{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1686"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1686","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Linear elastic mesh deformation via localized orthotropic material properties optimized by the adjoint method","abstract":"The finite element method has been shown to be a powerful tool in computational engineering with recent application to electromagnetics and fluid dynamics. However, achieving the high orders of accuracy easily available to the finite element method has proven difficult due to conforming higher-order meshes to curved geometries. If higher-order nodes are not placed on the surface of the geometry error is introduced into the simulated solution. This barrier is largely a non-issue for inviscid meshes where a mid-edge node can be projected onto the nearest geometry surface with minimal detrimental side effects. Viscous meshes however have to deform most of the boundary layers in order to avoid inverting the surface elements and to maintain an acceptable mesh quality. This research focuses on extending the application of the linear elastic analogy to this mesh movement problem by attributing orthotropic material properties individually to each node or element. This technique allows each node or element to behave differently under the stress of conforming to the boundary. These localized material properties are determined using the adjoint optimization method. To better determine mesh quality, a new mesh metric called Metric3 is introduced. This new metric resembles the included angle metric and is based on an element’s isoparametric transformation matrix.","abstract_html":"The finite element method has been shown to be a powerful tool in computational engineering with recent application to electromagnetics and fluid dynamics. However, achieving the high orders of accuracy easily available to the finite element method has proven difficult due to conforming higher-order meshes to curved geometries. If higher-order nodes are not placed on the surface of the geometry error is introduced into the simulated solution. This barrier is largely a non-issue for inviscid meshes where a mid-edge node can be projected onto the nearest geometry surface with minimal detrimental side effects. Viscous meshes however have to deform most of the boundary layers in order to avoid inverting the surface elements and to maintain an acceptable mesh quality. This research focuses on extending the application of the linear elastic analogy to this mesh movement problem by attributing orthotropic material properties individually to each node or element. This technique allows each node or element to behave differently under the stress of conforming to the boundary. These localized material properties are determined using the adjoint optimization method. To better determine mesh quality, a new mesh metric called Metric3 is introduced. This new metric resembles the included angle metric and is based on an element’s isoparametric transformation matrix.","abstract_has_math":false,"creators":["Shoemake, William L."],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hilbert, C. Bruce","Sreenivas, Kidambi; Matthews, Matt; Newman, James C., III","College of Engineering and Computer Science"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:51Z","subjects":["Numerical grid generation (Numerical analysis)","Finite element method"],"languages":["English","eng"],"rights":[],"rights_urls":["https://rightsstatements.org/page/InC/1.0/?language=en"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/534","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hilbert, C. 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D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy."]},{"key":"dc:description.abstract","label":"Abstract","values":["The finite element method has been shown to be a powerful tool in computational engineering with recent application to electromagnetics and fluid dynamics. However, achieving the high orders of accuracy easily available to the finite element method has proven difficult due to conforming higher-order meshes to curved geometries. If higher-order nodes are not placed on the surface of the geometry error is introduced into the simulated solution. This barrier is largely a non-issue for inviscid meshes where a mid-edge node can be projected onto the nearest geometry surface with minimal detrimental side effects. Viscous meshes however have to deform most of the boundary layers in order to avoid inverting the surface elements and to maintain an acceptable mesh quality. This research focuses on extending the application of the linear elastic analogy to this mesh movement problem by attributing orthotropic material properties individually to each node or element. This technique allows each node or element to behave differently under the stress of conforming to the boundary. These localized material properties are determined using the adjoint optimization method. To better determine mesh quality, a new mesh metric called Metric3 is introduced. This new metric resembles the included angle metric and is based on an element’s isoparametric transformation matrix."]},{"key":"dc:title","label":"Title","values":["Linear elastic mesh deformation via localized orthotropic material properties optimized by the adjoint method"]}]}],"canonical_facts":{"dc:contributor":["Hilbert, C. Bruce","Sreenivas, Kidambi; Matthews, Matt; Newman, James C., III","College of Engineering and Computer Science"],"dc:creator":["Shoemake, William L."],"dc:date":["2017-12-01T08:00:00Z"],"dc:description":["Dept. of Computational Engineering","Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy."],"dc:description.abstract":["The finite element method has been shown to be a powerful tool in computational engineering with recent application to electromagnetics and fluid dynamics. However, achieving the high orders of accuracy easily available to the finite element method has proven difficult due to conforming higher-order meshes to curved geometries. If higher-order nodes are not placed on the surface of the geometry error is introduced into the simulated solution. This barrier is largely a non-issue for inviscid meshes where a mid-edge node can be projected onto the nearest geometry surface with minimal detrimental side effects. Viscous meshes however have to deform most of the boundary layers in order to avoid inverting the surface elements and to maintain an acceptable mesh quality. This research focuses on extending the application of the linear elastic analogy to this mesh movement problem by attributing orthotropic material properties individually to each node or element. This technique allows each node or element to behave differently under the stress of conforming to the boundary. These localized material properties are determined using the adjoint optimization method. To better determine mesh quality, a new mesh metric called Metric3 is introduced. This new metric resembles the included angle metric and is based on an element’s isoparametric transformation matrix."],"dc:identifier":["https://scholar.utc.edu/theses/534"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["https://rightsstatements.org/page/InC/1.0/?language=en"],"dc:subject":["Numerical grid generation (Numerical analysis)","Finite element method"],"dc:title":["Linear elastic mesh deformation via localized orthotropic material properties optimized by the adjoint method"],"dc:type":["Doctoral dissertations","Text"]},"updated_at":"2026-07-24T05:46:51Z"}