Abstract
Long compressed elastic struts on softening elastic foundations have a tendency to buckle locally. The same tendency is demonstrated here for the instantaneous response of elastic struts supported by visco-elastic media. A governing nonlinear partial differential equation is derived to describe the evolution of the localized form in time. Under the assumed constant end-shortening this is found to be approximated by a coupled set of seven ordinary differential (diffusion) equations. As the load drops to zero, the localized buckle pattern evolves towards the form of the single long wave, but remains aperiodic for all time. Three-dimensional plots show how this localized pattern changes over time.
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Hunt, G.W., Mühlhaus, HB. & Whiting, A.I.M. Evolution of localized folding for a thin elastic layer in a softening visco-elastic medium. PAGEOPH 146, 229–252 (1996). https://doi.org/10.1007/BF00876491
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DOI: https://doi.org/10.1007/BF00876491