Structural Engineering and Mechanics

  • 제14권1호
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  • Pages.99-118
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  • 2002
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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Semi-analytical elastostatic analysis of two-dimensional domains with similar boundaries

  • Deeks, Andrew J. (Department of Civil and Resource Engineering, The University of Western Australia)
  • 투고 : 2001.12.20
  • 심사 : 2002.04.16
  • 발행 : 2002.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

The scaled-boundary finite element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one coordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) coordinate direction. These coordinate directions are defined by the geometry of the domain and a scaling centre. This paper presents a general development of the scaled boundary finite-element method for two-dimensional problems where two boundaries of the solution domain are similar. Unlike three-dimensional and axisymmetric problems of the same type, the use of logarithmic solutions of the weakened differential equations is found to be necessary. The accuracy and efficiency of the procedure is demonstrated through two examples. The first of these examples uses the standard finite element method to provide a comparable solution, while the second combines both solution techniques in a single analysis. One significant application of the new technique is the generation of transition super-elements requiring few degrees of freedom that can connect two regions of vastly different levels of discretisation.

키워드

참고문헌

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피인용 문헌

  1. Using fundamental solutions in the scaled boundary finite element method to solve problems with concentrated loads vol.53, pp.4, 2014, https://doi.org/10.1007/s00466-013-0923-y
  2. Use of higher-order shape functions in the scaled boundary finite element method vol.65, pp.10, 2006, https://doi.org/10.1002/nme.1517