Dual-reduction order parallel simulation of large-scale problems with local material nonlinearities

Nonlinear finite element analysis is one of the primary techniques for static or transient nonlinear analysis of engineering structures, allowing accurate modelling of complex load-deformation behaviours. However, the significant computational requirements have traditionally made it difficult to apply to large-scale, real-world problems. In this study, researchers present an efficient dual-reduction order parallel simulation approach to overcome this limitation. First, the model dimensionality was reduced by domain decomposition and static condensation of subdomains. In addition, the use of a reduced-order Newton–Raphson method helped to reduce the orders of the governing equations during subdomain back-substitutions. As a result, the model order could be greatly reduced for problems involving local material nonlinearities. To demonstrate the approach, a simple truss model under concentrated force and a 48-storey steel frame structure under seismic loading were analysed. Numerical results showed that the presented method is both accurate and reliable, providing significantly higher efficiency than conventional parallel techniques such as primal domain decomposition. This study will provide an efficient way for eventually enabling detailed nonlinear finite element analysis of massive scale engineering challenges.