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Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for each macroelement and characterized by symmetric matricial operators, are similar in type to those obtainable for the FEM. The assembly of the macroelements based on the equilibrium conditions, or on the compatibility conditions, or on both of these conditions leads to three analysis methods: displacement, force, and mixed-value methods, respectively. The use of the fundamental solutions involves the punctual satisfaction of the compatibility and of the equilibrium inside each macroelement and it causes a stringent elastic response close to the actual solution. Some examples make it possible to perform numerical checks in comparison with solutions obtainable in closed form. These checks show that the numerical solutions are floating ones when the macroelement geometry obtained by subdividing the body changes.

The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals.\ud In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed and, by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the Somigliana Identity of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary. The latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one, defined as a Cauchy Principal Value, with which the related free term is associated. The expressions thus obtained for the displacements and the tractions, in which domain integrals are substituted by boundary integrals, were utilized in the Galerkin approach, for the evaluation in closed form of the load coefficients connected to domain inelastic actions.\ud This strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed; the obtained coefficients were implemented in the Karnak.sGbem calculus code

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