Polygonal type variable-node elements by means of the smoothed finite element method for analysis of two-dimensional fluid-solid interaction problems in viscous incompressible flows

Kim, Jungdo; Im, Seyoung

doi:10.1016/j.compstruc.2017.01.006

Cited by 19 publications

(4 citation statements)

References 41 publications

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“…On a semi‐implicitly staggered basis, He 26 applied the FEM for the incompressible fluid component and the cell‐based SFEM (CSFEM) 27 for the elastic solid component. Kim and Im 28 applied the CSFEM into fluid and solid equations for computing two‐dimensional FSI. In particular, they approximated the gradient‐related terms at centers, corners and Gauss points in the SCs built on variable‐node polygonal elements.…”

Section: Introductionmentioning

confidence: 99%

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

He,

Lu,

2024

Numerical Methods in Fluids

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This article describes an inexpensive partitioned coupling strategy for computational fluid–structure interaction (FSI) admitting negative‐Jacobian elements. The emphasis is very much on a reduced smoothed integration (RSI) scheme of the cell‐based smoothed finite element method (CSFEM) using four‐node quadrilateral (Q4) elements for a cost‐effective solution to the Navier–Stokes (NS) equations. In the discrete fluid field, each Q4 element is considered as one single smoothing cell so as to diminish the smoothed integration loops substantially. However, the RSI scheme does not respect the stability condition of smoothed Galerkin weak‐form integral in the CSFEM. To tackle this issue, a simple hourglass control is introduced to the under‐integrated formulation of the NS solver. Importantly, the stabilized RSI scheme has an inbuilt advantage of its enormous tolerance towards negative‐Jacobian elements. The developed technique is easy‐to‐implement and has been tested in various FSI examples adopting both fine and distorted meshes.

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Section: Introductionmentioning

confidence: 99%

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

He,

Lu,

2024

Numerical Methods in Fluids

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“…This element formulation has been applied to contact problems using a node-to-node algorithm [55]. Based on the smoothed finite element method (SFEM), a polygonal variable-node element is devised [56]. This method can straightforwardly be used to couple elements of different sizes.…”

Section: Introductionmentioning

confidence: 99%

High order transition elements: The xy-element concept—Part I: Statics

Duczek

Saputra

Gravenkamp

2020

Computer Methods in Applied Mechanics and Engineering

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Advanced transition elements are of utmost importance in many applications of the finite element method (FEM) where a local mesh refinement is required. Considering problems that exhibit singularities in the solution, an adaptive hp-refinement procedure must be applied. Even today, this is a very demanding task especially if only quadrilateral/hexahedral elements are deployed and consequently the hanging nodes problem is encountered. These element types, are, however, favored in computational mechanics due to the improved accuracy compared to triangular/tetrahedral elements. Therefore, we propose a compatible transition element -xNy-element -which provides the capability of coupling different element types. The adjacent elements can exhibit different element sizes, shape function types, and polynomial orders. Thus, it is possible to combine independently refined h-and p-meshes. The approach is based on the transfinite mapping concept and constitutes an extension/generalization of the pNh-element concept. By means of several numerical examples, the convergence behavior is investigated in detail, and the asymptotic rates of convergence are determined numerically. Overall, it is found that the proposed approach provides very promising results for local mesh refinement procedures.

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“…A naturally feasible means is to exclusively smooth the pressure Poisson equation and viscous stress tensor in line with the divergence theorem 34,35 . The gradient terms can also be approximated at some particular locations (e.g., centers, corners, and Gauss points) within the constructed SCs of polygonal element 36,37 . A similar scheme was subsequently operated by Jiang et al 38 to cope with incompressible laminar flow computations.…”

Section: Introductionmentioning

confidence: 99%

Extending the cell‐based smoothed finite element method into strongly coupled fluid–thermal–structure interaction

2020

Numerical Methods in Fluids

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This work generalizes the cell‐based smoothed finite element method (CS‐FEM) into fluid–thermal–structure interaction (FTSI) analysis under the arbitrary Lagrangian–Eulerian description. The thermal buoyancy is included with the incompressible Navier–Stokes equations through the Boussinesq approximation. The combined fluid flow and energy equations are solved by a smoothed characteristics‐based split algorithm that incorporates equal low‐order interpolations for the three primitive variables. The structural motions involving both oscillating rigid and flexible bodies are advanced by the generalized‐α method. Moreover, the nonlinear elastodynamics equations discretized with the CS‐FEM are linearized by the modified Newton–Raphson method. An efficient two‐level mesh updating scheme is subsequently discussed to account for large structural displacement and finite solid deformation. The cell‐based smoothing concept is then adopted to evaluate fluid forces acting on the immersed structure. The smoothed FTSI system is iteratively solved by the block‐Gauss–Seidel procedure. Transient FTSI examples are tested to demonstrate the effectiveness and robustness of the CS‐FEM.

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Polygonal type variable-node elements by means of the smoothed finite element method for analysis of two-dimensional fluid-solid interaction problems in viscous incompressible flows

Cited by 19 publications

References 41 publications

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

High order transition elements: The xy-element concept—Part I: Statics

Extending the cell‐based smoothed finite element method into strongly coupled fluid–thermal–structure interaction

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