Analysis and evaluation of singular integrals by the invariant imbedding approach

The invariant imbedding formulae for evaluating singular integrals on flat domains are used to analyse the singular integrals which arise in the Boundary Element Method. Although all orders of singularity are considered, the primary objective of the paper is the evaluation of Cauchy principal value integrals (CPV). Conditions for boundedness of the CPV aré derived, and evaluation techniques are presented for situations in which the singular point lies on, or is in close proximity to, an element boundary. Specific cases analysed include straight and curved element boundaries, and corners. Other numerical aspects of the formulae are also discussed. By way of example, the analysis techniques are applied to the volume integrals which arise in continuum, inelastic problems.