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A fictitious energy approach for shape optimization. (English) Zbl 1188.74045
Summary: This paper deals with shape optimization of continuous structures. As in early works on shape optimization, coordinates of boundary nodes of the FE-domain are directly chosen as design variables. Convergence problems and problems with jagged shapes are eliminated by a new regularization technique: an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design. The energy constraint defines a feasible design space whose size can be varied by one parameter, the upper energy limit. By construction, the proposed regularization is applicable to a wide range of problems; although in this paper, the application is restricted to linear elastostatic problems.

MSC:
74P10 Optimization of other properties in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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