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Optimality conditions for shakedown design of trusses. (English) Zbl 0849.73043
The paper deals with the problem of optimal shakedown design of truss structures constitued by elastic-perfectly plastic material. The design problem is formulated by means of a statical approach based on the shakedown lower bound theorem, and by means of a kinematical approach based on the shakedown upper bound theorem. In both cases, two different types of design problem are formulated: one searches for the minimum volume design assuming that the shakedown limit load is assigned; the other searches for the maximum shakedown limit load design assuming that the volume is assigned. The Kuhn-Tucker equations of the four afore-mentioned problems are found by a variational approach; these equations are used to prove the equivalence of the two types of design problem and provide useful information on the structure behaviour in optimality conditions. A suitable computational procedure of iterative type is presented for the minimum volume design.

MSC:
74P99 Optimization problems in solid mechanics
74R20 Anelastic fracture and damage
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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