Efficient Method for Derivatives of Nonlinear Stiffness Matrix

Structural design often includes geometrically nonlinear analysis to reduce structural weight and increase energy efficiency. The full-order finite element model can perform the analysis, but its computational cost is expensive. Therefore, reduced-order models (NLROMs) have been developed costs. non-intrusive NLROM has a lower than other due approximation of internal force by polynomial reduced coordinates based on Taylor expansion. constants in polynomial, named stiffnesses, are derived from derivative structure’s tangential stiffness matrix with respect coordinates. precision affects stiffness, which turn significantly influences accuracy NLROM. this study evaluates calculated methods: difference, complex step, hyper-dual step. Analytical derivatives provide references for evaluating numerical methods. We propose using central difference method calculate coefficients advantages, such as accuracy, low cost, compatibility commercial software.