A convergence‐enhanced Timoshenko beam element for the stochastic nonlinear analysis of reinforced concrete components

Abstract

AbstractAn effective and precise physical model is generally required for the performance assessment of reinforced concrete (RC) components. In this study, a convergence‐enhanced Timoshenko beam element considering finite deformation is proposed for the stochastic nonlinear analysis of RC components. The unified framework of the rank 2 correction matrix is obtained by approximating the iterative matrix through the linearly independent basis vectors, and two types of Broyden–Fletcher–Goldfarb–Shanno (BFGS) operators are constructed. Then, a consistent solution scheme with superior numerical stability and efficiency is proposed based on the second kind of BFGS operator and improved quasi‐Newton method. Accurate discretization of the displacement fields and description of nonlinear sectional behavior are achieved by the high‐order Lagrangian interpolation functions, concrete damage‐plasticity model and J2 plasticity model. In an updated Lagrangian formulation, these shape functions and constitutive relationships are used to develop a complete secant stiffness with higher‐order terms in the strain tensor and residual force vector. To validate the proposed Timoshenko beam element, numerical applications involving material nonlinearity and geometrical nonlinearity are conducted. The numerical stability and efficiency of the solution scheme, the shear‐locking free technique, and the oscillation of axial force are thoroughly examined and discussed by solution of RC columns, cantilever beam and progressive collapse of planar RC frame. Finally, the parametric study considering the geometric and material randomness indicates that the RC column designed for flexural failure mode suffered considerable degradation of loading capacity and a larger scatter of residual load.