弹性开口薄壁截面圆弧钢拱的稳定承载力研究
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摘要
曲梁因其优美的造型被广泛地应用在现代结构工程中。根据荷载作用平面的不同曲梁可分成两类，当荷载只作用在曲率平面内时称为拱，而当荷载作用平面与曲率平面垂直时称为水平曲梁。曲梁不同于直梁之处在于初始曲率的存在，这使得其弯曲、扭转、翘曲的几何方程大都是相互耦合的，其变形常为是弯扭变形，导致了曲梁理论分析的复杂性。目前尚缺乏对曲梁的复杂结构特性进行全面、精确的分析，使其应用仍受到较大限制。
曲梁的非线性方程与薄壁开口截面拱的稳定承载力是本文探讨的两大主题。本文在评述国内外本课题相关领域研究现状的基础上，从理论推导和数值分析两个方面对这两大主题进行了研究。
首先进行的是薄壁开口圆弧钢曲梁非线性方程的推导。基于薄壁构件分析的基本假定，采用薄壁圆弧曲梁的精确翘曲位移表达式，根据虚位移原理得到了曲梁的稳定平衡方程，并给出了曲梁考虑几何非线性情况下的总势能。推导中对应变高阶项采用合理的简化处理，使理论推导过程简单明了。本章的理论推导是后续的拱的屈曲荷载分析的理论基础。
其次介绍了一个经典的拱的弹性弯扭屈曲试验，并采用有限元商业软件ANSYS中的SHELL63单元和BEAM189单元分别进行了模拟。数值分析结果和试验结果都十分吻合，说明SHELL63壳单元、BEAM189梁单元都可较好地模拟弹性拱的整体弯扭屈曲荷载。用BEAM189梁单元分析时所需单元少，计算速度快，但只能模拟荷载作用在形心和截面为双轴对称的情况。拱在均匀受压和均匀受弯作用下的屈曲荷载公式可用有限元方法加以验证。
随后本文对薄壁开口截面圆弧拱的弹性屈曲荷载进行了理论分析，得出了双轴对称截面简支拱、单轴对称截面简支拱及固支拱在均匀受压和均匀受弯的受力状态下的屈曲荷载，并与其它研究结果、有限元模拟结果进行了比较，证明了本文理论推导的正确性和有效性。把计算公式进行了合理地简化，以便于工程中的应用。两端铰支拱在径向均布荷载作用下，在拱轴线展开长度不变的条件下，弯扭屈曲荷载随着拱圆心角的增大而逐渐减小，当圆心角为180°时，这时拱可绕其两端点连线作刚体自由转动，对平面外屈曲没有抵抗能力，屈曲荷载为零。简支拱在两端等弯矩作用下，当为正弯矩时，弯扭屈曲荷载随圆心
Curved beams have been widely used in structure engineering because of graceful shape. Curved beams can be classified into arch and horizontally curved beams based on the plane on which load is acted. When load is acted on the curvature plane, it is named arch; when load is acted on the plane perpendicular to the curvature plane, it is named horizontally curved beams. Curved beams differ from straight beams simply because of the presence of the initial curvature. The geometrical equations of flexure, torsion and warp of curved beams are coupled, which results in complexity of theoretical analysis. Now it is lack of the all-sided and exact analysis for curved beams, which limits the application of curved beams.
This dissertation focused on the nonlinear equations and stability capability of open thin-walled circular arches. On the basis of the investigation of the related home and overseas literatures, extensive researches are carried out on the subjects by theoretical and numerical analyses.
Firstly, the nonlinear equations of open thin-walled curved beams are derived. Based on the basic assumptions of thin-walled members, using the exact expression of warping displacement, the stability equations of curved beams are obtained by the principle of virtual displacements. The total potential energy is given also.
Secondly, a classical elastic flexural-torsional buckling tests on arch is introduced, which is simulated by shell element SHELL63 and beam element BEAM189 of commercial software ANSYS. Numerical results are consistent with test results, so elastic flexural-torsional buckling load of arches can be analysed by SHELL63 or BEAM189 elements. A fewer elements need be divided with beam element,and calculation speed is more rapid, but only when load acts on centroid of the section the arch of double symmetric section can be simulated by beam element. Succedent buckling load equations of arch under uniform compression or uniform bending can be verified by finite element method.
