105 有限要素法における薄板の四面体分割の分類とその影響に関する考察

This paper proposes tetrahedron meshing method of thin-plate structure. In analysis of thin-plate structure using solid element in Finite Element Method (FEM), it is known that scale of analysis tend to become huge. To solve this problem, various types of elements like shell element has been proposed. However, tetrahedron mesh is widely used in automatic meshing of 3D structure. In view point of user-friendliness of analysis in actual development or design of various machines, if coarse tetrahedron mesh of thin-plate structure can give accurate solution, it is beneficial. Objective of this paper is proposal of meshing method which enables accurate solution from coarse tetrahedron mesh. In automatic meshing of 3D structure, 3 dimensional Delaunay triangulation is widely used, and it is pointed that 3 dimensional Delaunay triangulation tends to generate sliver. From this, bad shape sliver is generated in automatic meshing of thin plate, especially in larger element size compared to plate thickness. In this paper, meshing of cuboid by tetrahedron is categorized, and it is shown that calculation error is increased in the mesh which includes sliver in the mode including torsional deformation. From this categorization, the authors found that tetrahedron mesh of cuboid can be categorized into 9 types of meshing. 5 types in the 9 types include sliver. Origin of inaccurate solutions in the mesh including sliver is high stiffness for torsional deformation. It is estimated that element size can be increased about 4 times in tetrahedron mesh of thin-plate without sliver compared to the mesh including sliver.