Steady Heat Conduction Solution Using Trigonometric Bezier Finite Element Method - Abidin, Mohamad Naufal Zainal (2024)
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.