基于共旋坐标法的空间桁架几何非线性分析

以往提出的共旋坐标法中，随动与整体坐标系的转换矩阵的计算需要中介值，对于大型工程结构会影响计算效率，且共旋坐标法在有限元程序中的实现多基于面向过程技术，以至数据不易管理、功能难以扩充，此外桁架何时考虑几何非线性也缺乏研究。本文归纳对比了两种常用的共旋坐标法理论，基于整体坐标系原点来建立随转坐标系，给出无需中介值的空间桁架转换矩阵及杆端抗力的具体表达式，并基于此法，使用C++语言在基于面向对象技术的程序Aduts中实现空间桁架单元，进一步简化了共旋坐标法的计算，使其在有限元程序中的数据管理、二次开发和维护更简便。设计典型算例验证了本文桁架单元的正确性，并通过参数分析研究桁架的几何非线性，结果表明桁架的几何非线性不能单纯以经验理论即应变达到5%为判断依据，而需结合拱跨比的值来确定。

Geometric non-linearity Analysis of Space Truss Based on Co-rotational Procedure

In the previous co-rotational procedure, intermediate value was needed in the calculation of the transformation matrix of the co-rotating and the global coordinate system. For large engineering structure, computational efficiency is impacted. Moreover, the realization of the co-rotational procedure in finite element program is mostly based on the process-oriented, so the management of the data and the extension of functionality are in difficulty. In addition, there is a little study on the theoretical criterion of the geometric non-linearity of the truss. In this paper, two common theories of co-rotational procedure are summarized and compared. The co-rotational coordinate system is established based on the origin of global coordinate system. The transformation matrix without intermediate value and the concrete formulation of bar end resistance of space truss are given. Based on this method, the space truss element is realized in the program Aduts based on object-oriented technology by using C++ language. The calculation of the co-rotational procedure is further simplified, and the data management, re-development and maintenance in the finite element program are easier. The correctness of the proposed truss element is verified by a typical design example. The geometric non-linearity of truss is studied by parameter analysis, and results show that the geometric non-linearity of the truss cannot be judged solely based on the empirical theory, that is, the strain reaches 5%, but needs to be determined by combining the value of arch-span ratio.