中文摘要：

虽然四面体网格具有强大的几何表征能力，但因其“过硬”特性而工程实践中较少采用。如何使四面体网格“变软”是目前数值计算研究重点。通过采用广义的应变光滑操作，对四面体网格采用一种新型基于四面体边的应变光滑方法（Edge-basedsmoothedfiniteelementmethodoftetrahedron，ES-FEM-T），并将该方法拓展到三维固体中黏弹塑性材料分析中。数值算例表明：在相同的网格时，ES-FEM-T计算效率要高于有限元和基于面光滑操作的有限元。由于该方法既继承四面体强大的几何表征能力，具有较好的计算效率和精度，具有广阔的工程运用前景。

英文摘要：

The tetrahedral mesh is good at building three-dimensional solid finite element discrete model because of its powerful geometric characterization, while it behaviors overly-stiff property leading to large errors, which greatly limit the widely use of the tetrahedral mesh. Since the tetrahedral mesh is an important issue in computational mechanics and is also a main focus. A new type of edge-based smoothed finite element method of tetrahedron mesh（ES-FEM-T） is extended to 3D solid mechanics visco-elastoplastic material. Numerical examples verified that computational efficiency of the ES-FEM-T is higher than the finite element method（FEM） and face-based smoothed finite element method. This method not only inherits the strong tetrahedral geometry characterization capabilities, but also improves the accuracy and efficiency of the tetrahedral mesh, which has a broad engineering application prospects.