Abstract
The adapted plate load optimization problem is formulated applying the non-linear mathematical programming methods. The load variation bounds satisfying the optimality criterion in concert with the strength and stiffness requirements are to be identified. The stiffness constraints are realized via residual displacements. The dual mathematical programming problems cannot be applied directly when determining actual stress and strain fields of plate: the strained state depends upon the loading history. Thus the load optimization problem at shakedown is to be stated as a couple of problems solved in parallel: the shakedown state analysis problem and the verification of residual deflections bounds. The Rozen project gradient method is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems. The mechanical interpretation of Rozen optimality criterions allows to simplify the shakedown plate optimization mathematical model and solution algorithm formulations.
Highlights
The present paper continues the investigations of mathematical programming method applications for perfectly elastic-plastic structures in the range of the shakedown theory [1,2,3,4,5,6,7,8,9,10,11,12]
The Rozen project gradient method [13] is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems
The mechanical interpretation of the Rozen algorithm optimality criterions in the structural analysis problem was explained in the investigations [14, 15] based on the application of the known in the mathematical programming method KuhnTucker conditions
Summary
The present paper continues the investigations of mathematical programming method applications for perfectly elastic-plastic structures in the range of the shakedown theory [1,2,3,4,5,6,7,8,9,10,11,12]. The mechanical interpretation of the Rozen algorithm optimality criterions in the structural analysis problem was explained in the investigations [14, 15] based on the application of the known in the mathematical programming method KuhnTucker conditions. The mechanical interpretation of Rozen optimality criterions allows to simplify the shakedown plate optimization mathematical model and solution algorithm formulations. The applications related to the circular bendable plate described by the Mises yield conditions are analysed in the paper
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