References of "Bordas, Stéphane 50000969"
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See detailA mass conservative Kalman filter algorithm for thermo-computational fluid dynamics
Introini, Carolina; Baroli, Davide UL; Lorenzi, Stefano et al

in Materials (n.d.)

Computational fluid-dynamics (CFD) is of wide relevance in engineering and science, due to its capability of simulating the three-dimensional flow at various scales. However, the suitability of a given ... [more ▼]

Computational fluid-dynamics (CFD) is of wide relevance in engineering and science, due to its capability of simulating the three-dimensional flow at various scales. However, the suitability of a given model depends on the actual scenarios which are encountered in practice. This challenge of model suitability and calibration could be overcome by a dynamic integration of measured data into the simulation. This paradigm is known as data-driven assimilation (DDA). In this paper, the study is devoted to Kalman filtering, a Bayesian approach, applied to Reynolds-Averaged Navier-Stokes (RANS) equations for turbulent flow. The integration of the Kalman estimator into the PISO segregated scheme was recently investigated by (1). In this work, this approach is extended to the PIMPLE segregated method and to the ther- modynamic analysis of turbulent flow, with the addition of a sub-stepping procedure that ensures mass conservation at each time step and the com- patibility among the unknowns involved. The accuracy of the algorithm is verified with respect to the heated lid-driven cavity benchmark, incorporat- ing also temperature observations, comparing the augmented prediction of the Kalman filter with the CFD solution obtained on a very fine grid. [less ▲]

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See detailA new one point quadrature rule over arbitrary star convex polygon/polyhedron
Natarajan, Sundararajan; Francis, Amrita; Atroshchenko, Elena et al

E-print/Working paper (n.d.)

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we ... [more ▼]

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲]

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See detailLinear smoothed polygonal and polyhedral finite elements
Francis, Amrita; Ortiz-Bernardin, Alejandro; Bordas, Stéphane UL et al

E-print/Working paper (n.d.)

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal ... [more ▼]

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision. [less ▲]

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See detailMinimum energy multiple crack propagation Part I: Theory.
Sutula, Danas UL; Bordas, Stéphane UL

in Engineering Fracture Mechanics (n.d.)

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and ... [more ▼]

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-I of this three-part paper are: (1) formulation of the total energy functional governing multiple crack behaviour, (2) three solution methods to the problem of competing crack growth for different fracture front stabilities (e.g. stable, unstable, or a partially stable configuration of crack tips), and (3) the minimum energy criterion for a set of crack tip extensions is posed as the criterion of vanishing rotational dissipation rates with respect to the rotations of the crack extensions. The formulation lends itself to a straightforward application within a discrete framework for determining the crack extension directions of multiple finite-length crack tip increments, which is tackled in Part-II, using the extended finite element method. In Part-III, we discuss various applications and benchmark problems. The open-source Matlab code, documentation, benchmark/example cases are included as supplementary material. [less ▲]

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See detailMinimum energy multiple crack propagation. Part II: Discrete Solution with XFEM.
Sutula, Danas UL; Bordas, Stéphane UL

in Engineering Fracture Mechanics (n.d.)

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and ... [more ▼]

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. This Part-II of our three-part paper examines three discrete solution methods for solving fracture mechanics problems based on the principle of minimum total energy. The discrete solution approach is chosen based on the stability property of the fracture configuration at hand. The first method is based on external load-control. It is suitable for stable crack growth and stable fracture configurations. The second method is based on fractured area-control. This method is applicable to stable or unstable fracture growth but it is required that the fracture front be stable. The third solution method is based on a gradient-descent approach. This approach can be applied to arbitrary crack growth problems; however, the gradient-descent formulation cannot be guaranteed to yield the optimal solution in the case of competing crack growth and an unstable fracture front configuration. The main focus is on the gradient-descent solution approach within the framework of the extended finite element discretisation. Although a viable solution method is finally proposed for resolving competing crack growth in the case of an unstable fracture front configuration, the method is not implemented within the present XFEM code but rather exists as a separate proof-of-concept algorithm that is tested against several fabricated benchmark problems. The open-source Matlab code, documentation and example cases are included as supplementary material. [less ▲]

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See detailAn extended finite element method with smooth nodal stress
Peng, Xuan; Kulasegaram, Sivakumar; Bordas, Stéphane UL et al

Report (n.d.)

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See detailLinear smoothing over arbitrary polytopes
Francis, Amrita; Natarajan, Sundararajan; Ortiz-Bernardin, Alejandro et al

Scientific Conference (n.d.)

The conventional constant strain smoothing technique yields less accurate solutions that other techniques such as the conventional polygonal finite element method [1, 2]. In this work, we propose a linear ... [more ▼]

The conventional constant strain smoothing technique yields less accurate solutions that other techniques such as the conventional polygonal finite element method [1, 2]. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex poly- topes. The method relies on sub-division of the polytope into simplical subcells; however instead of using a constant smoothing function, we employ a linear smoothing function over each subcell. This gives a new definition for the strain to compute the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the optimal convergence rate as in traditional quadrilateral and hexahedral finite elements. The accuracy is also improved, and all the methods tested pass the patch test to machine precision. [less ▲]

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See detailA well-conditioned and optimally convergent XFEM for 3D linear elastic fracture
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL et al

in International Journal for Numerical Methods in Engineering (n.d.)

A variation of the extended finite element method for 3D fracture mechanics is proposed. It utilizes global enrichment and point-wise as well as integral matching of displacements of the standard and ... [more ▼]

A variation of the extended finite element method for 3D fracture mechanics is proposed. It utilizes global enrichment and point-wise as well as integral matching of displacements of the standard and enriched elements in order to achieve higher accuracy, optimal convergence rates and improved conditioning for two and three dimensional crack problems. A bespoke benchmark problem is introduced to determine the method's accuracy in the general 3D case where it is demonstrated that the proposed approach improves the accuracy and reduces the number of iterations required for the iterative solution of the resulting system of equations by 40% for moderately refined meshes and topological enrichment. Moreover, when a fixed enrichment volume is used, the number of iterations required grows at a rate which is reduced by a factor of 2 compared to standard XFEM, diminishing the number of iterations by almost one order of magnitude. [less ▲]

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