An unstructured finite volume time domain method for structural dynamics

Zhu, Ming; Ming, Pingjian; Xuan, Liang; Zhang, Wenping

doi:10.1016/j.apm.2011.05.053

Cited by 6 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Care should be taken when interpreting the data, as the number of citations may not be directly proportional to impact on the field; for example, Weller et al [18] has by far the greatest number of citations; however, a significant percentage of its received citations are related to its computational fluid solid mechanics developments, rather than its solid mechanics contributions. Godunov-type - [342][343][344][345][346] [ [347][348][349][350][351][352] [ matrix-free -- [247,249,252,[376][377][378][379][380] [ 260,263,[381][382][383][384][385][386][387][388][389][390][391][392][393][394][395] meshless - [396] [ [397][398][399][400][401][402][403][404]…”

Section: History Of the Finite Volume Methods For Computational Solid...mentioning

confidence: 99%

“…A number of prior developments within CFD provided the foundation for the seminal paper on the cell-centred finite volume method for solid mechanics by Demirdžić et al [2]. In the past three decades, the finite volume method for solid mechanics has developed in a number of directions, differing in terms of discretisation, solution methodology and overall philosophy, including: (a) implicit cell-centred methods, based on the original work of Demirdžić et al [132][133][134][135][136][137][138][139][140][141][142][143][144][145]; (b) staggered-grid methods ; (c) vertex-centred methods ; (d) methods for periodic heterogenous microstructures ; (e) Godunov-type approaches ; (f) matrix-free approaches [247,249,252,260,263,[376][377][378][379][380][381][382][383][384][385][386][387][388][389][390][391][392][393][394][395]; (h) meshless approaches ; as well as several others.…”

Section: Introductionmentioning

confidence: 99%

“…Within the class of vertex-centred methods, there exists a subclass called dual-time-stepping matrix-free methods, where the solution is calculated in an explicit manner and a linear system is not directly formed [247,249,252,260,263]; these dual-time-stepping matrix-free formulations, which have also employed cell-centred frameworks, are considered further in a separate subsequent section below.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Thirty years of the finite volume method for solid mechanics

Cardiff,

Demirdžić

2018

Preprint

View full text Add to dashboard Cite

Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, including "cell-centred", "staggered", "vertex-centred", "periodic heterogenous microstructural", "Godunov-type", "matrix-free", "meshless", as well as others. This article gives an overview, historical perspective, comparison and critical analysis of the different approaches, including their relative strengths, weaknesses, similarities and dissimilarities, where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve widespread acceptance.

show abstract

Section: History Of the Finite Volume Methods For Computational Solid...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Thirty years of the finite volume method for solid mechanics

Cardiff,

Demirdžić

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…In recent years, Pan and Wheel [33,34] extended [24] to account for DOFs for six-node triangles. In 2012, Zhu et al [35] presented an unstructured FV time domain method aiming at simulation of stress wave propagation. The following year, Sabbagh-Yazdi and Amiri-SaadatAbadi [36] discussed application of the FVM to predicting cement hydration heat induced stress-strain fields in…”

Section: Developments Of the Method-historical Viewmentioning

confidence: 99%

“…Noticeably, the resulting EbFVM and FEM-Galerkin stiffness matrices and load vectors depend upon the choice of the CV and corresponding weight function, as discussed in the previous section. 35…”

Section: The Global Discretized Systemmentioning

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

View full text Add to dashboard Cite

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

show abstract

Thirty Years of the Finite Volume Method for Solid Mechanics

Cardiff

Demirdžić

2021

Arch Computat Methods Eng

View full text Add to dashboard Cite

An unstructured finite volume time domain method for structural dynamics

Cited by 6 publications

References 16 publications

Thirty years of the finite volume method for solid mechanics

Thirty years of the finite volume method for solid mechanics

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

Thirty Years of the Finite Volume Method for Solid Mechanics

Contact Info

Product

Resources

About