Elastostatic analysis using the boundary element method and the Aifantis gradient elasticity theory

Resumo

The increasing use of micro and nano-scale structures has sparked interest in theories incorporating the effect of scale since the classical continuum theory has limitations in capturing effects that depend on size. Therefore, three-dimensional elastostatic microstructure modeling is carried out in this work using the boundary element method (BEM).To account for microstructural effects, the simplified gradient theory proposed by Aifantis, a particularization of Mindlin's general theory, was employed. A variational argument was established to determine the governing equations and boundary conditions for the problem. This argument explains the fundamental solution of gradient elasticity, and the integral contour representation is constructed with the aid of the reciprocal identity. Curved triangular elements of Proriol spectral functions were used to approximate the geometry and the physical parameters for the discretization of the BEM. The presented formulation yielded results consistent with other analyses in the literature.