Abstract:The numerical manifold method (NMM) has been widely used for 2D problems. The construction of numerical manifold covers and weight functions on traditional 3D twenty-node iso-parametric element meshes of FEM is proposed in the paper. With Lagrange multiplier,Dirichlet boundary conditions are imposed along the essential boundaries. Formulae for static analysis are given. Then it is easier to model 3D problems with curved boundary surfaces by using the NMM without fine meshing in common FEM. Linear dependency of the approximation space is studied,and a method of applying enhanced cover functions only at physical covers connected to corner vertices is proposed to resolve this problem. Thus the scale of discrete system decreases more significantly than that in conventional implementations of the NMM. Example analyses show that the error energy norms decrease dramatically to about ten percent of the corresponding FEM results both in common and volume-locking cases. Convergence rates are also studied with examples and they are approximately equal in the NMM and the conventional FEM analyses for both material cases. The compatibility of the conventional FEM procedure with the 3D NMM analytical procedure is considered from the scratch of its design,which ensures a smooth and easy interface for developing an NMM analytical system from the existing FEM procedures.