Abstract
The problems of the optimization of bar structures made of work-hardening elasto-plastic materials are investigated on the basis of the deformation theory of plasticity. Two optimization criteria are discussed - the minimum of the total complementary energy and the minimum of the total elasto-plastic strain potential energy. It is proved that these criteria are equivalent and lead to equally-stressed structures, if the structures are statically determinate. Furthermore, a problem of the minimization of the integral over the structural volume of an arbitrary monotonously increasing strictly convex smooth function of the absolute value of a strain or a stress with prescribed volume of material for statically determinate bar structures also proves to lead to equally-stressed structures. On the basis of the results obtained, two algorithms for the optimization of statically indeterminate trusses are proposed and illustrated. It is noted that the example structure degenerates to a statically determinate one as a result of the optimization process.
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Selyugin, S.V. Optimization criteria and algorithms for bar structures made of work-hardening elasto-plastic materials. Structural Optimization 4, 218–223 (1992). https://doi.org/10.1007/BF01742748
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DOI: https://doi.org/10.1007/BF01742748