EFFICIENT NONLINEAR ANALYSIS METHOD OF MASONRY STRUCTURES BASED ON DISCRETE MACRO-ELEMENT
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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。
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关键词:
- 砌体结构 /
- 隔离非线性 /
- 剪切单元 /
- 无厚界面单元 /
- Woodbury公式
Abstract: Masonry is a composite material composed of blocks and mortar joints with different mechanical properties, and its material anisotropy causes the highly complex nonlinear behavior of masonry. The modeling strategies for masonry structures are classified into two main categories: discrete models and continuum models. Discrete models are assembled with rigid or deformable blocks and mortar bond interface elements, and they can reveal the nonlinear behavior and the failure modes of masonry accurately. However, their complicated modeling processes and material constitutive relationships cause a huge computational demand, so they are often used in analysis and simulation of structural components. In continuum approaches, the structures are idealized into panel-scale structural components, so the modeling processes are simple and convenient. These approaches are mainly focused on the global seismic response, and they are suitable for the analysis of large structures. During the process of seismic nonlinear analysis of masonry structures, whether discrete models or continuum models, the nonlinear behavior is expressed via the large-scale changing tangent stiffness matrix that needs to be updated and decomposed iteratively in real time, which reduces the calculation efficiency significantly. An efficient nonlinear analysis method of masonry structures based on the continuum spatial discrete macro-element model is proposed, in which each shear panel element can interact with other shear panel elements by means of zero-thickness interface elements to simulate the main in-plane and out-of-plane failures of masonry walls, the axial deformation of equivalent diagonal springs in shear panel element and the inter-laminar deformation of interface elements are decomposed into linear-elastic and inelastic components, and the decomposed inelastic component can be calculated by using additional plastic degrees of freedom. Consequently, the changing tangent stiffness matrix in the classical finite-element method is expressed as a small-rank perturbation of the global linear elastic stiffness matrix, and the global governing equation is solved via the efficient mathematical Woodbury formula. During iteration process, the updating and factorization of tangent stiffness matrix in the classical finite-element are avoided and the computational effort of structure nonlinearity analyses only focuses on the updating and factorization of a small dimension matrix that represents the local inelastic behavior, so the efficiency of the proposed method is improved greatly. -
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 11 砌体墙片本文方法计算滞回曲线
Figure 11. Numerical simulation results of piers (proposed method)
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 −6.2 0.1 500 0.275 
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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-1 1.0×0.25 2.00 0.6 Wall-2 1.0×0.25 1.35 0.6
