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The Boundary Contour Method (BCM) is a recent variant of the Boundary Element Method (BEM) resting on the use of boundary approximations which a-priori satisfy the field equations. For two-dimensional problems, the evaluation of all the line-integrals involved in the collocation BCM reduces to function evaluations at the end-points of each element, thus completely avoiding numerical integrations.

With reference to some initial-boundary-value problems formulated in the Laplace transform domain, a “regularized” symmetric BIE formulation is derived. The specific problems considered, i.e. diffusion, plane-strain elastodynamics and dynamics of elastic Kirchhoff plates, are formulated in terms of BIEs containing at most weakly (logarithmic) singular kernels. This regularization is achieved by means of the “derivative transfer” technique where, through integration by parts, derivatives are “transferred” from particular auxiliary kernels to the kinematic fields involved in the BIEs.

A procedure for the evaluation of the double integrals involved in the symmetric BE method is proposed, which consists in a regularization via integration by parts and in a successive numerical evaluation of weakly singular integrals. The procedure is applicable to curved elements and higher order shape functions and lends itself to a fairly straightforward implementation. Continuity is required for displacement modelling, while tractions may be modelled as piece-wise continuous. Some example problems characterized by the presence of curved boundaries or of cracks are analyzed using the proposed technique to demonstrate its effectiveness.

A boundary integral equation (BIE) formulation and a boundary element (BE) method which confer symmetry to key operators are concisely described with reference to quasi-static plasticity. This formulation is based on the combined use of static and kinematic sources, on Galerkin weighted residual enforcement of integral equations for displacements and tractions along the boundary and for stresses in the potentially yielding domain and on space discretizations in terms of generalized variables in Prager's sense. Typical theoretical results of computational interest not available in conventional nonsymmetric BE methods are surveyed. The subjectivity (mesh-dependence) implied by material instability is illustrated by examples. As a remedy, a symmetric BIE-BE formulation for nonlocal, gradient-dependent plasticity is developed and discussed on the basis of its variationally consistent discretization.