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High-Order Static and Dynamic Tetrahedral Mesh Generation Algorithms for Use in Finite Element Modeling and Simulation
dc.contributor.advisor | Shontz, Suzanne M | |
dc.contributor.advisor | Fischer, Kenneth J | |
dc.contributor.author | Mohammadi, Fariba | |
dc.date.accessioned | 2023-06-25T20:53:23Z | |
dc.date.available | 2023-06-25T20:53:23Z | |
dc.date.issued | 2022-12-31 | |
dc.date.submitted | 2021 | |
dc.identifier.other | http://dissertations.umi.com/ku:18621 | |
dc.identifier.uri | https://hdl.handle.net/1808/34445 | |
dc.description.abstract | Computational modeling and simulation of real-world problems, e.g., various automotive, aerospace,and biomedical applications, often involve geometric objects bounded by curved surfaces. Computational modeling of such objects using curvilinear high-order meshes ensures that the curved features present in the geometry are well-captured and preserved in the corresponding mesh. For a fixed level of accuracy, a high-order mesh paired with a high-order partial differential equation (PDE) solver requires fewer elements, making the mesh generation and PDE solve much less computationally expensive in total. We have developed a direct, high-order, curvilinear triangular and tetrahedral mesh generation method using an advancing front technique. Most other existing mesh generation techniques require computer-aided design (CAD) files to represent the geometric boundary, which is often unavailable for patient-specific biomedical applications. Our method requires only the element vertices and vertex connectivities to generate a high-order mesh. Thus, it can take a high-order boundary or surface mesh generated from either a CAD geometry or a set of a patient’s medical image segmentation masks as input and generate a high-order triangular or tetrahedral mesh directly from them. In addition to a high-order mesh generator, we have also developed a finite element-based highorder mesh warping algorithm using an incompressible, hyperelastic material model. Our mesh warping algorithm takes an initial undeformed mesh in Rd, where d = 2,3, and the corresponding boundary deformation for Rd−1. The latter could either come from mathematically-prescribed deformation fields or deformed surface meshes, e.g., deformation fields obtained from patientspecific medical images. Next, it computes the deformed mesh’s interior vertex positions using a static equilibrium condition and appropriate boundary conditions. We use our methods to generate several second-order triangular and tetrahedral static and dynamic meshes of various mechanical and anatomical models obtained from CAD models and medical images. | |
dc.format.extent | 145 pages | |
dc.language.iso | en | |
dc.publisher | University of Kansas | |
dc.rights | Copyright held by the author. | |
dc.subject | Mechanical engineering | |
dc.subject | Computer science | |
dc.subject | ||
dc.title | High-Order Static and Dynamic Tetrahedral Mesh Generation Algorithms for Use in Finite Element Modeling and Simulation | |
dc.type | Dissertation | |
dc.contributor.cmtemember | Friis, Elizabeth A | |
dc.contributor.cmtemember | Wilson, Sara E | |
dc.contributor.cmtemember | Wang, ZJ | |
dc.thesis.degreeDiscipline | Mechanical Engineering | |
dc.thesis.degreeLevel | Ph.D. | |
dc.identifier.orcid | ||
dc.rights.accessrights | embargoedAccess |
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