Hybridized enriched space–time finite element method for analysis of thin-walled structures immersed in generalized Newtonian fluids

Zilian, Andreas; Netuzhylov, Hennadiy

doi:10.1016/j.compstruc.2010.07.006

Cited by 7 publications

(5 citation statements)

References 37 publications

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“…(1) With respect to the solution method, one differentiates between monolithic approaches (e.g., [5,6,7]) or partitioned approaches (e.g., [8,9,10,11,12]). The monolithic approach includes the full solution process in one single solver: The main advantage gained is the robustness (in the sense of stability and the capability for large time steps); the price to pay is the significant implementation effort.…”

Section: Introductionmentioning

confidence: 99%

Fluid–structure interaction with NURBS-based coupling

Hosters

Helmig

Stavrev

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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Engineering design via CAD software relies on Non-Uniform Rational B-Splines (NURBS) as a means for representing and communicating geometry. Therefore, in general, a NURBS description of a given design can be considered the exact description. The development of isogeometric methods has made the geometry available to analysis methods [1]. Isogeometric analysis has been particularly successful in structural analysis; one reason being the wide-spread use of two-dimensional finite elements in this field. For fluid dynamics, where three-dimensional analysis is usually indispensable, isogeometric methods are more complicated, yet of course not impossible, to apply in a general fashion. This paper describes a method that enables the solution of fluid-structure-interaction with a matching spline description of the interface. On the structural side, the spline is used in an isogeometric setting. On the fluid side, the same spline is used in the framework of a NURBS-enhanced finite element method (extension of [2]). The coupling of the structural and the fluid solution is greatly facilitated by the common spline interface. The use of the identical spline representation for both sides permits a direct transfer of the necessary quantities, all the while still allowing an adjusted, individual refinement level for both sides.

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Section: Introductionmentioning

confidence: 99%

Fluid–structure interaction with NURBS-based coupling

Hosters

Helmig

Stavrev

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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“…Considering the term 1 J in Eq. (10), which is factorised and removed from mass conservation (in Eq. (49) to simplify the mathematical procedure), and neglecting the effects of J (1) in the expanded term 1 J (0) + J (1) , the full form of the transformed hydraulic conductivity takes the form…”

Section: Rve Numerical Testsmentioning

confidence: 99%

“…The ALE computational mesh follows the motion of solid material points and fluid-solid interface (Lagrangian), while it is fixed (Eulerian) inside the fluid domain. We use Description 5. to reduce the computational cost, since it does not require solving a fluid problem at every quadrature point and increment of the homogenised problem mesh-moving and mixed-hybrid velocity-based formulations [8][9][10]) the complexity imposed by the multi-scale nature of porohyperelastic problems does not allow for embracing Lagrangian techniques.…”

Section: Introductionmentioning

confidence: 99%

Finite strain poro-hyperelasticity: an asymptotic multi-scale ALE-FSI approach supported by ANNs

Dehghani

Zilian

2023

Comput Mech

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This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their characteristic multi-scale and multi-physics parameters. In the present work this is achieved by formulating a non-dimensionalised fluid–solid interaction problem (FSI) at the pore level using an arbitrary Lagrange–Euler description (ALE). The resulting coupled systems of PDEs on the reference configuration are expanded and analysed using the asymptotic homogenisation technique. This approach yields three partially novel systems of PDEs: the macroscopic/effective problem and two supplementary microscale problems (fluid and solid). The latter two provide the microscopic response fields whose average value is required in real-time/online form to determine the macroscale response (a concurrent multi-scale approach). In order to overcome the computational challenges related to the above multi-scale closure, this work introduces a surrogate approach for replacing the direct numerical simulation with an artificial neural network. This methodology allows for solving finite strain (multi-scale) porohyperelastic problems accurately using direct automated differentiation through the strain energy. Optimal and reliable training data sets are produced from direct numerical simulations of the fully-resolved problem by including a simple real-time output density check for adaptive sampling step refinement. The data-driven approach is complemented by a sensitivity analysis of the RVE response. The significance of the presented approach for finite strain poro-elasticity/poro-hyperelasticity is shown in the numerical benchmark of a multi-scale confined consolidation problem. Finally, to show the robustness of the method, the system response is dimensionalised using characteristic values of soil and brain mechanics scenarios.

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“…TDG methods have also given rise to other original methods such as the TX-FEM (Time Extended Finite Element Method) [54] also known as the enriched space-time FEM (eg. [58,59]), the Nitsche XFEM-DG method [38], or the combination of the TDG and the PGD (Proper Generalized Decomposition) [8].…”

Section: Introductionmentioning

confidence: 99%