Hexahedral Dominant Auto-Mesh Generator
Navy STTR 2020.A - Topic N20A-T004
NAVAIR - Ms. Donna Attick [email protected]
Opens: January 14, 2020 - Closes: February 26, 2020 (8:00 PM ET)


TITLE: Hexahedral Dominant Auto-Mesh Generator


TECHNOLOGY AREA(S): Air Platform, Ground/Sea Vehicles, Weapons

ACQUISITION PROGRAM: NAE Chief Technology Office

OBJECTIVE: Develop an automated interactive mesh generator using predominately Hexahedral Finite Elements to support finite element analysis of naval aviation structural components and weapons systems.

DESCRIPTION: The U.S. Navy is accelerating its development of solutions to meet Fleet needs. As part of this urgent need, this STTR topic provides the potential to develop several advantages to the U.S. Navy. First, the use of hexahedral elements in finite element processing is far more efficient than tetrahedral elements, providing more accurate solutions, faster. Second, the use of an automated hexahedral dominant mesh generator will decrease the time spent meshing and speed the overall development of a solution. Currently, automated mesh generators use tetrahedral elements for finite element analysis. This approach is computationally intensive, because, in order to increase accuracy in the current system, there is a need for more tetrahedral elements resulting in increased hardware requirements or longer meshing and solution times.

Much of today’s solid finite element analysis is performed with tetrahedral elements. Tetrahedral elements, poorly formulated mathematically, require a high element density to obtain answers to conform to classical analysis and benchmark solutions. Using large numbers of finite elements increases the computational burden on the computer by n2 for a fully stored stiffness matrix. Hexahedral elements are well-formulated showing superior performance in bending and torsion [Ref. 1]. Fewer hexahedral elements would be needed to achieve the same level of accuracy as a model built with tetrahedral elements. A hexahedral automated mesh generation requires specific geometric conditions.

A software is sought to analyze the geometry and create hexahedral mapable domains, with optional user interaction. The optional interaction should include (but not be limited to) providing options to the user to subdivide the geometry, optimize the number of hexahedral elements, and where necessary, use other elements to create a complete mesh for the user to apply boundary conditions. A graphical user interface (GUI) must allow for user inputs for variable mesh density/element size, type of elements, order of elements, and enforcement of topology. Ideally, the software would provide an interactive environment for the user to create the mesh and geometric conditions desired before applying boundary conditions. The software should be able to run on most major operating systems; Windows 10 is preferred. Software should be able to run on machine with 4gigabytes of random access memory using Intel i5 or equivalent central processing units (CPU). Inputs to the software should include, but not be limited to, generic geometry formats (e.g., Standard for the Exchange of Product model data (STEP), Initial Graphics Exchange Specification (IGES), Parasolids, ACIS, and Stereolithography (STL)). Outputs from the software should be compatible with major pre-processing software packages (e.g., FeMap, Patran, Hypermesh). This output should include NASA Structural Analysis (NASTRAN) compatibility with the option to be human readable.

PHASE I: Design a geometric decomposition algorithm on basic shapes. Basic shapes include spheres, cones, annular rings, plates with circular holes in them, and plates with “flagpoles” extending from them. Holes and like interior features should have elements feature aligned at their interior and in an annular ring around them.

Demonstrate the feasibility of the algorithm. Ensure that the software design creates the mesh using predominantly high-quality feature-aligned hexahedral elements, paying particular attention to the exterior boundary, using transition and tetrahedral elements to accommodate the remainder of the shape(s) and result in a fully meshed component. A feature-aligned element has a face parallel to the local external boundary of the geometric entity containing it, and adjacent faces that are as perpendicular to that face as is allowable by the geometric definition of that component. For example, not all faces can be orthogonal and perpendicular to a sharp corner such as the tip of a cone.

Quality metrics should be as defined in Reference 4, with the addition that all faces of the hex shall be mapable to a regular quadrilateral, i.e., no twisted or degenerate faces, no “bow-tie” faces.

Use the metrics for hexahedral elements as summarized in Reference 4.

The Phase I effort will include prototype plans to be developed under the Phase II.

PHASE II: Fully develop and demonstrate capability by importing various formats of computer-aided drawing (CAD) data to include, but not be limited to, STEP, IGES, Parasolid, STL, and ACIS. Show the geometric decomposition algorithm on Navy-provided CAD data. Develop the GUI to allow for geometric editing of the part to support hexahedral elements, provide optimal solutions, and allow users to mesh components manually.

PHASE III DUAL USE APPLICATIONS: Perform final development and testing, and demonstrate usage with other Finite Element Pre-processing software packages. Import finalized mesh for preprocessing with boundary/initial conditions.

Using hexahedral meshing is one of the most mathematically efficient methods of discretizing geometry. Automotive, Aerospace, Nuclear, and Consumer Electronic industries will benefit from the following:
Improved solution run times/faster delivery of products.
Improved efficiency: use of CPUs, company’s tech refresh cycle can be less frequent.
Improved efficiency: use of CPUs, company’s overall power consumption will decrease.


1. Sjaardama, G., Benzley, S. E., Perry, E., Merkley, K. and Clark, K.  “A Comparison of All Hexagonal and All Tetrahedral Finite Element Meshes for Elastic and Elasto-plastic Analysis.” Brigham Young University: Provo, UT and Sandia National Laboratories: Albuquerque, NM., January 1995.https://www.researchgate.net/publication/267259986_A_Comparison_of_All_Hexagonal_and_All_Tetrahedral_Finite_Element_Meshes_for_Elastic_and_Elasto-Plastic_Analysis

2. Owens, S. J., Canann, S. A. and Saigal, S.  “Pyramid Elements for Maintaining Tetrahedra to Hexahedra Conformability.” Sandia National Laboratories: Albuquerque, NM; Siemens: Austin, TX; and New Jersey Institute of Technology, January 1997. https://www.researchgate.net/publication/243766119_Pyramid_Elements_for_Maintaining_Tetrahedra_to_Hexahedra_Conformability

3. Meyers, R. J., Tautges, T. J. and Tuchinsky, P. M.  “The "Hex-Tet" Hex-Dominant Meshing Algorithm as Implemented in CUBIT.” Sandia National Laboratories: Albuquerque, NM and Argonne National Laboratory, January 1998. https://www.researchgate.net/publication/221561722_The_Hex-Tet_Hex-Dominant_Meshing_Algorithm_as_Implemented_in_CUBIT
4. Cubit 15.3 User Documentation, Metrics for Hexahedral Elements. https://cubit.sandia.gov/public/15.3/help_manual/WebHelp/mesh_generation/mesh_quality_assessment/hexahedral_metrics.htm

KEYWORDS: Hexahedral Meshing; Finite Element; Automated; CAD; Preprocessing; Computational Efficiency