华中科技大学学报（自然科学版）2016，Vol.44Issue(4)：101-105,132,6.DOI:10.13245/j.hust.160420
基于增量割线刚度的平面梁几何非线性分析
Geometric nonlinear analysis of planar beam structures based on incremental secant stiffness
摘要
Abstract
T he existing methods of geometric nonlinear analysis is generally considered as time‐consu‐ming and computational intensive under the framework of the incremental‐iterative scheme .By assum‐ing an inverse deformationprocess of the U .L .(updated Lagrangian) approach i .e .,natural deforma‐tion to rigid body motion ,a potential energy formulation was presented and applied to the planar beam member as an illustration .An explicit incremental secant stiffness matrix was correspondingly devel‐oped via the Castigliano′s theorem .The derived secant stiffness matrix was rigid body motion test qualified ,membrane locking free and symmetric as well as simple in form as compared with the one obtained by the U .L .approach making it suitable for a general use in the solutions of geometrical nonlinear problems .By applying the incremental secant stiffness matrix to both the ‘predictor’ and‘corrector’ phases of a typical iteration of geometric nonlinear analysis ,a direct iteration procedure making use of the cylindrical arc‐length constraint equation was proposed for tracing complete equilib‐rium path .Meanwhile ,a root selection algorithm which was capable of successfully giving correct so‐lution direction was presented for specifically dealing with the general cases of non‐proportional load‐ing .T he results of numerical validations demonstrate that the proposed method can reliably avoid the‘turning back’ of solution direction and the phenomenon of divergence during iterative process even in the case of tracing prudent equilibrium path .In comparison of the New ton‐Raphson method ,a reduc‐tion in the total number of incremental steps and computation time can be achieved to effectively im‐prove the analysis efficiency .关键词
几何非线性分析/增量割线刚度矩阵/简化列式/直接迭代法/柱面弧长法/选根算法Key words
geometric nonlinear analysis/incremental secant stiffness matrix/simplified formulation/direct iteration method/cylindrical arc-length method/root selection algorithm分类
数理科学引用本文复制引用
文颖,李特,孙明文,曾庆元..基于增量割线刚度的平面梁几何非线性分析[J].华中科技大学学报（自然科学版）,2016,44(4):101-105,132,6.基金项目
国家自然科学基金资助项目（51108460，51478475）；中国博士后科学基金资助项目（2012M511759）；湖南省科技计划资助项目（2014FJ6036）． （）
