Reduced-order modeling of nonlinear structural dynamical systems via element-wise stiffness evaluation procedure combined with hyper-reduction

In nonlinear analysis, performing iterative inverse calculation and nonlinear system construction procedures incurs expensive computational costs. This paper presents an element-wise stiffness evaluation procedure combined with hyper-reduction reduced-order modeling (HE-STEP ROM) method. The proposed approach constructs a non-intrusive reduced-order model based on an element-wise stiffness evaluation procedure (E-STEP) and hyper-reduction methods. Because the E-STEP evaluates nonlinear stiffness coefficients element-by-element using cubic polynomial, numerous number of polynomial variables are required. The number of variables directly affects the computational efficiency of the online and offline stages. Therefore, to enhance efficiency of the online/offline stages, the proposed method employs hyper-reduction method. By applying hyper-reduction, the full stiffness coefficients are approximated from the stiffness coefficients evaluated at a few sampling points. Subsequently, the number of polynomial equations and variables is prominently reduced, and the efficiency of the reduced system increases. The efficiency and accuracy of the proposed approach are validated via several structural dynamic problems with geometric and material nonlinearities.