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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