The optimization problems belong to the family of the most important engineering problems. The objective of this paper is to proposed a very efficient numerical algo- rithm which is involved in an optimal design procedure in the field of viscoplasticity phenomena. Because of the complexity of design procedure, particularly in the field of viscoplas- ticity, the finite element method is used. This method provides a good structural discretization and very efficient mathematical describing of time-rate effects. Accord- ing to the design specifications, which will dictate a limiting design strain, using the proposed algorithm, the design life of the considered structure will be covered. For the justification of the proposed method an example is presented. On the basis of specifications data and environment conditions, an operating pressure of a pressure vessel is obtained.
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