In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a mortar-tied contact formulation. The snapshots for the substructure projection matrices are computed on the substructure level by the proper orthogonal decomposition (POD) method. The snapshots are computed using a random sampling procedure based on a parametrization of boundary conditions. To reduce the computational effort of the snapshot computation full-order simulations of the substructures are only computed when the error of the reduced solution is above a threshold. In numerical examples, we show the accuracy and efficiency of the method for nonlinear problems involving material and geometric nonlinearity as well as non-matching meshes. We are able to predict solutions of systems that we did not compute in our snapshots.

翻译：本文提出了一种针对由部件组装而成的非线性结构的模型降阶技术。该降阶模型通过对子结构进行本征正交分解降阶，并采用砂浆绑定接触公式进行连接而构建。子结构投影矩阵所需的快照在子结构层级上通过本征正交分解方法计算。快照计算采用基于边界条件参数化的随机采样程序。为降低快照计算的计算成本，仅当降阶解的误差超过阈值时，才对子结构进行全阶模拟计算。在数值算例中，我们展示了该方法对于涉及材料非线性、几何非线性以及非匹配网格的非线性问题的准确性与效率。我们能够预测未在快照集中计算过的系统解。