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Gradient based biobjective shape optimization to improve reliability and cost of ceramic components. (English) Zbl 1452.74095
Summary: We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of the component under tensile load, while the cost is assumed to be proportional to the volume of the component. Two different gradient-based optimization methods are suggested and compared at 2D test cases. The numerical implementation is based on a first discretize then optimize strategy and benefits from efficient gradient computations using adjoint equations. The resulting approximations of the Pareto front nicely exhibit the trade-off between reliability and cost and give rise to innovative shapes that compromise between these conflicting objectives.

MSC:
74P10 Optimization of other properties in solid mechanics
49Q10 Optimization of shapes other than minimal surfaces
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
90B25 Reliability, availability, maintenance, inspection in operations research
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