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Smooth Finite Element Methods with Polynomial Reproducing Shape Functions

Electronic Theses of Indian Institute of Science

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Field Value
 
Title Smooth Finite Element Methods with Polynomial Reproducing Shape Functions
 
Creator Narayan, Shashi
 
Subject Finite Element Methods
Smooth Finite Element Methods
Polynomial Reproducing Shape Functions
Globally Smooth Space Functions
DMS-FEM (Tetrahedral B Splines-Finite Element Method) Shape Functions
Plate Bending Models
Mindlin Plate Bending
Simplex Splines
Mesh-Free Shape Functions
Tetrahedral B Splines (DMS)
Mesh-free Methods
Civil Engineering
 
Description A couple of discretization schemes, based on an FE-like tessellation of the domain and polynomial reproducing, globally smooth shape functions, are considered and numerically explored to a limited extent. The first one among these is an existing scheme, the smooth DMS-FEM, that employs Delaunay triangulation or tetrahedralization (as approximate) towards discretizing the domain geometry employs triangular (tetrahedral) B-splines as kernel functions en route to the construction of polynomial reproducing functional approximations. In order to verify the numerical accuracy of the smooth DMS-FEM vis-à-vis the conventional FEM, a Mindlin-Reissner plate bending problem is numerically solved. Thanks to the higher order continuity in the functional approximant and the consequent removal of the jump terms in the weak form across inter-triangular boundaries, the numerical accuracy via the DMS-FEM approximation is observed to be higher than that corresponding to the conventional FEM. This advantage notwithstanding, evaluations of DMS-FEM based shape functions encounter singularity issues on the triangle vertices as well as over the element edges. This shortcoming is presently overcome through a new proposal that replaces the triangular B-splines by simplex splines, constructed over polygonal domains, as the kernel functions in the polynomial reproduction scheme. Following a detailed presentation of the issues related to its computational implementation, the new method is numerically explored with the results attesting to a higher attainable numerical accuracy in comparison with the DMS-FEM.
 
Contributor Roy, Debasish
 
Date 2018-04-03T17:05:11Z
2018-04-03T17:05:11Z
2018-04-03
2013
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3332
http://etd.iisc.ernet.in/abstracts/4196/G25724-Abs.pdf
 
Language en_US
 
Relation G25724