Application of mesh adaptive technology combined with adaptive time stepping technology under strong earthquake liquefaction

Abstract

Mesh distortion caused by large deformations is a major problem that disrupts finite element (FE) analysis computations. For example, the traditional updating Lagrangian approach updates the spatial configuration of the node points, yet strong earthquakes exacerbate this issue. To address the problem, an arbitrary Lagrangian Euler (ALE) method has been developed based on the updated Lagrangian method and solid‒fluid two-phase mixing theory. This adaptive mesh technique reshapes the deformed mesh at each computational step and projects variables onto a new configuration. However, the constant modification of the mesh to avoid distortion increases the overall analysis time. To solve this problem, an adaptive time stepping methodology is introduced, which evaluates the mixed error through five control parameters and adjusts the calculation step size in real time. This method considers the effect of the time step on the required amount of time and the calculation accuracy and dynamically adjusts the time step to optimize the associated tradeoff between the two. Two FE examples demonstrate the effectiveness of the method. The results show that partitioning the time increment significantly influences the mesh distortion and calculation time and that the ALE method can maintain a nondistorted mesh. The method is optimized for accuracy and calculation time. Various working conditions and models affect the method differently, particularly regarding acceleration properties. Small excitations perform better than large excitation, and the maximum computation time can be reduced by more than 80% through adaptive solver optimization.