The objective of this study is to improve numerical stability of an elastic-plastic model with memory surface that realizes various hardening behaviors under different ranges of cyclic loading by combination between a primal-dual interior point method and a return mapping algorithm. The primal-dual interior point method allows us to smoothly optimize a minimization problem with inequality constraints such as a yield function and memory surface. More specifically, the inequality condition is replaced with the equal condition by introducing the slack variable and the duality gap is gradually reduced by employing the path-following method. On the other hand, the primal-dual interior method could require bigger computational cost than the conventional return mapping method because of the increase of the unknown variable and the path-following method. Thus, an implicit solution for an elastic-plastic model with the memory surface is proposed by combining with the primal-dual interior point method and the return-mapping algorithm. In addition to the numerical cost, the numerical accuracy of the primal-dual interior point method is evaluated by the comparison with the conventional return mapping algorithm by an iso-error map that has been often applied for the conventional elastic-plastic models. After then, the capability of the proposed implicit method for an elastic-plastic model with the memory surface is demonstrated throughout the simple numerical examples.
An Eulerian fluid-structure interaction (FSI) formulation, which numerically solves fluid and solid in a unified manner with a fixed mesh, is attractive for large deformation problems, high-performance computing, and quick mesh generation even for complex geometries. However, conventional Eulerian methods cannot stably compute FSI problems with the discontinuity of the velocity gradient near the fluid-structure interface. In order to avoid this problem, we propose a novel Eulerian FSI method using marker particles with the Reference map, which is the initial position vector of the solid region. Through the simulation of several benchmark tests, we have confirmed that the proposed method can stably compute the FSI problems mentioned above, and the present numerical results are in quantitatively good agreement with the reference solutions.
This study presents a method of real-time tsunami risk evaluation by combined use of proper orthogonal decomposition (POD) and Bayesian update. The validity of the proposed method is demonstrated through the numerical example targeting plausible tsunamis induced by Nankai-Trough events. First, tsunami simulations are carried out for plausible tsunami scenarios determined by various patterns of fault rupture, and the time histories of wave heights are stored at selected synthetic gauge points. Then, POD is applied to the resulting data matrix of the synthetic dynamics (SD) composed of dynamics modes and coefficients, the latter of which represent scenario-specific information. In the real-time risk evaluation phase, the wave sequences of an actual tsunami event are sequentially measured at the synthetic gauge points and used to estimate the corresponding dynamics coefficients of the constructed SD. At the same time, by the application of Bayesian update, the likelihood of each of the dynamics coefficients pre-calculated for the selected tsunami scenarios is evaluated at each time and sequentially updated to detect the most probable scenario. Finally, the pre-calculated tsunami arrival time and inundation depth distribution corresponding to the detected scenario are determined as risk assessment indices seven minutes after the tsunami generation.