An Explicit Coupled Method of FEM and Meshless Particle Method for Simulating Transient Heat Transfer Process of Friction Stir Welding

Friction stir welding (FSW) is a favorable welding technology for aluminum alloys. The FSW process involves complex heat and mass transfer. Explicit meshless particle methods are currently popular methods for simulating the process, but they require expensive computational cost. Coupling explicit finite element method (FEM) and meshless particle methods can ease the problem by making use of high efficiency of FEM and advantages of meshless particle methods. Though many efforts have been made to couple FEM and meshless particle methods for transient dynamics problems, coupling them for transient heat transfer problems is seldom addressed. In this work, we focus on treating this problem. We developed an explicit coupled method of FEM and the meshless particle method presented in a previous work and used it to simulate the thermal process during FSW. In the method, FEM using lumped heat capacity matrix and low-order numerical integration is constructed to obtain high efficiency. A new coupling algorithm is proposed to link thermal calculations of the weak-form FEM and the strong-form meshless particle method. Forward Euler method is used for time integration to achieve an explicit algorithm. The coupled method is used to calculate a numerical example having analytical solution. Calculated results show that it can achieve a good accuracy. The method is employed to simulate FSW of Al 6061-T6 plates. It predicts thermal cycles in good agreement with experimental results. It shows an accuracy comparable to that of the meshless particle method while having a higher efficiency than the latter.

A Coupled Model for Wave Run-up Simulation

Simplified models like the shallow water equations (SWE) are commonly adopted for describing a wide range of free surface flow problems, like flows in rivers, lakes, estuaries, or coastal areas. In the literature, numerical methods for the SWE are mostly mesh-based. However, this macroscopic approach is unable to accurately represent the complexity of flows near coastlines, where waves nearly break. This fact prompted the idea of coupling the mesh-based SWE model with a meshless particle method for solving the Euler equations. In a previous paper, a method to couple the staggered scheme SWE and the smoothed particle hydrodynamics (SPH) Euler equations was developed and discussed. In this article, this coupled model is used for simulating solitary wave run-up on a sloping beach. The results show strong agreement with the experimental data of Synolakis. Simulations of wave overtopping over a seawall were also performed.