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A Conforming to Interface Structured Adaptive Mesh Refinement for Modeling Complex Morphologies

Anand Nagarajan, .
http://orcid.org/0000-0003-1923-2728
http://rave.ohiolink.edu/etdc/view?acc_num=osu1574436067401755

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Mechanical Engineering.
Modeling of problems involving complex morphological features present significant challenges, particularly the creation of high quality conforming finite element meshes from realistic geometries. In addition to being computationally demanding, generating thousands of conforming meshes for problems such as design optimization and uncertainty quantification (UQ) is labor cost intensive. A new non-iterative mesh generation algorithm named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) is introduced for the automated generation of high quality finite element meshes for complex geometries. The CISAMR transforms a structured background mesh into a conforming mesh with an upper bound on element aspect ratios. For two dimensional problems, the CISAMR algorithm transforms an initially structured quadrilateral grid into a conforming hybrid mesh composed of triangular and quadrilateral elements. Similarly, a structured tetrahedral grid is transformed into a conforming mesh composed solely of Tet elements for problems in three dimensions. This mesh transformation is initiated with the Structured Adaptive Mesh Refinement (SAMR) of elements in the vicinity of material interfaces. An r-adaptivity algorithm is subsequently employed to non-iteratively relocate select nodes of nonconforming elements. The final conforming mesh is constructed by sub-dividing the remaining nonconforming elements, including those containing hanging nodes generated during the local refinement phase. Regardless of problem complexity, the CISAMR ensures that aspect ratios are limited to an upper bound of three and five respectively, for conforming meshes generated in two and three dimensions, without requiring iterative smoothing or optimization techniques. However, a small fraction of heavily distorted tetrahedrons in 3-D are eliminated by performing a non-iterative face-swapping operation following the r-adaptivity phase. Furthermore, a modified version of this approach is introduced for representing crack-type interfaces for the modeling of fracture problems. The singular stress fields in the vicinity of crack tips is efficiently approximated by automatic insertion of quarter-point elements. The algorithm and implementation of the CISAMR is presented in this work, along with recommendations for efficient computer implementation. This work also introduces a novel kirigami-inspired sub-tetrahedrilization scheme for robust generation of conforming sub-elements using a terse computer code. The convergence and element-wise errors are analyzed for meshes generated using CISAMR to highlight accurate gradient recovery. Further, several example problems are presented in this work to show the suitability of this method, and its vast benefits for modeling problems involving intricate morphologies.
Soheil Soghrati, Dr. (Advisor)
Carlos Castro, Dr. (Committee Member)
Stephen Niezgoda, Dr. (Committee Member)
182 p.
Mechanical Engineering
CISAMR, mesh generation, tetrahedral mesh, adaptive refinement, complex geometry, heterogeneous materials, branching crack, element sub-division

Recommended Citations

Citations

  • Anand Nagarajan, . (2019). A Conforming to Interface Structured Adaptive Mesh Refinement for Modeling Complex Morphologies [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574436067401755

    APA Style (7th edition)

  • Anand Nagarajan, .. A Conforming to Interface Structured Adaptive Mesh Refinement for Modeling Complex Morphologies. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1574436067401755.

    MLA Style (8th edition)

  • Anand Nagarajan, .. "A Conforming to Interface Structured Adaptive Mesh Refinement for Modeling Complex Morphologies." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574436067401755

    Chicago Manual of Style (17th edition)

osu1574436067401755
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