Stability and optimal shape of Pflüger micro/nano beam

摘要: Abstract This paper deals with optimal shapes against buckling of an elastic nonlocal small-scale Pfluger beams Eringen’s model for constitutive bending curvature relationship. By use the Pontryagin’s maximum principle optimality condition in form a depressed quartic equation is obtained. The shape lightest (having smallest volume) simply supported beam that will support given uniformly distributed follower type load and axial compressive force constant intensity without buckling, determined numerically. A special attention paid to influence characteristic small length scale parameter law both critical analyzed beams. For case when zero, our results reduce those obtained recently compressed beam. Also post optimally shaped rod studied