The Scaled Boundary Finite Element Method

The Scaled Boundary Finite Element Method describes a fundamental solution-less boundary element method, based on finite elements. As such, it combines the advantages of the boundary element method:

• spatial discretisation reduced by one
• boundary condition at infinity satisfied exactly

with those of the finite element method:

• no fundamental solution required
• no singular integrals
• the processing of anisotropic material without any additional computational effort

Other benefits include the fact that the analytical solution inside the domain permits stress singularities to be determined directly, and also that there is no spatial discretisation of certain boundaries such as crack faces and free surfaces and interfaces between different materials.

The scaled boundary finite element method can be used to analyse any bounded and unbounded media governed by linear elliptic, parabolic and hyperbolic partial differential equations.

The book serves two goals which can be pursued independently. Part I is a primer, with a model problem addressing the simplest wave propagation but still containing all essential features. Part II derives the fundamental equations for statics, elastodynamics and diffusion, and discusses the solution procedures from scratch in great detail.

In summary this comprehensive text presents a novel procedure which will be of interest not only to engineers, researchers and students working in engineering mechanics, acoustics, heat-transfer, earthquake engineering, electromagnetism, and computational mathematics, but also consulting engineers dealing with nuclear structures, offshore platforms, hardened structures, critical facilities, dams, machine foundations and other structures subjected to earthquakes, wave loads, explosions and traffic.