curves, which were both under axial pressures. The equation was expressed in the form of undetermined geometric parameters, the deformation equation was obtained by analyzing the boundary conditions and equilibrium conditions. The deformations of the equal cross section space truss booms were analyzed by using this method, comparisons with the results of nonlinear analysis of ANSYS and ABAQUS indicate the proposed method's feasibility and practicability.
引文
[1] 王勖成.有限单元法[M].北京:清华大学出版社,2003.WANG Xucheng.Finite Element Method[M].Beijing:Tsinghua University Press,2003.
[2] SCHARPF D W.New Method of Stress Calculation in the Matrix Displacement Analysis[J].Computers and Structures,1987,8(3/4):465-477.
[3] BIRNSTIE L C,IFFLAND J B.Factors Fluencing Frame Stability[J].Journal of the Structural Division,1980,106(2):491-504.
[4] TO C W S.Linearly Tapered Beam Finite Element Incorporating Shear Deformation and Rotary Inertia for Vibration Analysis[J].Journal of Sound and Vibration.1981,78(4):475-484.
[5] LI G Q,LI J J.A Tapered Timoshenko-Euler Beam Element for Analysis of Steel Portal Frames[J].Journal of Constructional Steel Research,2002,58(12):1531-1544.
[6] 谢贻权,何福保.弹性和塑性力学中的有限单元法[M].北京:机械工业出版社,1981.XIE Yiquan,HE Fubao.Finite Element Mechinery[M].Beijing:Industry Press,1981.
[7] 陆念力,孟丽霞.基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析[J].工程力学,2012,29(12):365-369.LU Nianli,MENG Lixia.Stiffness and Stability Analysis of Variable Cross-section Cantilever Beams Based on Second-order Theory [J].Engineering Mechanics,2012,29 (12):365-369.
[8] 刘晚成.压杆非线性问题的解析方法[M].哈尔滨:东北林业大学出版社,2002.LIU Wancheng.Analysis Method of the Non-linearity of Compression Rod [M].Harbin:Northeast Forestry University Press,2002.
[9] GEORGE J S.An Introduction to the Elastic Stability of Structures [M].Englewood Cliffs and New Jersey:Prentice-Hall,Inc.,1976:77-81.
[10] 安亭铮.履带起重机臂架系统回转平面稳定性研究[D].大连:大连理工大学,2015.AN Tingzheng.Research on Stability of Swing Plane of Crawler Crane Boom System [D].Dalian:Dalian University of Technology,2015.
[2] SCHARPF D W.New Method of Stress Calculation in the Matrix Displacement Analysis[J].Computers and Structures,1987,8(3/4):465-477.
[3] BIRNSTIE L C,IFFLAND J B.Factors Fluencing Frame Stability[J].Journal of the Structural Division,1980,106(2):491-504.
[4] TO C W S.Linearly Tapered Beam Finite Element Incorporating Shear Deformation and Rotary Inertia for Vibration Analysis[J].Journal of Sound and Vibration.1981,78(4):475-484.
[5] LI G Q,LI J J.A Tapered Timoshenko-Euler Beam Element for Analysis of Steel Portal Frames[J].Journal of Constructional Steel Research,2002,58(12):1531-1544.
[6] 谢贻权,何福保.弹性和塑性力学中的有限单元法[M].北京:机械工业出版社,1981.XIE Yiquan,HE Fubao.Finite Element Mechinery[M].Beijing:Industry Press,1981.
[7] 陆念力,孟丽霞.基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析[J].工程力学,2012,29(12):365-369.LU Nianli,MENG Lixia.Stiffness and Stability Analysis of Variable Cross-section Cantilever Beams Based on Second-order Theory [J].Engineering Mechanics,2012,29 (12):365-369.
[8] 刘晚成.压杆非线性问题的解析方法[M].哈尔滨:东北林业大学出版社,2002.LIU Wancheng.Analysis Method of the Non-linearity of Compression Rod [M].Harbin:Northeast Forestry University Press,2002.
[9] GEORGE J S.An Introduction to the Elastic Stability of Structures [M].Englewood Cliffs and New Jersey:Prentice-Hall,Inc.,1976:77-81.
[10] 安亭铮.履带起重机臂架系统回转平面稳定性研究[D].大连:大连理工大学,2015.AN Tingzheng.Research on Stability of Swing Plane of Crawler Crane Boom System [D].Dalian:Dalian University of Technology,2015.