A virtual work derivation of the scaled boundary finite-element method for elastostatics

The scaled-boundary finite element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. This paper develops a new virtual work formulation and modal interpretation of the method for elastostatics. This formulation follows a similar procedure to the traditional virtual work derivation of the standard finite element method. As well as making the method more accessible, this approach leads to new techniques for the treatment of body loads, side-face loads and axisymmetry that simplify implementation. The paper fully develops the new formulation, and provides four examples illustrating the versatility, accuracy and efficiency of the scaled boundary finite-element method. Both bounded and unbounded domains are treated, together with problems involving stress singularities.