Euler Buckling

Robert F. Brown

Chapter Chapter 25 in A Topological Introduction to Nonlinear Analysis, 2014, pp 205-210 from Springer

Abstract: Abstract The Euler buckling problem is − u ″ = λ sin u ( E ) u ′ ( 0 ) = u ′ ( π ) = 0 . $$\displaystyle\begin{array}{rcl} -u'' =\lambda \sin u\quad & & {}\\ (E)\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad & & {}\\ u'(0) = u'(\pi ) = 0.& & {}\\ \end{array}$$ Even though L u = − u ″ $$Lu = -u''$$ isn’t invertible with respect to the given boundary condition, we can apply Theorem 24.9 to the modified problem

Keywords: Euler Buckling; Nonlinear Sturm-Liouville Eigenvalue Problems; Column Buckling; Unrealistic Model; Flexural Rigidity (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-11794-2_25

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