Coupling of mesh-free methods with finite elements: basic concepts and test results

Abstract

SUMMARYThis paper reviews several novel and older methods for coupling meshfree particle methods, particularly the elementfree Galerkin (EFG) method and the Smooth Particle Hydrodynamics (SPH), with finite elements. We study master slave couplings where particles are fixed across the finite element boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent from the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods.

Domain Decomposition Methods for Domain Composition Purpose: Chimera, Overset, Gluing and Sliding Mesh Methods

“…A useful application of this hybrid combination is in enrichment purposes, see [63] and [53]. A general review of the existing methods for this family of hybrid formulations can be found in [73].…”

Meshless methods: A review and computer implementation aspects

“…[18,56,47,58,48,49]. Meanwhile, hybrid methods are available that exploit the advantages of meshfree methods and finite elements [55,74,60,106,107], e.g. the shape functions fulfill the Kronecker delta property while simultaneously exploiting the smoothness and higher-order continuity of meshfree shape functions.…”

Phase-field modeling of fracture in linear thin shells

“…The Dirichlet displacement and rotation boundary conditions are imposed with Lagrange multipliers, the interested reader is referred to [48,49,38,50].…”