The Scaled Boundary Finite Element Method
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Beschreibung
A novel computational procedure called the scaled boundaryfinite-element method is described which combines the advantages ofthe finite-element and boundary-element methods : Of thefinite-element method that no fundamental solution is required andthus expanding the scope of application, for instance toanisotropic material without an increase in complexity and thatsingular integrals are avoided and that symmetry of the results isautomatically satisfied. Of the boundary-element method that thespatial dimension is reduced by one as only the boundary isdiscretized with surface finite elements, reducing the datapreparation and computational efforts, that the boundary conditionsat infinity are satisfied exactly and that no approximation otherthan that of the surface finite elements on the boundary isintroduced. In addition, the scaled boundary finite-element methodpresents appealing features of its own : an analytical solutioninside the domain is achieved, permitting for instance accuratestress intensity factors to be determined directly and no spatialdiscretization of certain free and fixed boundaries and interfacesbetween different materials is required. In addition, the scaledboundary finite-element method combines the advantages of theanalytical and numerical approaches. In the directions parallel tothe boundary, where the behaviour is, in general, smooth, theweighted-residual approximation of finite elements applies, leadingto convergence in the finite-element sense. In the third (radial)direction, the procedure is analytical, permitting e.g.stress-intensity factors to be determined directly based on theirdefinition or the boundary conditions at infinity to be satisfiedexactly.
In a nutshell, the scaled boundary finite-element method is asemi-analytical fundamental-solution-less boundary-element methodbased on finite elements. The best of both worlds is achieved intwo ways: with respect to the analytical and numerical methods andwith respect to the finite-element and boundary-element methodswithin the numerical procedures.
The book serves two goals: Part I is an elementary text, withoutany prerequisites, a primer, but which using a simple model problemstill covers all aspects of the method and Part II presents adetailed derivation of the general case of statics, elastodynamicsand diffusion.
Autor*in
John P. Wolf
Themen in »The Scaled Boundary Finite Element Method«
Applied Mathematics in Science Computational / Numerical Methods Finite-Elemente-Methode Maschinenbau Mathematics Mathematik Mathematik in den Naturwissenschaften Mechanical Engineering Rechnergestützte / Numerische Verfahren im Maschinenbau