Codice | QDD 19 |
Titolo | A variational principle for plastic hinges in a beam |
Data | 2007-05-28 |
Autore/i | Percivale, D.; Tomarelli F. |
Link | Download full text |
Abstract | We focus the minimization of 1D free discontinuity problem with second order energy dependent on jump integrals but not on the cardinality of the discontinuity set, in the framework of $L^ infty$ load. The related energies are not lower semi continuous in $BH$. Nevertheless we show that if a safe load condition is fulfilled then minimizers exist and they belong actually to $SBH,$ say their second derivative has no Cantor part. If in addition a stronger condition on load is fulfilled then
minimizer is unique and belongs to $H^2$. Moreover we can always select one minimizer whose number of plastic hinges does not
exceed 2 and is the limit of minimizers of penalized problems.
When the load stays in the gap between safe load and regularity condition then minimizers with hinges are allowed; if in addition the load is symmetric and strictly positive then there
is uniqueness of minimizer, the hinges of such minimizer are exactly two and they are located at the endpoints.
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