曲梁单元的理论研究及其在桥梁中的应用
发布时间：2018-12-15 23:31
【摘要】：随着时代的飞速发展,曲梁结构因其优美的流线造型和良好的受力特性,在我们日常生活中被广泛地应用在各个领域。但是又因为曲梁受曲率的影响,引起了曲梁内的弯扭耦合,从而导致了对曲梁的研究比对直梁的研究还更加的困难,因而有必要对曲梁进行深入的研究。本文首先构造了一个能考虑轴向拉伸和弯曲效应,每节点有3个自由度的3节点平面曲梁单元,并推导了其在局部坐标下的单元刚度矩阵。利用Hermite和Lagrange插值函数构造该曲梁单元的位移函数,并得到了其单元的形函数,进而利用变分原理,推导了考虑几何非线性的平面曲梁单元的局部坐标下的单元刚度矩阵显示表达式。然后以所推导的平面曲梁单元刚度矩阵为基础,对其进行从局部坐标系向整体坐标系的坐标转换,得到了适用于整体坐标下的单元刚度矩阵。并分别对曲梁在径向分布荷载、集中荷载和集中力偶的情况下进行荷载等效的计算。接着在算例中将使用本文方法所得结果与理论推导结果进行对比,验证曲梁单元的正确性。最后在以上理论研究的基础上,利用有限元软件ANSYS的二次开发功能,将理论推导的曲梁单元形式通过用户自定义单元在ANSYS中定义出来,并将其应用到桥梁工程实例分析中,同时采用桥梁专用软件Midas Civil进行对比分析,通过实例说明了本文推导的新型曲梁单元能较好的应用于桥梁工程实例分析中。
[Abstract]:With the rapid development of the times, curved beam structure has been widely used in our daily life because of its beautiful streamline modeling and good mechanical properties. However, because curved beam is affected by curvature, the bending and torsional coupling in curved beam is caused, which leads to more difficulties in the study of curved beam than that of straight beam, so it is necessary to deeply study curved beam. In this paper, a 3-node plane curved beam element with three degrees of freedom per node, which can take account of axial stretching and bending effects, is constructed, and its stiffness matrix in local coordinates is derived. The displacement function of the curved beam element is constructed by using Hermite and Lagrange interpolation functions, and the shape function of the curved beam element is obtained, and then the variational principle is used. The display expression of element stiffness matrix in local coordinates of plane curved beam element considering geometric nonlinearity is derived. Then, based on the stiffness matrix of plane curved beam element, the element stiffness matrix suitable for the whole coordinate system is obtained by transforming it from the local coordinate system to the global coordinate system. The equivalent loads of curved beams under radial distributed load, concentrated load and concentrated couple are calculated respectively. The results obtained by the method are compared with the theoretical results to verify the correctness of the curved beam element. Finally, on the basis of the above theoretical research, using the secondary development function of the finite element software ANSYS, the curved beam element form derived from the theory is defined in ANSYS by the user-defined element, and it is applied to the bridge engineering example analysis. At the same time, the bridge special software Midas Civil is used to carry on the contrast analysis, and the example shows that the new curved beam element derived in this paper can be used in the bridge engineering case analysis.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441
本文编号：2381465
[Abstract]:With the rapid development of the times, curved beam structure has been widely used in our daily life because of its beautiful streamline modeling and good mechanical properties. However, because curved beam is affected by curvature, the bending and torsional coupling in curved beam is caused, which leads to more difficulties in the study of curved beam than that of straight beam, so it is necessary to deeply study curved beam. In this paper, a 3-node plane curved beam element with three degrees of freedom per node, which can take account of axial stretching and bending effects, is constructed, and its stiffness matrix in local coordinates is derived. The displacement function of the curved beam element is constructed by using Hermite and Lagrange interpolation functions, and the shape function of the curved beam element is obtained, and then the variational principle is used. The display expression of element stiffness matrix in local coordinates of plane curved beam element considering geometric nonlinearity is derived. Then, based on the stiffness matrix of plane curved beam element, the element stiffness matrix suitable for the whole coordinate system is obtained by transforming it from the local coordinate system to the global coordinate system. The equivalent loads of curved beams under radial distributed load, concentrated load and concentrated couple are calculated respectively. The results obtained by the method are compared with the theoretical results to verify the correctness of the curved beam element. Finally, on the basis of the above theoretical research, using the secondary development function of the finite element software ANSYS, the curved beam element form derived from the theory is defined in ANSYS by the user-defined element, and it is applied to the bridge engineering example analysis. At the same time, the bridge special software Midas Civil is used to carry on the contrast analysis, and the example shows that the new curved beam element derived in this paper can be used in the bridge engineering case analysis.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441
【参考文献】
相关期刊论文 前2条
1 夏飞;辛克贵;;薄壁曲梁振动分析的样条有限杆元法[J];工程力学;2009年03期
2 武兰河,刘淑红,周敏娟;圆弧曲梁面内自由振动的微分容积解法[J];振动与冲击;2004年01期
，本文编号：2381465
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