大跨度桁架几何大变形结构分析的一种数值方法  

An algorithm for analysis of large span truss structures with large deformation

作　　者：许强[1] 陈庆[1] 孙焕纯[2] 

机构地区：[1]同济大学,上海200092 [2]大连理工大学,大连116023

出　　处：《土木工程学报》2009年第1期16-22,共7页China Civil Engineering Journal

摘　　要：基于ANSYS平台的二次开发,针对桁架结构几何大变形分析问题提出了一种有效的数值算法。主要思路为:采用两步交替迭代逐步逼近,使平衡状态与变形状态协调、统一,建立并求出变形后的平衡方程及其解;也就是说,首先由已知杆件内力建立计算节点位移的连续方程并求解,然后由已知节点位移建立计算杆件内力的平衡方程并求解,通过多次迭代求得平衡状态与变形状态协调统一的非线性大变形结构分析的精确解。本文方法在整个求解过程中仅需做一次结构分析,此在几何大变形桁架结构的优化设计中更突显其优点。本文方法对扁桁架、大跨度桁架尤其有用。通过编制相应的ANSYS二次开发程序,并由数值算例验证了本文方法的可行性、计算精确和计算效率。An efficient algorithm based on the re-development function of ANSYS is presented for nonlinear analysis of large span truss structures undergoing large deflection. Successive approximation method through alternative stepwise iteration was adopted to make equilibrium and deformation compatibility consistent. In other words, the continuity equations after deformation are formulated： first formulating the geometric equations for calculating the nod displacements using the known axial force of the members, and second formulating the equilibrium equations for calculating the axial forces of the members using the known node displacements. The solutions of node displacements and axial forces of members were found, respectively, in each step. Through multiple iterations the accurate nonlinear solutions of node displacement and axial forces of the members at a unified state were obtained. This method has obvious advantage for the optimization design of truss structures with the large deformation, because it only needs analyzing the structure once in the entire process. This method is especially effective for fiat truss and large span truss structures. Several examples are presented to show that this method is feasible, accurate and efficient.

关 键 词：桁架结构 大跨度 大变形 近似二次逼近 结构分析 

分 类 号：O342[理学—固体力学] TU323.4[理学—力学]