An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues

Jiang, Chen; Zhang, Zhi‐Qian; Liu, G.R.; Han, Xu; Zeng, Wei

doi:10.1016/j.enganabound.2015.04.019

Cited by 49 publications

(21 citation statements)

References 51 publications

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“…At first, a distortion parameter α is also introduced as reference, which will control differences between the new coordinates of distorted mesh and initial coordinates. The new coordinates of distorted mesh are given as below

({, \begin{array}{l} x^{'} = x + h \cdot r_{c} \cdot α, \\ y^{'} = y + h \cdot r_{c} \cdot α, \end{array})

where h is the characteristic length of element and r c is a random number between −1 and 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The S‐FEM was firstly developed using strain smoothing techniques using quadrilateral (Q4) elements, and then many other types of novel ways of constructing smoothing domains was proposed. In general, S‐FEM can be classified, by the type of smoothing domains used, as cell‐based S‐FEM (CS‐FEM), edge‐based S‐FEM (ES‐FEM) for 2D problems, face‐based S‐FEM (FS‐FEM) for 3D problem, 3D–edge‐based S‐FEM (3D‐ES‐FEM), node‐based S‐FEM (NS‐FEM), and alpha S‐FEM . In these S‐FEMs, the ES‐FEM with 3‐node triangular elements and FS‐FEM with 4‐node tetrahedral elements are most preferred in solid mechanics, which is stable and much more accurate and robust than FEM using the same element.…”

Section: Introductionmentioning

confidence: 99%

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A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

Jiang

Zhang

Han

et al. 2017

Numerical Methods in Fluids

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SummaryIn this paper, the cell-based smoothed finite element method (CS-FEM) with the semi-implicit characteristic-based split (CBS) scheme (CBS/CS-FEM) is proposed for computational fluid dynamics. The 3-node triangular (T3) element and 4-node quadrilateral (Q4) element are used for present CBS/CS-FEM for two-dimensional flows. The 8-node hexahedral element (H8) is used for three-dimensional flows.Two types of CS-FEM are implemented in this paper. One is standard CS-FEM with quadrilateral gradient smoothing cells for Q4 element and hexahedron cells for H8 element. Another is called as n-sided CS-FEM (nCS-FEM) whose gradient smoothing cells are triangles for Q4 element and pyramids for H8 element. To verify the proposed methods, benchmarking problems are tested for two-dimensional and three-dimensional flows. The benchmarks show that CBS/CS-FEM and CBS/nCS-FEM are capable to solve incompressible laminar flow and can produce reliable results for both steady and unsteady flows. The proposed CBS/CS-FEM method has merits on better robustness against distorted mesh with only slight more computation time and without losing accuracy, which is important for problems with heavy mesh distortion. The blood flow in carotid bifurcation is also simulated to show capabilities of proposed methods for realistic and complicated flow problems.

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({, \begin{array}{l} x^{'} = x + h \cdot r_{c} \cdot α, \\ y^{'} = y + h \cdot r_{c} \cdot α, \end{array})

where h is the characteristic length of element and r c is a random number between −1 and 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

Jiang

Zhang

Han

et al. 2017

Numerical Methods in Fluids

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“…Now, we need to create the subdomain or smoothing domain (SD)

Ω_{L}^{s}

to apply the gradient smoothing. The construction of the smoothing domain can be based on the element itself, which is called cell‐based SD (CSD), based on element edge, which is called edge‐based SD,(–) based on node which is call node‐based SD (NSD)(–) as Figure or their combinations . In linear elasticity, similar to the reduced integration of the Q4 element, the NS‐FEM for T3 element also shows instability.…”

Section: Cbp Methodsmentioning

confidence: 99%

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

Jiang

Zhang

Han

et al. 2018

Numerical Meth Engineering

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Summary In this paper, a novel characteristic–based penalty (CBP) scheme for the finite‐element method (FEM) is proposed to solve 2‐dimensional incompressible laminar flow. This new CBP scheme employs the characteristic‐Galerkin method to stabilize the convective oscillation. To mitigate the incompressible constraint, the selective reduced integration (SRI) and the recently proposed selective node–based smoothed FEM (SNS‐FEM) are used for the 4‐node quadrilateral element (CBP‐Q4SRI) and the 3‐node triangular element (CBP‐T3SNS), respectively. Meanwhile, the reduced integration (RI) for Q4 element (CBP‐Q4RI) and NS‐FEM for T3 element (CBP‐T3NS) with CBP scheme are also investigated. The quasi‐implicit CBP scheme is applied to allow a large time step for sufficient large penalty parameters. Due to the absences of pressure degree of freedoms, the quasi‐implicit CBP‐FEM has higher efficiency than quasi‐implicit CBS‐FEM. In this paper, the CBP‐Q4SRI has been verified and validated with high accuracy, stability, and fast convergence. Unexpectedly, CBP‐Q4RI is of no instability, high accuracy, and even slightly faster convergence than CBP‐Q4SRI. For unstructured T3 elements, CBP‐T3SNS also shows high accuracy and good convergence but with pressure oscillation using a large penalty parameter; CBP‐T3NS produces oscillated wrong velocity and pressure results. In addition, the applicable ranges of penalty parameter for different proposed methods have been investigated.

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“…For example, the probable overestimation of stiffness in solid structures may lead to locking behavior and inaccurate stress-solving [30]. By adding strain smoothing into FEM [31], Liu et al established a series of cell-based [32][33][34][35][36], node-based [37,38], edge-based [39][40][41], or face-based [42,43] smoothed FEMs (S-FEMs) and their combinations [44][45][46][47]. ese S-FEMs with different properties can be used to get desired solutions for a variety of benchmarks and practical mechanic issues [48][49][50].…”

Section: Introductionmentioning

confidence: 99%

A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

Cai

Wang

2019

Advances in Materials Science and Engineering

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To accurately simulate the continuous property change of functionally graded piezoelectric materials (FGPMs) and overcome the overstiffness of the finite element method (FEM), we present an electromechanical inhomogeneous cell-based smoothed FEM (ISFEM) of FGPMs. Firstly, ISFEM formulations were derived to calculate the transient response of FGPMs, and then, a modified Wilson-θ method was deduced to solve the integration of the FGPM system. The true parameters at the Gaussian integration point in FGPMs were adopted directly to replace the homogenization parameters in an element. ISFEM provides a close-to-exact stiffness of the continuous system, which could automatically and more easily generate for complicated domains and thus significantly decrease numerical errors. The accuracy and trustworthiness of ISFEM were verified as higher than the standard FEM by several numerical examples.

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An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues

Cited by 49 publications

References 51 publications

A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

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