Efficient Multilayered Shell Model and Its Application in Large Reinforced Concrete Structures

Abstract

When using the traditional multilayered shell element to perform material nonlinearity analysis of large structures, the computation time is often overwhelming because of the repeated updating and factorization of the large-size global stiffness matrix. This paper aims to provide an efficient and general solution to such problems. To this end, a novel flat multilayered shell model is proposed by adding additional inelastic degrees of freedom (IDOFs) to describe the inelastic behavior of elements and adopting the approximate Woodbury formula that is an efficient solution method based on matrix perturbation theory as a solver. In this way, the entire nonlinear solution process only needs to factorize a sparse matrix called approximate Schur complement, whose dimension is consistent with the IDOF number, instead of the global stiffness matrix. To avoid the performance degradation of the proposed approach due to the activation of too many IDOFs when performing material nonlinearity analysis on large reinforced concrete (RC) structures, an improved concrete constitutive model and a two-level sparseness strategy are further developed. These measures are helpful to numerically reduce the IDOF number of the RC multilayered shell model, thus saving the computational overhead of factorizing and constructing the approximate Schur complement matrix. The accuracy and efficiency of the proposed scheme are verified by numerical examples.