Papargyri-Beskou, S.; Tsepoura, K. G.; Polyzos, D.; Beskos, D. E. Bending and stability analysis of gradient elastic beams. (English) Zbl 1022.74010 Int. J. Solids Struct. 40, No. 2, 385-400 (2003). Summary: The problems of bending and stability of Bernoulli–Euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement. The additional boundary conditions are obtained by both variational and weighted residual approaches. Two boundary value problems (one for bending and one for stability) are solved, and the gradient elasticity effect on the beam bending response and its critical (buckling) load is assessed for both cases. It is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient, while the surface energy effect is small and insignificant for bending and buckling, respectively. Cited in 1 ReviewCited in 93 Documents MSC: 74G60 Bifurcation and buckling 74K10 Rods (beams, columns, shafts, arches, rings, etc.) Keywords:microstructural effects; linear theory of gradient elasticity; surface energy; bending; stability; variational principle; non-classical boundary conditions; Bernoulli-Euler beams; boundary value problems; critical buckling load PDFBibTeX XMLCite \textit{S. Papargyri-Beskou} et al., Int. J. Solids Struct. 40, No. 2, 385--400 (2003; Zbl 1022.74010) Full Text: DOI