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Partial drainage during earthquake-induced liquefaction
Published in Andrew McNamara, Sam Divall, Richard Goodey, Neil Taylor, Sarah Stallebrass, Jignasha Panchal, Physical Modelling in Geotechnics, 2018
O. Adamidis, G.S.P. Madabhushi
Contrary to the chamber of OA2, the chamber of OA3 responded by increasing in height during the earthquake. This chamber could not expand due to the presence of the fishing line. Along any horizontal section of this chamber, the perimeter could not change in length. Any deviation from the initial circular shape would result in a reduction of the enclosed surface due to the isoperimetric inequality, which states that for a shape of a certain perimeter, a circle contains the maximum area. Since the volume inside the sealed chamber had to remain constant, deviations from the original cylindrical shape would necessarily result in an increase of the chamber’s height. It is hypothesised that due to the rocking of the soil mass in the box, larger horizontal displacements on one side of the chamber distorted its cylindrical shape and led to the recorded displacements. This effect was not pronounced in OA2, where the periphery could expand. On the contrary, it was prominent in OA3, overshadowing the effect of the weight of the cap.
Closed-form solution for optimization of buckling column
Published in Mechanics Based Design of Structures and Machines, 2023
For the optimization problem in Lagrange sense, the isoperimetric inequality could be formulated as the strict inequality (Chavel, 2001). This isoperimetric inequality is sharp. The optimal solution could not be attained for any positive value of parameter The analogous consideration, but using completely different arguments, was deliberated by Cox and McCarthy (1998). In other words, the original Lagrange problem possesses no attainable solution from the both points of view of the optimal control theory and variational calculus.