References of "Ortiz-Bernardin, Alejandro"
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See detailA volume-averaged nodal projection method for the Reissner-Mindlin plate model
Ortiz-Bernardin, Alejandro; Köbrich, Philip; Hale, Jack UL et al

in Computer Methods in Applied Mechanics & Engineering (2018), 341

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and ... [more ▼]

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses. [less ▲]

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See detailLinear smoothing over arbitrary polytopes for compressible and nearly incompressible linear elasticity
Natarajan, Sundararajan; Tomar, Satyendra UL; Bordas, Stéphane UL et al

Scientific Conference (2016, June)

We present a displacement based approach over arbitrary polytopes for compressible and nearly incompressible linear elastic solids. In this approach, a volume-averaged nodal projection operator is ... [more ▼]

We present a displacement based approach over arbitrary polytopes for compressible and nearly incompressible linear elastic solids. In this approach, a volume-averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower-order than the approximation space for the displacement field, resulting in a locking-free method. The formulation uses the usual Wachspress interpolants over arbitrary polytopes and the stability of the method is ensured by the addition of bubble like functions. The smoothed strains are evaluated based on the linear smoothing procedure. This further softens the bilinear form allowing the procedure to search for a solution satisfying the divergence- free condition. The divergence-free condition of the proposed approach is verified through systematic numerical study. The formulation delivers optimal convergence rates in the energy and L2-norms. Inf-sup tests are presented to demonstrated the stability of the formulation. [less ▲]

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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 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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