Abidin, Mohamad Naufal Zainal
(2024)
Steady Heat Conduction Solution Using Trigonometric Bezier Finite Element Method.
Masters thesis, Universiti Sains Malaysia.
Abstract
The Finite Element Method (FEM) is a numerical technique used to solve several
forms of partial differential equations, which are commonly utilized in engineering and
mathematical modelling. Basic polygons such as triangles and quadrilaterals are used
as element shapes in FEM. Due to the rigid sides of these basic shapes, they have
resulted in sharp edges and are limited in handling irregular or curved geometries. To
address this issue, mesh refinement is required to maintain the original geometry of
the model, resulting in a larger number of elements and an increase in computational
time. The spline functions are used as basis functions in isogeometric Finite Element
Analysis(FEA). Isogeometric analysis (IGA) is a technique that recently developed in
computational mechanics that offers the possibility of integrating the analysis and the
design process into a single and unified process. This technique has the advantage of
providing seamless integration of accurate geometry, thus bridging the gap between
computer-aided geometric design and finite element analysis. Commonly, nonuniform
rational B-splines (NURBS) and Bernstein-Bézier are used as basis functions in IGA.
However, in this study, Trigonometric Bézier basis function will be used to solve the
heat conduction problem in a two-dimensional curvilinear duct pipe. In summary, the
findings indicate that the results obtained using the Trigonometric Bézier method are
promising. The mean error recorded is minimal compared to the existing method,
namely the Bernstein Bézier.
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