拟牛顿法求解堆石坝结构非线性方程
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摘要
探讨了求解堆石坝结构非线性方程的拟牛顿法，详细阐明了拟牛顿法在堆石坝结构分析中的实施过程，并编制了相应的三维非线性有限元分析程序，将拟牛顿法与中点增量法同时用于实例计算，表明拟牛顿法收敛速度较快且数值稳定性好，优越于中点增最法。
he quasi-Newton method,one of solving methods for noninear FEM equation of rockfill dams,is discussed and the practive process of quasi-Newton method in stucture analysis of rockfill dams is also described in detail.A corresponding FEM program for 3-D material nonlinear analysis is developed,Stress and strain of a rockfill dam are calculated by both the quasi-Newton method and the middle point incremental method. Through comparision and analysis, the conclution is drawn that the quasi-Newton method is better than the middle point incremental method.The calculating process shows that quasi-Newton method has better convergence rate and numerical stability and is one of the most successful nonlinear solving methods.
he quasi-Newton method,one of solving methods for noninear FEM equation of rockfill dams,is discussed and the practive process of quasi-Newton method in stucture analysis of rockfill dams is also described in detail.A corresponding FEM program for 3-D material nonlinear analysis is developed,Stress and strain of a rockfill dam are calculated by both the quasi-Newton method and the middle point incremental method. Through comparision and analysis, the conclution is drawn that the quasi-Newton method is better than the middle point incremental method.The calculating process shows that quasi-Newton method has better convergence rate and numerical stability and is one of the most successful nonlinear solving methods.
引文
1殷有泉。固体力学非线性有限元引论，北京大学出版社、清华大学出版社，1987．8～162BrodlieKW，GourlayAR，GreenstadtJ．Rank－oneandRank－twoCorrectionstoPositiveDefiniteMatricesExpressedinProductForm．JInstMathApplics，1973，11：73～823MatthiesH，StrangG，TheSolutionofNonliearFiniteElementEquations．IntJNumMethEng，1979，14：1613～16294顾淦臣，土石坝地震工程，河海大学出版社，1989．166～178
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