The scaled boundary finite-element method - a primer: solution procedures

The scaled boundary finite-element equations in displacement and dynamic st iffness, which are ordinary differential equations, derived in the accompan ying paper involve the discretization of the boundary only. The general sol ution procedure is demonstrated addressing an illustrative example which co nsists of a two-dimensional out-of-plane (anti-plane) motion with a single degree of freedom on the boundary. For statics and dynamics in the frequenc y domain, the displacements in the domain and the stiffness matrix with deg rees of freedom on the boundary only are obtained analytically for bounded and unbounded media. The radiation condition is satisfied exactly using the high-frequency asymptotic expansion for the dynamic-stiffness matrix of an unbounded medium. The mass matrix for a bounded medium is determined analy tically. Body loads in statics are calculated analytically. Numerical proce dures to calculate the dynamic-stiffness and unit-impulse response matrices for an unbounded medium are also presented. The scaled boundary finite-element method is semi-analytical as the ordinar y differential equations in displacement are solved analytically, which per mits an efficient calculation of displacements, stresses and stress intensi ty factors. This boundary-element method based on finite elements leads to a reduction of the spatial dimension by one. As no fundamental solution is required, no singular integrals are evaluated and anisotropic material is a nalysed without additional computational effort. (C) 2000 Civil-Comp Ltd. a nd Elsevier Science Ltd. All rights reserved.