On the solution of multi-point constraints  Application to FE analysis of reinforced concrete structures
The paper presents an efficient way of implementing general multi-point constraint conditions in a finite element solver. The proposed method of applying and processing the multi-point constraints on the primary unknown variables of finite element method is computationally efficient and memory economical, because all constrained degrees of freedoms (DOFs) are already eliminated during the assembly of the global stiffness matrix and right-hand side vectors. The adopted concept has a wide range of use, and several of its possibilities are discussed. At the end of the paper, sample analyses of reinforced concrete structures are presented that demonstrate the advantages of the developed form for modelling discrete reinforcement bars in non-linear FE calculation in engineering practice.
multi-point constraints finite element method engineering practice dirichlet boundary conditions embedded reinforcement modelling mesh generation