Topology and shape optimization for elastoplastic structural response. (English) Zbl 1067.74052
The paper deals with an elastoplastic von Mises material model with linear isotropic hardening/softening for small strains. The objective of the design problem is to maximize the structural ductility in the elastoplastic range while the mass in the design space is prescribed. With respect of the specific features of either topology or shape optimization, for example the number of optimization variables or their local-global influence of the structural response, different methods are applied. For topology optimization problems, the gradient of the ductility is determined by the variational adjoint approach. In shape optimization, the derivatives of state variables with respect to the optimization variables are evaluated analytically by a variational direct approach. The topology optimization problem is solved by optimality criteria method, and the shape optimization problem by mathematical programming method. The procedures are verified by two-dimensional design problems under plane stress conditions.
Reviewer: Stefan Jendo (Warszawa)
MSC:
| 74P15 | Topological methods for optimization problems in solid mechanics |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
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