桁架结构几何大变形分析的精确方法  

Accurate Algorithm for Geometrically Large Deflection Analysis of Truss Structures

作　　者：孙焕纯[1] 许强[2] 龙武智[2] 

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

出　　处：《应用力学学报》2009年第1期45-50,共6页Chinese Journal of Applied Mechanics

基　　金：大连理工大学211工程建设项目资助

摘　　要：以往对桁架结构的大变形非线性分析,都是应用最小势能原理建立关于节点位移的非线性联立平衡方程,求解的工作量大,尤其对多自由度的大型复杂桁架更为突出。为了克服这个困难,本文采用两步交替迭代线性逐步逼近法,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。第一步,由已知杆件内力建立计算节点位移的连续方程并求解;第二步,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分析的精确解。若干例题计算证明,本法是有效、精确的。尤其是对几何大变形桁架结构的优化设计,可将结构分析的迭代过程与优化过程相结合,省去了多次结构重分析的迭代过程,只在一次结构分析的迭代过程中即可完成优化设计,大大节省了时间。本法对扁桁架尤其有用。So far,accurate algorithm for nonlinear structure analysis of truss structures undergoing large deflection following the nonlinear minimum principle of potential energy has often been adopted to formulate the nonlinear equilibrium equations about the nod displacements,it is obviously difficult for large scale complex truss structures.Here a linear approximating method with two steps of alternative iteration was adopted to make the equilibrium and deformation states harmonic and identical.In the first step,formulating the continuity equations for calculation of the nod displacements from the known axial force of members;and in the second step,formulating the equilibrium equations for computing the axial forces of members from known nod displacements.And the solution of nod displacements and axial forces of members were found respectively in each step.the accurate nonlinear solutions of nod displacement and axial forces of members at a unified state were solved finally by multi-round ite rations.Two examples show that this algorithm is effective and accurate,especially for the optimum design of truss structures undergoing large deflection.

关 键 词：桁架结构 扁桁架 大变形 结构分析 最小势能原理 

分 类 号：O343[理学—固体力学]