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[1] Lourenço P B, Rots J G. Multisurface interface model for analysis of masonry structures [J]. Journal of Engineering Mechanics-ASCE, 1997, 123(7): 660 − 668. doi: 10.1061/(ASCE)0733-9399(1997)123:7(660) [2] Sandoval C, Arnau O. Experimental characterization and detailed micro-modeling of multi-perforated clay brick masonry structural response [J]. Materials and Structures. 2017, 50(1): 34. [3] Calderón S, Sandoval C, Arnau O. Shear response of partially-grouted reinforced masonry walls with a central opening: Testing and detailed micro-modelling [J]. Materials and Design, 2017, 118: 122 − 137. [4] Lourenço P B. Computations on historic masonry structures [J]. Progress in Structural Engineering and Materials, 2002, 4(3): 301 − 319. doi: 10.1002/pse.120 [5] Roca P, Cervera M, Gariup G, et al. Structural analysis of masonry historical constructions. classical and advanced approaches [J]. Archives of Computational Methods in Engineering, 2010, 17(3): 299 − 325. doi: 10.1007/s11831-010-9046-1 [6] Minga E, Macorini L, Izzuddin B A. A 3D mesoscale damage-plasticity approach for masonry structures under cyclic loading [J]. Meccanica, 2018, 53(7): 1591 − 1611. doi: 10.1007/s11012-017-0793-z [7] Bertolesi E, Milani G, Casolo S. Homogenization towards a mechanistic Rigid Body and Spring Model (HRBSM) for the non-linear dynamic analysis of 3D masonry structures [J]. Meccanica, 2018, 53(7): 1819 − 1855. doi: 10.1007/s11012-017-0665-6 [8] Petracca M, Pelà L, Rossi R, et al. Regularization of first order computational homogenization for multiscale analysis of masonry structures [J]. Computational Mechanics, 2016, 57(2): 257 − 276. doi: 10.1007/s00466-015-1230-6 [9] Leonetti L, Greco F, Trovalusci P, et al. A multiscale damage analysis of periodic composites using a couple-stress/Cauchy multidomain model: Application to masonry structures [J]. Composites Part B-Engineering, 2017, 141: 50 − 59. [10] Quagliarini E, Maracchini G, Clementi F. Uses and limits of the equivalent frame model on existing unreinforced masonry buildings for assessing their seismic risk: A review [J]. Journal of Building Engineering, 2017, 10: 166 − 182. doi: 10.1016/j.jobe.2017.03.004 [11] Parisi F, Augenti N. Seismic capacity of irregular unreinforced masonry walls with openings [J]. Earthquake Engineering and Structural Dynamics, 2013, 12(1): 101 − 121. [12] Berti M, Salvatori L, Orlando M, et al. Unreinforced masonry walls with irregular opening layouts: Reliability of equivalent-frame modelling for seismic vulnerability assessment [J]. Bulletin of Earthquake Engineering, 2017, 15(3): 1213 − 1239. doi: 10.1007/s10518-016-9985-5 [13] Lagomarsino S, Penna A, Galasco A, et al. TREMURI program: An equivalent frame model for the nonlinear seismic analysis of masonry buildings [J]. Engineering Structures, 2013, 56: 1787 − 1799. doi: 10.1016/j.engstruct.2013.08.002 [14] Siano R, Roca P, Camata G, et al. Numerical investigation of non-linear equivalent-frame models for regular masonry walls [J]. Engineering Structures, 2018, 173: 512 − 529. doi: 10.1016/j.engstruct.2018.07.006 [15] Magenes G, Fontana A. Simplified non-linear seismic analysis of masonry buildings [C]// Proceedings of the 5th International Masonry Conference. London, UK: The Society Stoke-on-Trent, 1998, 8: 190 − 195. [16] Kappos A J, Penelis G G, Drakopoulos C G. Evaluation of simplified models for lateral load analysis of unreinforced masonry buildings [J]. Journal of Structural Engineering, 2002, 128(7): 890 − 897. doi: 10.1061/(ASCE)0733-9445(2002)128:7(890) [17] Roca P, Molins C, Marí A R. Strength capacity of masonry wall structures by the equivalent frame method [J]. Journal of Structural Engineering-ASCE, 2005, 131(10): 1601 − 1610. doi: 10.1061/(ASCE)0733-9445(2005)131:10(1601) [18] Belmouden Y, Lestuzzi P. An equivalent frame model for seismic analysis of masonry and reinforced concrete buildings [J]. Construction and Building Materials, 2009, 23(1): 40 − 53. doi: 10.1016/j.conbuildmat.2007.10.023 [19] Grande E, Imbimbo M, Sacco E. A beam finite element for nonlinear analysis of masonry elements with or without fiber-reinforced plastic (FRP) reinforcements [J]. International Journal of Architectural Heritage, 