摘要：A combination between a meshless method and a Lagrangian formulation will be presented. The capability of the meshless methods for solving complicated geometries and the natural way that Lagrangian formulations have to represent problems with big deformations of the domain will be put together in this work. The resulting approach showed to be robust from the CFD point of view and easy to implement from the computational point of view. All contacts and free surface calculations are embedded in the meshless method, making their computation straight forward. Lagrangian formulations also have the advantage of solving the convection of velocity by moving the material points, thus avoiding the tedious convection terms in the Navier-Stokes equations. As a meshless method, the Meshless Finite Element Method has been implemented. This method conserves the useful properties of the Finite Element Method so adding the benefits of the meshless methods. The connection between material points is calculated using the Extended Delaunay Tessellation. To solve Finite Element, simplicial elements are used in most of the domain, except when the element quality is not good enough, then polyhedrons are taken automatically as elements. The Non- Sibsonian shape function adapts to the polyhedrons keeping the good properties that Finite Element shape functions have. The presented scheme has found to have remarkable results in a large variety of contact problems with free surfaces.
其他摘要：A combination between a meshless method and a Lagrangian formulation will be presented. The capability of the meshless methods for solving complicated geometries and the natural way that Lagrangian formulations have to represent problems with big deformations of the domain will be put together in this work. The resulting approach showed to be robust from the CFD point of view and easy to implement from the computational point of view. All contacts and free surface calculations are embedded in the meshless method, making their computation straight forward. Lagrangian formulations also have the advantage of solving the convection of velocity by moving the material points, thus avoiding the tedious convection terms in the Navier-Stokes equations. As a meshless method, the Meshless Finite Element Method has been implemented. This method conserves the useful properties of the Finite Element Method so adding the benefits of the meshless methods. The connection between material points is calculated using the Extended Delaunay Tessellation. To solve Finite Element, simplicial elements are used in most of the domain, except when the element quality is not good enough, then polyhedrons are taken automatically as elements. The Non- Sibsonian shape function adapts to the polyhedrons keeping the good properties that Finite Element shape functions have. The presented scheme has found to have remarkable results in a large variety of contact problems with free surfaces.
