A Class of Novel Tetrahedron Elements with Curved Surfaces for Three-Dimensional Solid Mechanics Problems with Curved Boundaries

Abstract

Linear tetrahedral elements with four nodes (Te4) are currently the simplest and most widely used ones in the finite element (FE) developed for solving three-dimensional (3D) mechanics problems. However, the standard Te4 element cannot be used to simulate accurately the 3D problems with curved boundaries because of the flat surfaces. In this paper, we develop a set of new elements having curved surfaces to properly simulate the curved boundaries. At the same time, additional nodes are put on the curved boundaries to improve the accuracy of the approximation. These novel elements are defined as five-noded, six-noded, and seven-noded tetrahedron elements (Te5, Te6, and Te7) according to the number of the nodes in one element. Based on the Te4 FE mesh, a hybrid mesh can be conveniently built for 3D problems with curved boundaries, in which the standard Te4 elements are used for the interior elements, and Te5, Te6, and Te7 elements are used for the curved boundary elements. Compared with the standard FEM using Te4 elements, our hybrid mesh can significantly improve the accuracy of the solutions at the curved boundaries. Several solid mechanics problems are studied using the hybrid meshes to validate the effectiveness of the present new elements.