A three-dimensional numerical manifold method based on tetrahedral meshes
A three-dimensional NMM based on tetrahedral meshes is developed in this paper. First, the displacement functions of manifold elements are formulated by the partition of unity function. Then, the global equilibrium equations for three-dimensional elasto-statics problem are established by minimizing the total potential energy. The stiffness matrix, loading matrix, displacement resistance matrix are derived for program coding. Thereafter, the computational cost of the global stiffness matrix in the NMM is discussed and compared with that in the classical finite element techniques. Finally, two typical examples are investigated to demonstrate the validity of the proposed method. The results indicate that an enough accuracy of approximation will be obtained with decreasing size of the mathematical mesh. The proposed method can be used as potentially powerful tool for three-dimensional structural analysis.
numerical manifold method partition of unity finite cover system simplex integration scheme