The scaled boundary finite element method
Creator  
Publisher 
20030314

ISBN  0471486825, 9780471486824,

Language 
English

Category  
Subject  Boundary element methods. Boundary element methods.  fast  (OCoLC)fst00837093 Finite element method. Finite element method.  fast  (OCoLC)fst00924897 TECHNOLOGY & ENGINEERING  Engineering (General)  bisacsh TECHNOLOGY & ENGINEERING  Reference.  bisacsh 
Description
A novel computational procedure called the scaled boundary finiteelement method is described which combines the advantages of the finiteelement and boundaryelement methods : Of the finiteelement method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundaryelement method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finiteelement method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finiteelement method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weightedresidual approximation of finite elements applies, leading to convergence in the finiteelement sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stressintensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finiteelement method is a semianalytical fundamentalsolutionless boundaryelement method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finiteelement and boundaryelement methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.