This paper presents a first implementation of the LArge Time INcrement (LATIN) method along with the model reduction technique called Proper Generalized Decomposition (PGD) for solving nonlinear low-frequency dynamics problems when dealing with a quasi-brittle isotropic damage constitutive relations. The present paper uses the Time-Discontinuous Galerkin Method (TDGM) for computing the temporal contributions of the space-time separate-variables solution of the LATIN-PGD approach, which offers several advantages when considering a high number of DOFs in time. The efficiency of the method is tested for the case of a 3D bending beam, where results and benchmarks comparing LATIN-PGD to classical time-incremental Newmark/Quasi-Newton nonlinear solver are presented. This work represents a first step towards taking into account uncertainties and carrying out more complex parametric studies imposed by seismic risk assessment.

翻译：本文首次实现了大时间增量（LATIN）方法，并结合称为适当广义分解（PGD）的模型降阶技术，用于求解涉及准脆性各向同性损伤本构关系的非线性低频动力学问题。本文采用时间间断伽辽金方法（TDGM）来计算LATIN-PGD方法时空变量分离解的时间分量贡献，该方法在处理时间维度上大量自由度时具有若干优势。通过一个三维弯曲梁的案例测试了该方法的效率，并给出了将LATIN-PGD与经典的时间增量Newmark/Quasi-Newton非线性求解器进行比较的结果和基准测试。本工作是迈向考虑不确定性并开展由地震风险评估所要求的更复杂参数化研究的第一步。