“依赖应变历史材料”结构动力松弛法静力分析中规避虚假应变历史的非线性弹性增量算法  

NONLINEAR-ELASTIC-INCREMENT ALGORITHM FOR ELIMINATING FICTITIOUS STRAIN HISTORY IN STATIC ANALYSIS OF SHDM STRUCTURES USING THE DYNAMIC RELAXATION METHOD

作　　者：苏小卒[1] 王伟 SU Xiao-zu;WANG Wei(College of Civil Engineering,Tongji University,Shanghai 200092,China;School of Civil Engineering,Shaoxing University,Zhejiang 312000,China)

机构地区：[1]同济大学土木工程学院,上海200092 [2]绍兴文理学院土木工程学院,浙江312000

出　　处：《工程力学》2020年第3期120-130,共11页Engineering Mechanics

基　　金：国家自然科学基金项目(51178328)。

摘　　要：针对SHDM结构(由依赖应变历史材料制成的结构)有限元非线性静力平衡方程组动力松弛法(DRM)迭代求解时的积分点应力更新步骤,提出非线性弹性增量算法,即在一个静力增量步内固定材料的加卸载路径,使之在该增量步内成为非线性弹性材料。该应力更新算法能使包括收敛解在内的迭代序列中不含虚假应变历史。此外,该算法还可避免静力解答精度依赖于静力增量步长的局限性。通过三个SHDM结构的数值试验对该算法进行了验证。该算法可望对SHDM结构非线性有限元静力问题DRM分析技术的发展起促进作用。This study is to formulate a stress-updating method when solving static equilibrium equations of finite element models of structures with strain-history dependent material(SHDM).Using the dynamic relaxation method(DRM),the nonlinear-elastic-increment algorithm was employed so that the loading and unloading paths were fixed within one increment and the material became nonlinear elastic within the increment.The algorithm eliminated the fictitious strain history from the iterative series including the final converged solution.Moreover,this method removed the limitation whereby the accuracy of the solution was dependent upon the increment step size.Three numerical examples were used to verify the proposed algorithm.It is expected that the algorithm promotes the development of DRM for solving static problems of nonlinear finite element analyses of SHDM structures.

关 键 词：结构工程 静力分析 有限元方法 动力松弛法 依赖应变历史材料 非线性弹性增量算法 

分 类 号：TU313[建筑科学—结构工程]