Automated p-Version Mesh Generation for Naval Structures

Abstract

Abstract : This research study considered the technologies needed to realize the promise of optimum rates of convergence of adaptive high-order methods based on hp-discretization. The study focused on the development of the technologies needed to support robust p-version mesh generation of general non-manifold geometric domains of interest to the NAVY. To meet the goal of providing appropriate meshes for p-version finite element analysis for general domains, the authors developed an automatic mesh generation procedure to create curved finite element meshes with sufficient order of geometric approximation based on the order of polynomial used in the finite element basis. Although the initial straight-sided mesh generated by automatic mesh generators has all valid elements, the process of curving the mesh edges and faces to the appropriate model boundaries often yields elements with invalid shapes. Therefore, the developed procedures perform mesh modifications to produce a set of valid curved elements. A key ingredient is the geometric representation of the mesh entities. The standard method of Lagrangian interpolation does not lend itself to effective procedures as the order of the elements increases. Therefore, an alternative geometric form based on Bezier approximating geometry was developed. Many of the physical domains of interest to the Navy are structures dominated by thin sections for which the desired finite element discretizations employ thin volume elements. For the most effective application of p-version finite elements it is desirable to generate elements in these thin volumes that do not have long diagonals going through the thick- ness direction. This creates problems for current automatic mesh generators that use only tetrahedra. Therefore, procedures were developed to eliminate, to the greatest possible extent, such diagonals. (3 figures, 10 refs.)