Shape optimization against buckling of micro- and nano- rods

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Atanackovic, Teodor M, Novakovic, Branislava N and Vrcelj, Zora (2012) Shape optimization against buckling of micro- and nano- rods. Archive of Applied Mechanics, 82 (10/11). pp. 1303-1311. ISSN 0939-1533 (print) 1432-0681 (online)


In this paper, we analyze elastic buckling of micro- and nano-rods based on Eringen's nonlocal elasticity theory. By using the Pontryagin's maximum principle, we determine optimality condition for a rod simply supported at both ends and loaded with axial compressive force only. Thus, the problem that we treat represents a generalization of the classical Clausen problem formulated for Bernoulli–Euler rod theory. Several concrete examples are treated in details, and the increase in buckling load capacity is determined. In solving the problem numerically, we used a first integral of the resulting system of equations, which helped us to monitor error of the numerical procedure. Our results show that nonlocal effects decrease the buckling load of optimally shaped rod. However, nonlocal theory leads to the optimal rod with the cross-sectional area at the rod ends different from zero. This is important property since zero value of the cross-section at the ends, which optimally shaped rod according to Bernoulli–Euler rod theory has, is unacceptable in applications.

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Item type Article
DOI 10.1007/s00419-012-0661-1
Official URL
Subjects Current > Division/Research > College of Science and Engineering
Historical > FOR Classification > 0905 Civil Engineering
Historical > SEO Classification > 8702 Construction Design
Keywords ResPubID26222, nonlocal column, Pontryagin’s principle, optimal shape, beam–columns, elastic buckling, distortional buckling
Citations in Scopus 7 - View on Scopus
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