桁架结构有限元模型的坐标变换方法

Coordinate transformation method of finite element model for truss structure

在利用有限元方法进行结构分析的过程中,坐标转换是一个重要的步骤。本文利用三角函数和应变能关系分别建立了二维和三维坐标系中桁架单元局部刚度矩阵和整体刚度矩阵之间的转换关系,并利用功能原理推导了荷载向量的局部坐标和整体坐标转换方法,与目前常用的基于几何投影关系推导出来的有限元转换公式相比,本文所建立的坐标变换方法具有代数逻辑严谨、物理意义明确的优点,适合理解和应用。

Coordinate transformation is am important step in structural analysis using finite element method （FEM）. In this study 2D and 3D element stiffness matrices for truss structure were calculated in local coordinate systems and then transformed into the global coordinate systems,the transformation matrix was induced from the relationship of trigonometric functions and strain energy, the load vector was transformed by work-energy theorem. Compared with the general derivation method with geometric projection principle, the new coordinate transformation method results in rigorous logic reasoning and clear physical significance, and it is simple for comperahension and calculation.