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An analysis of initial post‐buckling of a micro‐scaled beam with hinged‐hinged ends based on the strain gradient elasticity is presented. At the first bifurcation point, the second variation of the potential energy is analytically proved to be positive semidefinite when the compression equals to the critical load. The fourth variation of the potential energy is positive when the disturbance of the...
Based on the conjugate point theory in calculus of variations, sufficient conditions on stability of all Euler elasticas for a column clamped at one end and guided at the other are proposed in this paper. For the Euler elasticas, an initial value problem is solved numerically by the Euler iteration. Sufficient conditions are satisfied that Euler elasticas with one half wave are stable and the others...
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