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Numerical investigation of circle defining curve for two-dimensional problem with general boundaries using the scaled boundary finite element method

Chung Nguyen VAN

Frontiers of Structural and Civil Engineering 2019, Volume 13, Issue 1, Pages 92-102 doi: 10.1007/s11709-018-0472-8

Abstract: The scaled boundary finite element method (SBFEM) is applied to the static analysis of two dimensional

Keywords： exact geometry circular defining curve general boundaries SBFEM

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Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media

Jaroon RUNGAMORNRAT, Chung Nguyen VAN

Frontiers of Structural and Civil Engineering 2019, Volume 13, Issue 1, Pages 201-214 doi: 10.1007/s11709-018-0488-0

Abstract: This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with a domain completely described by a circular defining curve. The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems, bounded and unbounded bodies, distributed body source, and general boundary conditions to be treated in a unified fashion. The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve, exact geometry of the domain, and exact spatial differential operators. Standard finite element shape functions are employed in the discretization of both trial and test functions in the circumferential direction and the resulting eigenproblem is solved by a selected efficient algorithm. The computational performance of the implemented procedure is then fully investigated for various scenarios to demonstrate the accuracy in comparison with standard linear elements.

Keywords： multi-field problems defining curve exact geometry general boundary conditions SBFEM