Accuracy Improvements on Free Mesh Method: A High Performance Quadric Triangular/Tetrahedral Element with Only Corners

摘要

The good-performance conventional quadric-elements with midsides severely handicap the local mesh generation technique of Free Mesh Method. The paper presents a high performance triangular and tetrahedral element with only corner nodes on the basis of the Partition of Unity (PU) theory. Implementations of the background partition of unity theory are by a concept of generalized node that contains vertex rotational dofs, which are equivalent to Allman's rotational dofs, and node defined enhanced strain terms. While with only corner nodes the new triangular and tetrahedral elements are quadric. Numerical tests indicate that the new triangle exceeds the standard quadric 8-node quadrilateral for distorted meshes. The new tetrahedron is most accurate among all 4-node tetrahedrons found in literatures and more accurate than the standard quadric 10-node tetrahedron. For regular meshes the tetrahedron possesses a comparable accuracy with the quadric 20-node hexahedron but also out-performs it when the element is distorted.