Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 40, Issue 2, Pages 385-400Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0020-7683(02)00522-X
Keywords
microstructural effects; gradient elasticity; surface energy; bending of beams; stability of beams; variational principle; non-classical boundary conditions
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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. (C) 2002 Elsevier Science Ltd. All rights reserved.
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