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

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.