The scaled boundary finite-element method – a fundamental solution-less boundary-element method

✍ Scribed by John P. Wolf; Chongmin Song

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 250 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00183-9

✦ Synopsis

In this boundary-element method based on ®nite elements only the boundary is discretized with surface ®nite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary and thus no singular integrals must be evaluated and general anisotropic material can be analysed. For an unbounded (semi-in®nite or in®nite) medium the radiation condition at in®nity is satis®ed exactly. No discretization of free and ®xed boundaries and interfaces between dierent materials is required. The semi-analytical solution inside the domain leads to an ecient procedure to calculate the stress intensity factors accurately without any discretization in the vicinity of the crack tip. Body loads are included without discretization of the domain. Thus, the scaled boundary ®nite-element method not only combines the advantages of the ®nite-element and boundary-element methods but also presents appealing features of its own. After discretizing the boundary with ®nite elements the governing partial dierential equations of linear elastodynamics are transformed to the scaled boundary ®nite-element equation in displacement, a system of linear second-order ordinary dierential equations with the radial coordinate as independent variable, which can be solved analytically. Introducing the de®nition of the dynamic stiness, a system of nonlinear ®rst-order ordinary dierential equations in dynamic stiness with the frequency as independent variable is obtained. Besides the displacements in the interior the static-stiness and mass matrices of a bounded medium and the dynamic-stiness and unit-impulse response matrices of an unbounded medium are calculated.