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.

在非线性分析中，执行迭代逆计算和非线性系统构建过程会产生昂贵的计算成本。本文提出了一种结合超简化降阶建模（HE-STEP ROM）方法的逐元刚度评估程序。所提出的方法基于元素级刚度评估程序（E-STEP）和超缩减方法构造了一个非侵入式降阶模型。由于E-STEP使用三次多项式逐个元素地评估非线性刚度系数，因此需要大量的多项式变量。变量的数量直接影响在线和离线阶段的计算效率。因此，为了提高在线/离线阶段的效率，所提出的方法采用了超简化方法。通过应用超还原，从在几个采样点评估的刚度系数可以估算出整个刚度系数。随后，多项式方程式和变量的数量显着减少，简化系统的效率提高。该方法的效率和准确性通过具有几何和材料非线性的几个结构动力学问题得到了验证。