Efficient nonlinear analysis method of masonry structures based on an inelasticity-separated discrete macro-element

Purpose The nonlinear behavior of masonry structures is expressed via the global tangent stiffness matrix with large dimensions that needs to be updated and decomposed in real time, which reduces the calculation efficiency. The purpose of this paper is to propose an efficient nonlinear analysis method of masonry structures based on the inelasticity-separation concept and the discrete macro-element. Design/methodology/approach First, in the discrete macro-element model, each shear panel element interacts with other panels through interface elements to simulate the main failure modes of masonry walls, and the interaction is established by introducing multi-point constraints and relative displacement functions. Then, the inelasticity-separation concept is adopted to decompose the deformations of the shear panel elements and interface elements into linear-elastic and inelastic components, and the inelastic components are modeled using additional inelastic degrees of freedom. Thus, the global tangent stiffness matrix 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. Findings Consequently, the updating and factorization of the global tangent stiffness matrix are avoided, and the computational effort of structural nonlinear analyses only focuses on the updating and factorization of a small-dimensional matrix representing the local inelastic behavior, which greatly improves the efficiency of the proposed method. Practical implications The proposed method provides an effective structural analysis tool for design and performance evaluation of masonry structures. Originality/value This study proposes an efficient implementation of the discrete macro-element with the aim of speeding up the simulations through an inelasticity-separated strategy.