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dc.contributor.advisorSurana, Karan S.
dc.contributor.authorMaduri, Rajesh Kumar
dc.date.accessioned2008-07-31T03:58:29Z
dc.date.available2008-07-31T03:58:29Z
dc.date.issued2008-02-01
dc.date.submitted2008
dc.identifier.otherhttp://dissertations.umi.com/ku:2380
dc.identifier.urihttp://hdl.handle.net/1808/4006
dc.description.abstractThe primary focus of this thesis is to present a framework to develop higher order global differentiability local approximations for 2-D and 3-D distorted element geometries. The necessity and superiority of higher order global differentiability approximations in designing finite element computational processes has been demonstrated by Surana and co-workers [1-4]. It has been shown by Surana et al. [5] that when the element geometry is rectangular, higher order global differentiability approximations can be easily derived using tensor product of 1-D higher order continuity approximations. When the element geometries are distorted, the tensor product approach cannot be utilized in deriving these approximation functions. This thesis presents a systematic procedure for deriving desired order global differentiability approximations for 2-D and 3-D elements of distorted geometries. The curved element in 2-D or 3-D physical coordinate space is mapped to a master element in 2-D or 3-D natural coordinate space. The master elements considered for 2-D quadrilateral, 2-D triangular and 3-D hexahedral elements are a 2 unit square, a 2 unit equilateral triangle and a 2 unit cube respectively. For the master element, 2-D C00 or 3-D C000 p-version local approximations are considered and appropriate degrees of freedom and the corresponding approximation functions from appropriate nodes are borrowed to derive the higher order approximations and the corresponding derivative degrees of freedom at the corner nodes. These degrees of freedom can be transformed from natural coordinate space to the physical coordinate space by using Jacobians of transformations for the derivatives of various orders. The choice of these degrees of freedom and the corresponding functions being borrowed in deriving these desired functions for the derivative dofs is not arbitrary and must be made in such a way that all lower degree admissible functions and the corresponding dofs are borrowed before considering the higher degree functions and the corresponding dofs. Pascal's rectangle, Pascal's triangle and Pascal's pyramid provide a systematic selection process for accomplishing this selection process for 2-D quadrilateral, 2-D triangular and 3-D hexahedral geometries respectively. Numerical studies are presented to illustrate the behavior and performance of the approximations developed. The applicability of the developed approximation functions to all physical problems is demonstrated by solving model problems which are described by self-adjoint, non self-adjoint and non-linear differential operators. In all cases, various finite element quantities of interest (error or residual functional, error norms) are computed and a study of their convergence rates with h, p and k refinement is made.
dc.format.extent225 pages
dc.language.isoEN
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMechanical engineering
dc.subjectFinite element method
dc.subjectHigher order global differentiability
dc.subjectHpk framework
dc.subjectDistorted elements
dc.titleHigher order global differentiability local approximations for 2-D and 3-D distorted element geometries
dc.typeDissertation
dc.contributor.cmtememberTenPas, Peter W.
dc.contributor.cmtememberSorem, Robert
dc.contributor.cmtememberTaghavi, Ray
dc.contributor.cmtememberRomkes, Albert
dc.thesis.degreeDisciplineMechanical Engineering
dc.thesis.degreeLevelPH.D.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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