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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.

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