Abstract:
Resilience-based earthquake engineering methodology plays an important role in the field of structural aseismic design. Within a framework to assess the aseismic resilience of buildings, accurately determining damage states for individual buildings under earthquake excitations is basic to predict buildings’ functionality loss and recoverability. Existing studies determined a damage state for each component with phenomenological engineering demand parameters (EDPs) such as the storey drift ratio, the nodal rotation at the beam end, etc., from the nonlinear dynamic processes data. Nevertheless, phenomenological EDPs may not suffice to predict refined structural damage in irregular complex structures, which leads to the resilience assessment results arising a large uncertainty, and phenomenological EDPs are lack of clear physical meanings. In addition, the nonlinear dynamic analysis based on the classical finite element method (FEM) requires the large-scale tangent stiffness matrix that needs to be updated and decomposed iteratively in real time to calculate structural damage, which reduces the calculation efficiency exceedingly. Aiming to solve the problems mentioned above, an efficient seismic damage analysis method of structures is proposed upon the inelasticity-separated theory. First the novel method proposed decomposes the total strain of a nonlinear material into three parts, elastic strain, damage strain and plastic strain, and defines the damage and plastic strain distribution fields within elements. Further a novel governing equation with the feature that is capable of realizing the elasticity, damage and plasticity separation is established by the grounds of the principle of virtual work, and the proposed governing equation is solved via the efficient mathematical Woodbury formula. Consequently, the computational effort of the nonlinear structural dynamic analysis only focuses on the updating and factorization of the damage and plastic matrices with small-rank, and during the iteration process the updating and factorization of tangent stiffness matrix in the classical FEM are avoided, which significantly improves the efficiency of nonlinear calculation. Finally, a local damage quantification approach for structures is established by the basis of the decomposed damage and plastic strains. Because the plastic and damage strains, introduced by the governing equation proposed and obtained in real time during the iteration process, have definite physical meanings, the refined structural damage distribution and evolution can be depicted accurately.