Trigonometric Bézier-based isogeometric engineering analysis for heat conduction in curvilinear ducts
The Finite Element Method (FEM) is widely used in engineering to solve partial differential equations. Traditional FEM typically employs polygonal elements such as triangles and quadrilaterals for meshing, which are often inadequate for accurately representing curved geometries. While mesh refinemen...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-09-01
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| Series: | Case Studies in Thermal Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214157X25009281 |
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| Summary: | The Finite Element Method (FEM) is widely used in engineering to solve partial differential equations. Traditional FEM typically employs polygonal elements such as triangles and quadrilaterals for meshing, which are often inadequate for accurately representing curved geometries. While mesh refinement can improve accuracy, it significantly increases computational cost. Isogeometric Analysis (IGA) offers an alternative by integrating design and analysis through the use of spline-based basis functions. While IGA commonly employs NURBS or Bernstein-Bézier functions, this study introduces a Trigonometric Bézier basis function within the FEM framework to solve a heat conduction problem in a 2D curvilinear duct. Numerical results show that the proposed Trigonometric Bézier FEM yields a mean absolute error of 0.33199 °C, compared to 0.21455 °C for the Bernstein-Bézier FEM, when benchmarked against the 8-node quadrilateral FEM. In terms of relative error, the Bernstein-Bézier FEM achieved 0.23929%, while the Trigonometric Bézier FEM recorded 0.37084%, indicating that although the Bernstein-Bézier FEM offers slightly higher accuracy, the difference is minor. Both methods outperform standard 4-node quadrilateral and triangular FEMs in capturing the expected temperature drop from 100 °C to 80 °C. The proposed method demonstrates strong potential for accurately resolving localized thermal gradients in geometrically complex domains, confirming its viability and efficiency for engineering heat conduction analysis. |
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| ISSN: | 2214-157X |