Evaluation effect of force equilibrium prediction on using secant stiffness in nonlinear displacement-based finite element method

Abstract The convergence rate of iterative solvers is a critical performance metric in nonlinear finite element analysis (FEA). While traditional h- and p-refinement techniques enhance convergence by modifying the spatial discretization, this paper introduces a novel algorithmic-level refinement strategy. We present a computationally efficient mutation algorithm founded on a secant stiffness approach within a modified Newton-Raphson framework. The proposed method leverages the structural response trend to correct assumed displacements, significantly reducing the number of iterations required for equilibrium without altering the mesh topology or element order. Numerical experiments demonstrate that the algorithm achieves a superior convergence rate compared to standard incremental methods. Its straightforward implementation and computational efficiency make it a compelling alternative for large-scale nonlinear structural analysis, offering significant advantages for both research and industrial applications.