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基于离散宏单元的砌体结构高效非线性分析方法

郭勇 余丁浩 李钢

郭勇, 余丁浩, 李钢. 基于离散宏单元的砌体结构高效非线性分析方法[J]. 工程力学, 2022, 39(8): 185-199. doi: 10.6052/j.issn.1000-4750.2021.04.0323
引用本文: 郭勇, 余丁浩, 李钢. 基于离散宏单元的砌体结构高效非线性分析方法[J]. 工程力学, 2022, 39(8): 185-199. doi: 10.6052/j.issn.1000-4750.2021.04.0323
GUO Yong, YU Ding-hao, LI Gang. EFFICIENT NONLINEAR ANALYSIS METHOD OF MASONRY STRUCTURES BASED ON DISCRETE MACRO-ELEMENT[J]. Engineering Mechanics, 2022, 39(8): 185-199. doi: 10.6052/j.issn.1000-4750.2021.04.0323
Citation: GUO Yong, YU Ding-hao, LI Gang. EFFICIENT NONLINEAR ANALYSIS METHOD OF MASONRY STRUCTURES BASED ON DISCRETE MACRO-ELEMENT[J]. Engineering Mechanics, 2022, 39(8): 185-199. doi: 10.6052/j.issn.1000-4750.2021.04.0323

基于离散宏单元的砌体结构高效非线性分析方法

doi: 10.6052/j.issn.1000-4750.2021.04.0323
基金项目: 国家重点研发计划项目(2018YFD1100404);国家自然科学基金项目(52008075);辽宁省“兴辽英才计划”项目(XLYC1902043);中央高校基本科研业务费专项项目(DUT20ZD401)
详细信息
    作者简介:

    郭 勇(1996−),男,山西运城人,博士生,主要从事结构非线性分析等研究(E-mail: 1041783946@qq.com)

    余丁浩(1989−),男,河北邯郸人,助理研究员,博士,主要从事结构非线性分析等研究(E-mail: 954545127@qq.com)

    通讯作者:

    李 钢(1979−),男,辽宁葫芦岛人,教授,博士,博导,主要从事结构工程抗震等研究(E-mail: gli@dlut.edu.cn)

  • 中图分类号: TU365;TU311.4

EFFICIENT NONLINEAR ANALYSIS METHOD OF MASONRY STRUCTURES BASED ON DISCRETE MACRO-ELEMENT

  • 摘要: 砌体结构由力学性能不同的块体和砂浆构成,材料的各向异性使结构非线性行为体现出高度复杂性。砌体结构非线性分析模型主要包括分离式和整体式两种:分离式模型将块体、砂浆及二者粘结界面分开建模,可以精细化揭示砌体非线性行为和破坏形态,但非线性分析计算量大,多用于局部构件的细部分析和模拟;整体式模型将块体和砂浆假定为连续的匀质体,建模过程简单、易行,适用于整体结构的宏观分析。无论是分离式还是整体式,结构非线性计算分析中大规模刚度矩阵的实时更新与分解降低了分析效率。该文提出了一种基于整体式空间离散宏单元模型的砌体结构高效非线性分析方法,该方法采用剪切单元模拟砌体墙的斜截面剪切破坏模式,采用无厚界面单元模拟砌体墙的正截面弯曲破坏模式、正截面剪切滑移破坏模式和平面外剪扭破坏模式,进一步将剪切单元等效斜向弹簧的轴向变形和无厚界面单元上下表面的相对变形分解为线弹性和非线性两部分,并引入塑性自由度描述分离出的非线性部分,可将任意时刻的切线刚度矩阵表示为初始弹性刚度矩阵的低秩摄动形式,引入Woodbury公式进行求解,该文方法避免了大规模整体刚度矩阵的迭代更新,非线性分析的主要计算量仅集中于小规模非线性矩阵的更新与分解,显著提升了计算效率。
  • 图  1  空间离散宏单元模型

    Figure  1.  Spatial discrete macro-element model

    图  2  砌体墙平面内外主要失效模式

    Figure  2.  Main in-plane and out-of-plane failure mechanisms of a masonry portion

    图  3  离散宏单元模型模拟砌体墙平面内外主要失效模式(为简化说明,图(b)、(c)、(d)仅画出一根斜向弹簧)

    Figure  3.  Simulation of the main in-plane and out-of-plane failure mechanisms of a masonry portion by means of the macro-element (For simplicity, only one diagonal spring is shown in figures (b), (c) and (d))

    图  4  砌体材料的单轴本构关系

    Figure  4.  Uniaxial constitutive laws of masonry material

    图  5  非线性材料应变分解

    Figure  5.  Decomposition of nonlinear material strain

    图  6  剪切单元结点自由度

    Figure  6.  Shear element nodal degrees of freedom

    图  7  剪切单元剪切变形模式

    Figure  7.  Shear deformation mode of shear element

    图  8  等效斜向弹簧变形图

    Figure  8.  Deformation of equivalent diagonal spring

    图  9  无厚纤维界面单元

    Figure  9.  Zero-thickness fiber interface element

    图  10  砌体墙片试验滞回曲线

    Figure  10.  Experimental behaviour of simple piers

    图  11  砌体墙片本文方法计算滞回曲线

    Figure  11.  Numerical simulation results of piers (proposed method)

    图  12  砌体墙片CP方法计算滞回曲线

    Figure  12.  Numerical simulation results of piers (CP method)

    图  13  砌体墙片骨架曲线

    Figure  13.  Skeleton curves of simple piers

    图  14  结构平面简图

    注:图中字母C-1代表窗;M-1代表门;Z-1代表构造柱。

    Figure  14.  Plane of the masonry structure

    图  15  卧龙地震波加速度记录

    Figure  15.  Acceleration record of Wolong earthquake

    图  16  约束砌体结构数值分析模型

    Figure  16.  Discrete macro-element model of the masonry structure

    图  17  各楼层位移时程曲线

    Figure  17.  Time-history curves of all floors

    图  18  结构基底剪力时程曲线

    Figure  18.  Base shear force curve of the masonry structure

    图  19  外横墙损伤分布图

    Figure  19.  Damage distribution of outer transversal wall

    图  20  塑性自由度时程曲线

    Figure  20.  Time-history curves of plastic degrees of freedom

    图  21  时间复杂度时程曲线

    Figure  21.  Time-history curves of time complexity

    表  1  墙体材料属性

    Table  1.   Material properties of masonry walls

    压弯受力/MPa剪切受力/MPa
    弹性模量抗压强度抗拉强度剪切模量抗剪强度
    2100−6.20.15000.275
    下载: 导出CSV

    表  2  墙体几何属性

    Table  2.   Geometry properties of masonry walls

    名称截面尺寸/m2高度/m竖向压应力/MPa
    Wall-11.0×0.252.000.6
    Wall-21.0×0.251.350.6
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-29
  • 修回日期:  2021-09-26
  • 网络出版日期:  2021-10-21
  • 刊出日期:  2022-08-01

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