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An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

Safran Tech, Modelling and Simulation, Rue des Jeunes Bois, Châteaufort, 78114 Magny-Les-Hameaux, France
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Math. Comput. Appl. 2019, 24(2), 41; https://doi.org/10.3390/mca24020041
Received: 26 February 2019 / Revised: 30 March 2019 / Accepted: 15 April 2019 / Published: 19 April 2019
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Abstract

The industrial application motivating this work is the fatigue computation of aircraft engines’ high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes the classical unenriched proper orthogonal decomposition method fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the error indicator becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving five million degrees of freedom, where the whole procedure is computed in parallel with distributed memory. View Full-Text
Keywords: nonlinear reduced order model; elastoviscoplastic behavior; nonlinear structural mechanics; proper orthogonal decomposition; empirical cubature method; error indicator nonlinear reduced order model; elastoviscoplastic behavior; nonlinear structural mechanics; proper orthogonal decomposition; empirical cubature method; error indicator
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Casenave, F.; Akkari, N. An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades. Math. Comput. Appl. 2019, 24, 41.

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