A NURBS-based scaled boundary finite element method for the analysis of heat conduction problems with heat fluxes and temperatures on side-faces
•SBFEM combined with IGA is first applied to two-dimensional steady-state heat transfer problems.•The formula of SBFEM with IGA is derived in detail.•The solution is semi-analytical and very high accuracy.•Heat transfer problem with complex curve geometry can be simulated with higher precise and few...
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| Published in: | International journal of heat and mass transfer Vol. 113; pp. 764 - 779 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
Elsevier Ltd
01.10.2017
Elsevier BV |
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| ISSN: | 0017-9310, 1879-2189 |
| Online Access: | Get full text |
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| Abstract | •SBFEM combined with IGA is first applied to two-dimensional steady-state heat transfer problems.•The formula of SBFEM with IGA is derived in detail.•The solution is semi-analytical and very high accuracy.•Heat transfer problem with complex curve geometry can be simulated with higher precise and few nodes.•This paper present study aids to choose design data suitable to the user's requirements.
The scaled boundary finite element method (SBFEM) combined with isogeometric analysis (IGA) is proposed to solve the two-dimensional steady-state heat conduction problems in complex geometries. The main benefit of SBFEM is that the spatial dimension of analyzed domain is reduced by one and the solution is analytical in the radial direction. In this method, only the boundary of the computational domain requires discretization with finite elements leading to the reduction of computational efforts. However, SBFEM suffers from the finite element method related drawbacks. In the case of the complex geometric shapes, a large number of elements are necessary to obtain the exact representation of geometry in finite element method. Isogeometric analysis is a novel numerical technique based on the non-uniform rational B-splines (NURBS), where the geometry can be exactly represented. Moreover, this technique yields superior numerical accuracy, efficiency and convergence property in comparison to finite element method. In the proposed method, the segments of domain boundary with complex geometries are described with NURBS basis functions in IGA, while the straight segments of boundary are represented with polynomial basis functions as in the conventional SBFEM. Thus, the present approach combines the advantages of both SBFEM and IGA. The heat conduction problems of complex geometry can be more effectively handled with the proposed method considering the prescribed heat fluxes and temperatures on side-faces. The accuracy and efficiency of the proposed formulation are demonstrated by modeling five numerical examples involving the complicated geometry. |
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| AbstractList | The scaled boundary finite element method (SBFEM) combined with isogeometric analysis (IGA) is proposed to solve the two-dimensional steady-state heat conduction problems in complex geometries. The main benefit of SBFEM is that the spatial dimension of analyzed domain is reduced by one and the solution is analytical in the radial direction. In this method, only the boundary of the computational domain requires discretization with finite elements leading to the reduction of computational efforts. However, SBFEM suffers from the finite element method related drawbacks. In the case of the complex geometric shapes, a large number of elements are necessary to obtain the exact representation of geometry in finite element method. Isogeometric analysis is a novel numerical technique based on the non-uniform rational B-splines (NURBS), where the geometry can be exactly represented. Moreover, this technique yields superior numerical accuracy, efficiency and convergence property in comparison to finite element method. In the proposed method, the segments of domain boundary with complex geometries are described with NURBS basis functions in IGA, while the straight segments of boundary are represented with polynomial basis functions as in the conventional SBFEM. Thus, the present approach combines the advantages of both SBFEM and IGA. The heat conduction problems of complex geometry can be more effectively handled with the proposed method considering the prescribed heat fluxes and temperatures on side-faces. The accuracy and efficiency of the proposed formulation are demonstrated by modeling five numerical examples involving the complicated geometry. •SBFEM combined with IGA is first applied to two-dimensional steady-state heat transfer problems.•The formula of SBFEM with IGA is derived in detail.•The solution is semi-analytical and very high accuracy.•Heat transfer problem with complex curve geometry can be simulated with higher precise and few nodes.•This paper present study aids to choose design data suitable to the user's requirements. The scaled boundary finite element method (SBFEM) combined with isogeometric analysis (IGA) is proposed to solve the two-dimensional steady-state heat conduction problems in complex geometries. The main benefit of SBFEM is that the spatial dimension of analyzed domain is reduced by one and the solution is analytical in the radial direction. In this method, only the boundary of the computational domain requires discretization with finite elements leading to the reduction of computational efforts. However, SBFEM suffers from the finite element method related drawbacks. In the case of the complex geometric shapes, a large number of elements are necessary to obtain the exact representation of geometry in finite element method. Isogeometric analysis is a novel numerical technique based on the non-uniform rational B-splines (NURBS), where the geometry can be exactly represented. Moreover, this technique yields superior numerical accuracy, efficiency and convergence property in comparison to finite element method. In the proposed method, the segments of domain boundary with complex geometries are described with NURBS basis functions in IGA, while the straight segments of boundary are represented with polynomial basis functions as in the conventional SBFEM. Thus, the present approach combines the advantages of both SBFEM and IGA. The heat conduction problems of complex geometry can be more effectively handled with the proposed method considering the prescribed heat fluxes and temperatures on side-faces. The accuracy and efficiency of the proposed formulation are demonstrated by modeling five numerical examples involving the complicated geometry. |
| Author | Zhang, Pengchong Lin, Gao Li, Peng Liu, Jun Yang, Guotao |
| Author_xml | – sequence: 1 givenname: Peng surname: Li fullname: Li, Peng organization: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 2 givenname: Jun surname: Liu fullname: Liu, Jun email: liujun8128@126.com organization: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 3 givenname: Gao surname: Lin fullname: Lin, Gao organization: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 4 givenname: Pengchong surname: Zhang fullname: Zhang, Pengchong organization: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 5 givenname: Guotao surname: Yang fullname: Yang, Guotao organization: School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia |
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| Keywords | Isogeometric analysis Scaled boundary finite element method Complex geometry Steady-state heat conduction problems NURBS |
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| Snippet | •SBFEM combined with IGA is first applied to two-dimensional steady-state heat transfer problems.•The formula of SBFEM with IGA is derived in detail.•The... The scaled boundary finite element method (SBFEM) combined with isogeometric analysis (IGA) is proposed to solve the two-dimensional steady-state heat... |
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| SubjectTerms | Accuracy Basis functions Boundary element method Complex geometry Computation Conduction heating Conductive heat transfer Finite element analysis Finite element method Geometry Heat flux Heat transfer Isogeometric analysis Mathematical analysis Mathematical models NURBS Scaled boundary finite element method Segments Splines Steady-state heat conduction problems |
| Title | A NURBS-based scaled boundary finite element method for the analysis of heat conduction problems with heat fluxes and temperatures on side-faces |
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