Following theoretical investigations on buckling of thin-walled circular arch
曲梁的非线性方程与薄壁开口截面拱的稳定承载力是本文探讨的两大主题。本文在评述国内外本课题相关领域研究现状的基础上，从理论推导和数值分析两个方面对这两大主题进行了研究。
首先进行的是薄壁开口圆弧钢曲梁非线性方程的推导。基于薄壁构件分析的基本假定，采用薄壁圆弧曲梁的精确翘曲位移表达式，根据虚位移原理得到了曲梁的稳定平衡方程，并给出了曲梁考虑几何非线性情况下的总势能。推导中对应变高阶项采用合理的简化处理，使理论推导过程简单明了。本章的理论推导是后续的拱的屈曲荷载分析的理论基础。
其次介绍了一个经典的拱的弹性弯扭屈曲试验，并采用有限元商业软件ANSYS中的SHELL63单元和BEAM189单元分别进行了模拟。数值分析结果和试验结果都十分吻合，说明SHELL63壳单元、BEAM189梁单元都可较好地模拟弹性拱的整体弯扭屈曲荷载。用BEAM189梁单元分析时所需单元少，计算速度快，但只能模拟荷载作用在形心和截面为双轴对称的情况。拱在均匀受压和均匀受弯作用下的屈曲荷载公式可用有限元方法加以验证。
随后本文对薄壁开口截面圆弧拱的弹性屈曲荷载进行了理论分析，得出了双轴对称截面简支拱、单轴对称截面简支拱及固支拱在均匀受压和均匀受弯的受力状态下的屈曲荷载，并与其它研究结果、有限元模拟结果进行了比较，证明了本文理论推导的正确性和有效性。把计算公式进行了合理地简化，以便于工程中的应用。两端铰支拱在径向均布荷载作用下，在拱轴线展开长度不变的条件下，弯扭屈曲荷载随着拱圆心角的增大而逐渐减小，当圆心角为180°时，这时拱可绕其两端点连线作刚体自由转动，对平面外屈曲没有抵抗能力，屈曲荷载为零。简支拱在两端等弯矩作用下，当为正弯矩时，弯扭屈曲荷载随圆心
Curved beams have been widely used in structure engineering because of graceful shape. Curved beams can be classified into arch and horizontally curved beams based on the plane on which load is acted. When load is acted on the curvature plane, it is named arch; when load is acted on the plane perpendicular to the curvature plane, it is named horizontally curved beams. Curved beams differ from straight beams simply because of the presence of the initial curvature. The geometrical equations of flexure, torsion and warp of curved beams are coupled, which results in complexity of theoretical analysis. Now it is lack of the all-sided and exact analysis for curved beams, which limits the application of curved beams.
This dissertation focused on the nonlinear equations and stability capability of open thin-walled circular arches. On the basis of the investigation of the related home and overseas literatures, extensive researches are carried out on the subjects by theoretical and numerical analyses.
Firstly, the nonlinear equations of open thin-walled curved beams are derived. Based on the basic assumptions of thin-walled members, using the exact expression of warping displacement, the stability equations of curved beams are obtained by the principle of virtual displacements. The total potential energy is given also.
Secondly, a classical elastic flexural-torsional buckling tests on arch is introduced, which is simulated by shell element SHELL63 and beam element BEAM189 of commercial software ANSYS. Numerical results are consistent with test results, so elastic flexural-torsional buckling load of arches can be analysed by SHELL63 or BEAM189 elements. A fewer elements need be divided with beam element,and calculation speed is more rapid, but only when load acts on centroid of the section the arch of double symmetric section can be simulated by beam element. Succedent buckling load equations of arch under uniform compression or uniform bending can be verified by finite element method.
Following theoretical investigations on buckling of thin-walled circular arch
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