Sequential Buckling: A Variational Analysis. Modeling, Analysis and Simulation

摘要

The authors estimate a variational problem from elastic stability theory: a thin211u001eelastic strut on an elastic foundation. The strut has infinite length, and its 211u001elateral deflection is represented by u : R-> R. Deformation takes place under 211u001econditions of prescribed total shortening, leading to the variational problem. 211u001eSolutions of this minimization problem solve the Euler-Lagrange equation. The 211u001efoundation has a nonlinear stress-strain relationship F(sup 1), combining a 211u001edestiffening character for small deformation with subsequent stiffening for large 211u001edeformation. The authors prove that for every value of the shortenting lambda > 0 211u001ethe minimization problem has at least one solution. In the limit lambda -> 211u001einfinity these solutions converge on bounded intervals to a periodic profile, 211u001ethat is characterized by a related variational problem.