有限元软件梁杆单元局部坐标系的简化确定方法

A Simplified Determination Method for the Local Coordinate System of Beam Element in Finite Element Software

有限元软件(如SAP2000、ETABS、Midas等)的梁杆单元在工程结构设计和理论分析中有着广泛的应用。对于复杂三维空间结构,需要确定梁杆单元局部坐标系以定义单元截面几何特性、输入单元荷载、处理软件输出的结构内力和变形等结果。上述软件中,确定梁杆单元最终局部坐标系涉及三维坐标转换问题,传统的方法是基于泰勒级数展开的线性模型转换方法和基于罗德里格矩阵的三维坐标转换方法等,以上计算方法涉及繁琐的矩阵变换和计算,不利于理解和应用。在现有传统方法基础上,简化了旋转矩阵的确定过程,建立了最终局部坐标系在整体坐标系中的简化确定方法。简化方法无传统方法对旋转角和精度的限制。验算结果表明,与基于罗德里格矩阵的三维坐标转换方法相比,简化方法是正确和有效的。

The beam unit of finite element software,such as SAP2000,ETABS,Midas,etc.,is widely applied in engineering design and theoretical analysis.For complex three-dimensional structures,the local coordinate system of the beam elements needs to be identified so that the elements geometric features can be defined,the element of the load can be input,and the output results of internal structure force and deformation can be solved.Among the aboved software,the three-dimensional coordinate transformation needs to be considered to define the final coordinate system of the beam unit.The traditional methods include linear model transformation which bases on Taylor series expansion and three-dimensional coordinate transformation which bases on Roderick matrix and others.Meanwhile,the traditional calculation methods are against the understanding and application because of the complicated matrix transformation and calculation.On the basis of the traditional methods,this paper simplifies the process of determining the rotation matrix and establishes a simplified determination method which is the final local coordinate system in the global coordinate system,and the simplified method has no limitation on rotation angle and accuracy.The results show that the simplified method is correct and effective compared with the three-dimensional coordinate transformation based on Roderick matrix.