A 3D implicit unstructured-grid finite volume method for structural dynamics

Xia, Guohua; Zhao, Yong; Yeo, Joon Hock; Lv, Xuebin

doi:10.1007/s00466-006-0100-7

Cited by 17 publications

(13 citation statements)

References 21 publications

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“…The governing equation for a continuum undergoing motion is given by Cauchy’s equation in three dimensions60, 61:

ρ \frac{\partial ν_{i}}{\partial t} = \nabla \cdot σ_{i j} + f_{i}

where the subscript i is a free index as before, f i is the external force, and v i is the velocity of the structure. The constitutive relationship between stress and strain is the generalized Hooke’s law.…”

Section: Methodsmentioning

confidence: 99%

“…Thus the information about mesh deformation, velocity and the fluid pressure is exchanged through this interface. The construction of the FSI method is implemented by coupling a computational fluid dynamics (CFD) solver27 with a computational structural dynamics (CSD) solver60, 61. The two component solvers can be substituted with any other similar-functioned CFD and CSD solvers for various FSI phenomena.…”

Section: Methodsmentioning

confidence: 99%

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Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways

et al. 2010

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The airflow characteristics in a computed tomography (CT) based human airway bifurcation model with rigid and compliant walls are investigated numerically. An in-house three-dimensional (3D) fluid-structure interaction method is applied to simulate the flow at different Reynolds numbers and airway wall stiffness. As the Reynolds number increases, the airway wall deformation increases and the secondary flow becomes more prominent. It is found that the peak wall shear stress on the rigid airway wall can be five times stronger than that on the compliant airway wall. When adding tethering forces to the model, we find that these forces, which produce larger airway deformation than without tethering, lead to more skewed velocity profiles in the lower branches and further reduced wall shear stresses via a larger airway lumen. This implies that pathologic changes in the lung such as fibrosis or remodeling of the airway wall -both of which can serve to restrain airway wall motion -have the potential to increase wall shear stress and thus can form a positive feed-back loop for the development of altered flow profiles and airway remodeling. These observations are particularly interesting as we try to understand flow and structural changes seen in, for instance, asthma, emphysema, cystic fibrosis, and interstitial lung disease.

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“…The governing equation for a continuum undergoing motion is given by Cauchy’s equation in three dimensions60, 61:

ρ \frac{\partial ν_{i}}{\partial t} = \nabla \cdot σ_{i j} + f_{i}

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways

et al. 2010

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“…The existing finite volume paradigms discussed in the structural mechanics community can be classified into two families, depending on the localisation of the unknowns in the computational mesh: the cell-centred finite volume (CCFV) method [4,11,22,25] defines the unknowns at the centroid of the mesh elements, whereas the vertex-centred finite volume (VCFV) strategy [40,42,49] sets the unknowns at the mesh nodes. A major limitation of the CCFV method is the poor approximation of the gradient of the displacements at the faces using unstructured meshes [2,7].…”

Section: Introductionmentioning

confidence: 99%

A locking-free face-centred finite volume (FCFV) method for linear elastostatics

Sevilla

Giacomini

Huerta

2019

Computers & Structures

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A face-centred finite volume (FCFV) method is proposed for the linear elasticity equation. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the unknowns on the faces (edges in two dimensions) of the mesh elements. The symmetry of the stress tensor is strongly enforced using the well-known Voigt notation and the displacement and stress fields inside each cell are obtained element-wise by means of explicit formulas. The resulting FCFV method is robust and locking-free in the nearly incompressible limit. Numerical experiments in two and three dimensions show optimal convergence of the displacement and the stress fields without any reconstruction. Moreover, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. Classical benchmark tests including Kirch's plate and Cook's membrane problems in two dimensions as well as three dimensional problems involving shear phenomenons, pressurised thin shells and complex geometries are presented to show the capability and potential of the proposed methodology.

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“…In 2005, large strain hyperelastic problems were addressed by Bijelonja et al [27] using FV. In 2007, Xia et al [28] solved an elastic 3D problem using an implicit FVM scheme and Lv et al [29], based also on an implicit formulation and by adopting unstructured meshes, applied FV to both solid and fluid flow problems. In the same year, Limache and Idelsohn [30] emphasized that the FVM approach is a very interesting route for solving solid mechanics problems, indicating several positive factors.…”

Section: Developments Of the Method-historical Viewmentioning

confidence: 99%

A physical perspective of the element‐based finite volume method and FEM‐Galerkin methods within the framework of the space of finite elements

Filippini

Maliska

Vaz

2014

Numerical Meth Engineering

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The literature shows an increasing number of works focused on investigating the behaviour of methods that uses concepts of control volumes in the solution of structural problems. In recent years, new approaches using unstructured meshes have been proposed, most of which addressing new applications and, to a lesser extent, the underling physical perspective. This paper presents a unified approach to the element-based finite volume method and FEM-Galerkin within the framework of the finite element space. Numerical examples highlight some accuracy issues associated with the element-based finite volume method developed in this work. 25solving fluid mechanics problems (e.g., element stabilization strategies in advection-dominant problems). Contrastingly, the literature shows comparatively less attention to improve FVM technologies to approach solid mechanics problems. This work describes a generalization of an element-based FVM (EbFVM) technique, successfully employed in computational fluid dynamics, to solve solid mechanics problems. The work is focused on elasticity and highlights the physical perspective of the general EbFVM formulation, which is established based on the same space of discretized solutions generally used by the classical FEM-Galerkin. A general discrete equation is also derived, which leads to the FEM-Galerkin and EbFVM methods as limiting cases. The numerical examples illustrate some accuracy aspects associated to the EbFVM method. 26 G. FILIPPINI, C. R. MALISKA AND M. VAZ JR.concrete dams, and Tuković et al. [37] presented an application of the FV method for discretization of multi-materials aiming at handling traction at interfaces.The aforementioned works comprise much of the research in the area. An overall evaluation of the reported results has proved very positive, motivating further investigation on the use of FV techniques in this class of problems. The literature indicates the following general characteristics of the method (see also [30]):Good convergence and stability of the numerical solution. Easy of implementation in existing fluid flow computational algorithms. Facilitates exchanging of information in multiple domains and in multi-physics problems. The strict conservation of physical quantities at the discrete CV level ensures a priori respect to point-level requirements of partial differential equations. EQUILIBRIUM EQUATIONS AND CONSTITUTIVE RELATIONSThe governing equations consist of the linear and angular momentum equations, which for a differential volume, , and corresponding boundary, , are

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A 3D implicit unstructured-grid finite volume method for structural dynamics

Cited by 17 publications

References 21 publications

Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways

Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways

A locking-free face-centred finite volume (FCFV) method for linear elastostatics

A physical perspective of the element‐based finite volume method and FEM‐Galerkin methods within the framework of the space of finite elements

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