Material nonlinearity analyses are widely used to determine the safety of structural components or engineering structures. Although advanced computer hardware technology has considerably improved the computational performance of such analyses, large and complex emerging structures and expensive computational process still attract the attention of researchers toward finding more efficient and accurate numerical solution methods. This paper combines an inelasticity-separated (IS) concept with the finite-element method (FEM) to establish a novel and efficient framework (IS-FEM) for structures with material nonlinear behavior that only occurs within certain small local domains. The IS concept presented in this paper begins by decomposing the strain on a nonlinear material into its linear-elastic and inelastic components and runs through the whole framework. Based on the principle of virtual work, a novel governing equation for structures with an IS form is derived by treating the decomposed inelastic strain as additional degrees of freedom. Moreover, the changing stiffness matrix in the classical FEM is expressed as the sum of the invariant global linear elastic stiffness matrix and another changing inelastic stiffness matrix with a small rank, and it represents the material nonlinearity of local domains so that the efficient solution method can be applied to perform nonlinear analyses via the mathematical Sherman–-Morrison–Woodbury (SMW) formula. Because the unchanging global stiffness matrix is used throughout the whole nonlinear analysis and the computational effort only focuses on a small dimension matrix that represents the local inelastic behavior, the efficiency of the proposed IS-FEM is improved greatly. The proposed method is validated against the results of classical FEM via three separate numerical examples and its value and potential for use in any material nonlinearity analyses are also demonstrated.

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.

Nonlinear analysis has become an indispensable means for structural performance evaluation, but is still an expensive process especially for large and complex structures. Although the computer technology has largely improve the performance of nonlinear analysis, more efficient and accurate methods still attract the attention of the researchers. The Woodbury nonlinear method which uses the Woodbury formula to solve the incremental displacement response is an efficient kind of method for local nonlinear analysis, but it is no longer applicable for problems with large part of nonlinearity. Although some approximate methods have been proposed to improve the solution of linear equations in Woodbury nonlinear method, the induced error cannot be effectively controlled which leads to decreasing the convergence rate of the iterative computation and offsetting the improved computational efficiency. To address this problem, this paper proposes the Inexact Newton Woodbury (INW) method for efficient nonlinear analysis, which comprehensively considers the efficiency of both the solution of the linear equations and iterative computation. In terms of the linear equations, the improved Woodbury method is presented, where the approximation method is combined with the Woodbury formula, considerably enhancing the solution efficiency of the linear equations and largely extending the application range of the Woodbury formula. Moreover, to ensure the convergence rate which is another important influence factor of the overall nonlinear analysis efficiency, the inexact Newton condition with a new proposed forcing term applicable for the INW method is employed to make the iterative computation with superlinear convergence rate. Then, the time complexity analysis is conducted to make a comprehensive evaluation of the proposed INW method and the traditional Finite Element Method (FEM) from the aspects of the linear equations solution and iterative computation. The results show that the INW method is more efficient than the FEM especially for problems with large part of nonlinearity. Finally, a simulation example is presented to validate the efficiency and accuracy of the INW method. The results demonstrate that the INW method has higher efficiency under comparable accuracy with the Woodbury nonlinear method so that it has significantly potential for large part of nonlinearity problems. CE Database Subject Headings: Engineering structures; finite element method; material nonlinearity; time complexity

Pre-tensioned concrete T-beams with draped strands have been gradually promoted and used in bridge construction in recent years due to their advantages such as simple structure, efficient force distribution, and few defects. However, the current design codes exhibit conservative provisions for the calculation of the shear capacity of such beams under a small shear span ratio, which may lead to a large design value of beam web thickness. This is primarily due to insufficient experimental data. This paper details a full-scale experimental investigation on the shear failure mechanisms of two 30 m pre-tensioned concrete T-beams with draped strands, under a shear span ratio of 1, at which the shear capacity of the beams represents their upper limit. The specimens were tested to analyze their mechanical behavior, including load-deflection response, crack distribution, stirrup strain, and strand slip. The ultimate shear capacities of the test beams were 7107 kN and 6742 kN. To evaluate the applicability of current design codes, the experimental results were compared with theoretical predictions from five international design codes. The analysis revealed that the AASHTO code provided the highest upper limit of shear capacity for pre-tensioned concrete T-beams with draped strands, whereas the Chinese code (JTG 3362-2018) exhibited a significantly high safety factor of 4.09. These findings provide a basis for the optimized design of pre-tensioned concrete T-beams with draped strands and the determination of the upper limit of shear capacity.