应变局部化分析的嵌入强间断多尺度有限元法

发布时间：2018-02-04 08:39

本文关键词： 多尺度有限元法嵌入强间断模型应变局部化增强粗单元弹塑性分析　出处：《力学学报》2017年03期 　论文类型：期刊论文

【摘要】：固体材料的应变局部化行为是导致结构破坏失效的重要因素之一,开展相关数值模拟分析对于结构安全性评估具有重要意义.然而由于材料的非均质和多尺度特性,采用传统数值方法进行求解时通常需要从最小特征尺度离散求解的结构,这将大幅度增加计算规模和成本.针对这一问题,本文提出了一种基于嵌入强间断模型的多尺度有限元方法.该方法从粗细两个尺度离散求解模型,首先在细尺度单元上引入嵌入强间断模型来描述单元间断特性,所附加的跳跃位移自由度则通过凝聚技术进行消除,从而保持细尺度单元刚度阵维度不变.其次,提出了一种增强多节点粗单元技术,其可根据局部化带与粗单元边界相交情况自适应动态地增加粗节点,新构造的增强数值基函数可以捕捉细尺度间断特性,完成物理信息从细单元到粗单元的准确传递以及宏观响应的快速分析;再次,在细尺度解的计算中,将细尺度解分解为降尺度解与单胞局部摄动解,从而消除弹塑性分析时单胞内部的不平衡力.最后,通过两个典型算例分析,并与完全采用细单元的嵌入有限元结果进行对比,验证了所提出算法的正确性与有效性.
[Abstract]:Strain localization behavior of solid materials is one of the important factors leading to structural failure. It is important to carry out relevant numerical simulation analysis for structural safety assessment. However, due to the heterogeneity and multi-scale characteristics of materials. In order to solve the problem, the traditional numerical method usually needs to discrete the structure from the minimum characteristic scale, which will greatly increase the scale and cost of the calculation. In this paper, a multi-scale finite element method based on embedded strongly discontinuous model is proposed. Firstly, the embedded strong discontinuity model is introduced to describe the discontinuity of the element, and the additional jump displacement degree of freedom is eliminated by the condensation technique. In order to keep the dimensions of the fine scale element stiffness matrix unchanged. Secondly, an enhanced multi-node coarse element technique is proposed, which can increase the coarse nodes dynamically and adaptively according to the intersection of the localization band and the coarse element boundary. The newly constructed enhanced numerical basis function can capture the discontinuous characteristics of the fine scale, complete the accurate transfer of the physical information from the fine unit to the coarse element and the rapid analysis of the macro response. Thirdly, in the calculation of the small scale solution, the fine scale solution is decomposed into downscaling solution and local perturbation solution of unit cell, so as to eliminate the unbalance force in the unit cell in elastic-plastic analysis. Finally, two typical examples are given. The correctness and validity of the proposed algorithm are verified by comparison with the results of the embedded finite element method.
【作者单位】：大连理工大学国际计算力学研究中心工业装备结构分析国家重点实验室运载工程与力学学部工程力学系;
【基金】：国家自然科学基金(11232003,11672062) 中央高校基本科研业务费(DUT14YQ217)资助项目
【分类号】：O302
【正文快照】： 2016 12 27收稿,2017 03 12录用,2017 03 13网络版发表.2)郑勇刚,教授,主要研究方向:多尺度与多场耦合计算力学.E-mail:zhengyg@dlut.edu.cn引用格式:卢梦凯,张洪武,郑勇刚.应变局部化分析的嵌入强间断多尺度有限元法.力学学报,2017,49(3):649-658Lu Mengkai,Zhang Hong

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