2011, 5: 693 − 716. doi: 10.1080/15583058.2010.490616 [20] Addessi D, Mastrandrea A, Sacco E. An equilibrated macro-element for nonlinear analysis of masonry structures [J]. Engineering Structures, 2014, 70: 82 − 93. doi: 10.1016/j.engstruct.2014.03.034 [21] Addessi D, Liberatore D, Masiani R. Force-based beam finite element (FE) for the pushover analysis of masonry buildings [J]. International Journal of Architectural Heritage, 2015, 9(3): 231 − 243. doi: 10.1080/15583058.2013.768309 [22] Caliò I, Marletta M, Pantò B. A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings [J]. Engineering Structures, 2012, 40: 327 − 338. doi: 10.1016/j.engstruct.2012.02.039 [23] Pantò B, Cannizzaro F, Caliò I, et al. Numerical and experimental validation of a 3d macro-model for the in-plane and out-of-plane behavior of unreinforced masonry walls [J]. International Journal of Architectural Heritage, 2017, 11(7): 946 − 964. [24] Chácara C, Cannizzaro F, Pantò B, et al. Assessment of the dynamic response of unreinforced masonry structures using a macroelement modeling approach [J]. Earthquake Engineering and Structural Dynamics, 2018, 47(12): 2426 − 2446. [25] Caliò I, Pantò B. A macro-element modelling approach of infilled frame structures [J]. Computers and Structures, 2014, 143: 91 − 107. doi: 10.1016/j.compstruc.2014.07.008 [26] Pantò B, Caliò I, Lourenço P B. Seismic safety evaluation of reinforced concrete masonry infilled frames using macro modelling approach [J]. Bulletin of Earthquake Engineering, 2017, 15(9): 3871 − 3895. doi: 10.1007/s10518-017-0120-z [27] Pantò B, Caliò I, Lourenço P B. A 3D discrete macro-element for modelling the out-of-plane behaviour of infilled frame structures [J]. Engineering Structures, 2018, 175: 371 − 385. doi: 10.1016/j.engstruct.2018.08.022 [28] Pantò B, Silva L, Vasconcelos G, et al. Macro-modelling approach for assessment of out-of-plane behavior of brick masonry infill walls [J]. Engineering Structures, 2019, 181: 529 − 549. doi: 10.1016/j.engstruct.2018.12.019 [29] Chácara C, Cannizzaro F, Pantò B, et al. Seismic vulnerability of URM structures based on a Discrete Macro-Element Modeling (DMEM) approach [J]. Engineering Structures, 2019, 201: 109715. doi: 10.1016/j.engstruct.2019.109715 [30] Drosopoulos G A, Stavroulakis G E. A computational homogenization approach for the study of localization of masonry structures using the XFEM [J]. Archive of Applied Mechanics, 2018, 88(12): 2135 − 2152. doi: 10.1007/s00419-018-1440-4 [31] Giambanco G, Ribolla Emma L M, Spada A. Meshless meso-modeling of masonry in the computational homogenization framework [J]. Meccanica, 2018, 53(7): 1673 − 1697. doi: 10.1007/s11012-017-0664-7 [32] Silva L C, Lourenço P B, Milani G. Derivation of the out-of-plane behaviour of masonry through homogenization strategies: Micro-scale level [J]. Computers and Structures, 2018, 209: 30 − 43. doi: 10.1016/j.compstruc.2018.08.013 [33] Krejci T, Kruis J, Sejnoha M, et al. Hybrid parallel approach to homogenization of transport processes in masonry [J]. Advances in Engineering Software, 2017, 113(SI): 25 − 33. [34] Clough R W, Wilson E L. Dynamic analysis of large structural systems with local nonlinearities [J]. Computer Methods in Applied Mechanics and Engineering, 1979, 17: 107 − 129. [35] 孙宝印, 古泉, 张沛洲, 等. 钢筋混凝土框架结构弹塑性数值子结构分析方法[J]. 工程力学, 2016, 33(5): 44 − 49. doi: 10.6052/j.issn.1000-4750.2015.07.ST08Sun Baoyin, Gu Quan, Zhang Peizhou, et al. Elastoplastic numerical substructure method of reinforced concrete frame structures [J]. Engineering Mechanics, 2016, 33(5): 44 − 49. (in Chinese) doi: 10.6052/j.issn.1000-4750.2015.07.ST08 [36] 孙宝印, 古泉, 张沛洲, 等. 考虑P-Δ效应的框架结构弹塑性数值子结构分析[J]. 