应用数学和力学2017，Vol.38Issue(9)：1029-1040,12.DOI:10.21656/1000-0887.370229
基于S-R和分解定理的几何非线性问题的数值计算分析
Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem
摘要
Abstract
To explore the numerical solution method for geometrically nonlinear problems,the theoretical derivation,the MATLAB programming and the finite element simulation were used together.Based on the S-R decomposition theorem,the interpolated element-free Galerkin method was applied to deduce the incremental variational equations through the updated comoving coordinate formulation,which were solved with the 4-point Gauss integration method and the fixed point iteration method.Finally,the large deformations of exemplary elastic and elastoplastic planar cantilever beams were calculated and the results agreed well with those from the ANSYS simulation.The examples illustrate the correctness and rationality of the proposed geometrically nonlinear mechanics theory and the present numerical calculation method.The work provides a new basis for the solutions to geometrically nonlinear problems.关键词
几何非线性问题/S-R和分解定理/更新拖带坐标法/插值型无单元Galerkin法Key words
geometrically nonlinear problem/S-R decomposition theorem/updated co-moving coordinate formulation/interpolated element-free Galerkin method分类
数理科学引用本文复制引用
宋彦琦,郝亮钧,李向上..基于S-R和分解定理的几何非线性问题的数值计算分析[J].应用数学和力学,2017,38(9):1029-1040,12.基金项目
国家自然科学基金(41430640) （41430640）
深部岩土力学与地下工程国家重点实验室开放基金(SKLGDUEK1728)The National Natural Science Foundation of China (41430640) （SKLGDUEK1728）
