An error indicator-based adaptive reduced order model for nonlinear structural mechanics -- application to high-pressure turbine blades

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 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory

Analysis of vibration induced error in turbulence velocity measurements from an aircraft wing tip boom

The effect of rolling motion of a wing on the magnitude of error induced due to the wing vibration when measuring atmospheric turbulence with a wind probe mounted on the wing tip was investigated. The wing considered had characteristics similar to that of a B-57 Cambera aircraft, and Von Karman's cross spectrum function was used to estimate the cross-correlation of atmospheric turbulence. Although the error calculated was found to be less than that calculated when only elastic bendings and vertical motions of the wing are considered, it is still relatively large in the frequency's range close to the natural frequencies of the wing. Therefore, it is concluded that accelerometers mounted on the wing tip are needed to correct for this error, or the atmospheric velocity data must be appropriately filtered

Nonintrusive approximation of parametrized limits of matrix power algorithms -- application to matrix inverses and log-determinants

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones

Intercultural education in Brazil: Between conservatism and radical transformations

This article analyses the emergence of intercultural education in the Brazilian educational system. After summarizing the debate on international convergence in intercultural education, it traces the development of interethnic relations in Brazil, describing the heavy legacy of slavery and colonization. It then investigates recently adopted legislation that encourages the inclusion of cultural diversity in education. Finally, it explores intercultural approaches in the training and work of teachers. The Brazilian example is interesting because it reflects both an ongoing conservatism that resists the teaching of intercultural material in schools and a profound debate about cultural identities and the need for education to take into account all of the nation's historical inequalitie

Arab countries and the global education agenda 2030: Incomplete path

The 2030 global education agenda sets a progression path for all countries. About ten years before this deadline, this paper explores potential trajectories for Arab countries to achieve significant advances in education. The article examines major challenges related to access and quality of education. While most countries made major progress on quantitative dimensions of education (enrollment, years of schooling), important challenges remain such as limited learning outcomes, persistent illiteracy, inequalities and poor governance of education. This paper proposes new ways to rethink education in this region. The tension between credentials(prioritized by students, family and the state) and skills (needed by society and the job market)is one of the most relevant issue in reforming education in the region

On Matroid Connectivity.

Certain classes of 2- and 3-connected matroids are studied in this thesis. In Chapter 2 we give a characterization of those 2-connected matroids M with the property that, for a given positive integer m, the deletion of every non-empty subset of M having at most m elements is disconnected. A bound on the maximum number of elements of such a matroid in terms of its rank is also given, along with a complete description of the matroids attaining this bound. These results extend results of Murty and Oxley for minimally 2-connected matroids. A characterization of the 3-connected matroids M that have the property that every 2-element deletion of M is disconnected is given in Chapter 3. It is shown that these matroids are exactly the duals of Sylvester matroids having at least four elements. In Chapter 4 we prove the following result: Let M be a 3-connected matroid other than a wheel of rank greater than three, and let C be a circuit of M. If the deletion of every pair of elements of C is disconnected, then every pair of elements of C is contained in a triad of M. For an integer t greater than one, an n-element matroid M is t-cocyclic if every deletion having at least n $-$ t + 1 elements is 2-connected, and every deletion having exactly n $-$ t elements is disconnected. A matroid is t-cyclic if its dual is t-cocyclic. In Chapter 5 we investigate the matroids that are both t-cocyclic and t-cyclic. It is shown that these matroids are exactly the uniform matroids U (t,2t) and the Steiner Systems S(t, t + 1, 2t + 2)