Optimum design of beams surrounded by a Winkler medium

FENU, LUIGI;SERRA M.

1995-01-01

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Abstract

In the present work the analytical approach is used to study the optimization of a beam loaded laterally at the top, not constrained at its ends and surrounded by a Winkler medium. In the literature there are a few examples of studies regarding the optimization of structures constrained both by local constraints and by contact with a medium; in this case the Winkler medium around the beam is the only constraint. The nonlinear system of differential equations governing the problem is solved with an adequate iterative finite difference algorithm. The optimum design of such a beam distributes the great part of the mass near the top; it is seen that the length of beams that are too long is also optimized limiting, in this way, the driving. In the particular case where the moment of inertia is proportional to the area of the cross-section, an analytical solution is also obtained.