Issue 29

S. Terravecchia et al., Frattura ed Integrità Strutturale, 29 (2014) 61-73; DOI: 10.3221/IGF-ESIS.29.07 73 he table of fundamental solutions for isotropic strain gradient elasticity is similar to an analogous table used within classical boundary element method. Computational techniques have been pursued in order to eliminate the singularities of order 1/ r , 2 1/ r , in the blocks of the coefficients related to the corners of the solid and new techniques based on the rigid motion strategy have been introduced in order to test the coefficients of the blocks of the solving system. The displacement and internal deformation fields were obtained. Numerical techniques in order to remove the singularity of higher order like 3 1/ r and 4 1/ r are in advanced study. R EFERENCES [1] Polizzotto, C., Panzeca, T., Terravecchia, S., A symmetric Galerkin BEM formulation for a class of gradient elastic materials of Mindlin type. Part I: Theory, (2014). In preparation. [2] Mindlin, R.D., Second gradient of strain and surface tension in linear elasticity, Int. J. Solids Struct., 1.(1965) 417- 438. [3] Mindlin, R.D., Eshel, N.N., On first strain-gradient theories in linear elasticity, Int. J. Solids Struct., 28 (1968) 845- 858. [4] Wu, C.H., Cohesive elasticity and surface phenomena, Quart. Appl. Math., L(1) (1968) 73-103. [5] Aifantis, E.C., On the role of gradients in the localization of deformation and fracture, Int. J. Eng. Sci., 30 (1992) 1279-1299. [6] Askes, H., Aifantis, E.C., Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, Int. J. Solids Struct., 48 (2011) 1962- 1990. [7] Polyzos, D., Tsepoura, K.G., Tsinopoulos, S.V., Beskos, D.E., A boundary element method for solving 2-D and 3-D static gradient elastic problems. Part.I: integral formulation, Comput. Meth. Appl. Mech. Engng., 192 . (2003) 2845- 2873. [8] Karlis, G. F. , Charalambopoulos, A., Polyzos, D., An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain gradient theory of elasticity, Int. J. Numer. Meth. Engng., 83 (2010) 1407-1427. [9] Panzeca, T., Cucco, F., Terravecchia S., Symmetric Boundary Element Method versus Finite Element Method, Comp. Meth. Appl. Mech. Engrg., 191 (2002) 3347-3367. [10] Cucco F., Panzeca T., Terravecchia S., The program Karnak.sGbem Release 2.1, (2002) Palermo University. [11] Polizzotto C., An energy approach to the boundary element method. Part.I: elastic solids, Comput. Meth. Appl. Mech. Engng., 69 (1988) 167-184. T