工程力学, 2018, 35(2): 153 − 159. doi: 10.6052/j.issn.1000-4750.2016.10.0773Sun Baoyin, Gu Quan, Zhang Peizhou, et al. Elastoplastic numerical substructure method of frame structure considering P-Δ effects [J]. Engineering Mechanics, 2018, 35(2): 153 − 159. (in Chinese) doi: 10.6052/j.issn.1000-4750.2016.10.0773 [37] Akgün M A, Garcelon J H, Haftka R T. Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas [J]. International Journal for Numerical Methods in Engineering, 2002, 50(7): 1587 − 1606. [38] Kirsch U. Reanalysis and sensitivity reanalysis by combined approximations [J]. Structural and Multidisciplinary Optimization, 2010, 40(1/2/3/4/5/6): 1 − 15. doi: 10.1007/s00158-009-0369-1 [39] Li G, Wong K. Theory of nonlinear structural analysis: the force analogy method for earthquake engineering [M]. Singapore: John Wiley & Sons, 2014. [40] Li G, Zhang Y, Li H. Nonlinear seismic analysis of reinforced concrete frames using the force analogy method [J]. Earthquake Engineering and Structural Dynamics, 2014, 43(14): 2115 − 2134. doi: 10.1002/eqe.2439 [41] 靳永强, 李钢, 李宏男. 基于拟力法的钢支撑非线性滞回行为模拟[J]. 工程力学, 2017, 34(10): 139 − 148. doi: 10.6052/j.issn.1000-4750.2016.06.0444Jin Yongqiang, Li Gang, Li Hongnan. Numerical simulation of steel brace hysteretic behavior based on the force analogy method [J]. Engineering Mechanics, 2017, 34(10): 139 − 148. (in Chinese) doi: 10.6052/j.issn.1000-4750.2016.06.0444 [42] 李钢, 吕志超, 余丁浩. 隔离非线性分层壳有限单元法[J]. 工程力学, 2020, 37(3): 18 − 27. doi: 10.6052/j.issn.1000-4750.2019.01.0189Li Gang, Lü Zhichao, Yu Dinghao. The finite element model for inelasticity-separated multi-layer shell [J]. Engineering Mechanics, 2020, 37(3): 18 − 27. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.01.0189 [43] Li G, Yu D. Efficient inelasticity-separated finite-element method for material nonlinearity analysis [J]. Journal of Engineering Mechanics-ASCE, 2018, 144(4): 04018008. doi: 10.1061/(ASCE)EM.1943-7889.0001426 [44] 苏璞, 李钢, 余丁浩. 基于子结构的Woodbury非线性分析方法[J]. 工程力学, 2020, 37(5): 26 − 35. doi: 10.6052/j.issn.1000-4750.2019.07.0419Su Pu, Li Gang, Yu Dinghao. A woodbury nonlinear analysis approach based on the substructuring method [J]. Engineering Mechanics, 2020, 37(5): 26 − 35. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.07.0419 [45] 李佳龙, 李钢, 李宏男. 基于隔离非线性的实体单元模型与计算效率分析[J]. 工程力学, 2019, 36(9): 40 − 49, 59. doi: 10.6052/j.issn.1000-4750.2018.07.0383Li Jialong, Li Gang, Li Hongnan. The inelasticity-separated solid element model and computational efficiency analysis [J]. Engineering Mechanics, 2019, 36(9): 40 − 49, 59. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.07.0383 [46] Li G, Jia S, Yu D, et al. Woodbury approximation method for structural nonlinear analysis [J]. Journal of Engineering Mechanics-ASCE, 2018, 144(7): 04018052. doi: 10.1061/(ASCE)EM.1943-7889.0001464 [47] Anthoine A, Magonette G, Magenes G. Shear compression testing and analysis of brick masonry walls [C]// Proceedings of 10th European Conference on Earthquake Engineering. Vienna Austria: Central Institute for Meteorology and Geodynamics, 1995: 1657 − 1662. [48] Li G, Yu D, Li H. Seismic response analysis of reinforced concrete frames using inelasticity-separated fiber beam-column model [J]. Earthquake Engineering and Structural Dynamics, 2018, 47(5): 1291 − 1308. doi: 10.1002/eqe.3018 [49] 熊立红, 吴文博, 孙悦. 汶川地震作用下约束砌体房屋的抗震能力分析[J]. 土木工程学报, 2012, 45(增刊 2): 103 − 108.Xiong Lihong, Wu Wenbo, Sun Yue. Seismic performance of confined masonry buildings during the Wenchuan earthquake [J]. China Civil Engineering Journal, 2012, 45(Suppl 2): 103 − 108. (in Chinese) [50] Li G, Jia S, Li H. Efficiency evaluation of structural nonlinear analysis method based on the Woodbury formula [J]. Engineering Computations, 2019, 36(4): 1082 − 1100. doi: 10.1108/EC-09-2018-0393 -
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