Steady and transient heat transfer analysis using a stable node-based smoothed finite element method

Cui, Xiangyang; Li, Z.C.; Feng, Hui; Feng, Shizhe

doi:10.1016/j.ijthermalsci.2016.06.027

Cited by 69 publications

(12 citation statements)

References 31 publications

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“…The results from these finite element experiments are promising, demonstrating that a high level of precision can be achieved in real-time simulations using the proposed methodology. Some newly developed numerical methods such as the node-based smoothed FEM [24,38], smoothed point interpolation method [39], gradient weighted FEM [23], and "Tri-Prism" FEM [21] are focused more on the numerical accuracy, convergence and stability rather than the real-time computational performance, the proposed FED-FEM algorithm may be incorporated into these methods for improved computational performance.…”

Section: Discussionmentioning

confidence: 99%

Fast explicit dynamics finite element algorithm for transient heat transfer

Zhang

Chauhan

2019

International Journal of Thermal Sciences

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This paper presents a novel methodology for fast simulation and analysis of transient heat transfer problems. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of computationally efficient explicit dynamics, (ii) proposing an element-level thermal load computation to eliminate the need for assembling global thermal stiffness matrix, leading to (iii) an explicit formulation of nodal temperature computation to eliminate the need for iterations anywhere in the algorithm, (iv) pre-computing the constant matrices and simulation parameters to facilitate online calculation, and (v) utilising computationally efficient finite elements to efficiently obtain thermal responses in the spatial domain, all of which lead to a significant reduction in computation time for fast run-time simulation. The proposed fast explicit dynamics finite element algorithm (FED-FEM) employs nonlinear thermal material properties, such as temperature-dependent thermal conductivity and specific heat capacity, and nonlinear thermal boundary conditions, such as heat convection and radiation, to account for the nonlinear characteristics of transient heat transfer problems. Simulations and comparison analyses demonstrate that not only can the proposed methodology handle isotropic, orthotropic, anisotropic and temperature-dependent thermal properties but also satisfy the standard patch tests and achieve good agreement with those of the commercial finite element analysis packages for numerical accuracy, for three-dimensional (3-D) heat conduction, convection, radiation, and thermal gradient concentration problems. Furthermore, the proposed FED-FEM algorithm is computationally efficient and only consumes a small computation time, capable of achieving real-time computational performance, leading to a novel methodology suitable for real-time simulation and analysis of transient heat transfer problems.

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Section: Discussionmentioning

confidence: 99%

Fast explicit dynamics finite element algorithm for transient heat transfer

Zhang

Chauhan

2019

International Journal of Thermal Sciences

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“…(11) into Eq. (20), the smoothed strain on the smoothing domain Ω ( ) can be written based on nodal displacements:…”

Section: Smoothed Finite Element Methodsmentioning

confidence: 99%

“…Problems such as vibration and dynamic analysis [12,13], elastic-plastic analysis [14,15], fracture mechanics [16,17,18], heat transfer [19,20], structural acoustics [21,22,23], contact problems [24], adaptive analysis [25,26], impact problem [27] and many more. These researches show that compared with the FEM, SFEMs have many advantages in treating different problems, specifically when there are large deformations and nonlinear material behavior.…”

Section: Introductionmentioning

confidence: 99%

Application of smoothed finite element method in coupled hydro-mechanical analyses

Karimian

Oliaei

2017

Scientia Iranica

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Smoothed finite element method (SFEM) was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. In this method, integration is performed on "smoothing domains" rather than elements. Smoothing domains are created based on cells, nodes or edges for two dimensional problems. Based on the smoothing domain creation method, different types of SFEM are developed that have different properties. It has been shown that these methods are insensitive to mesh distortion and are generally more computationally efficient than mesh-free and finite element methods for the same accuracy level. Because of their interesting features, they have been used to solve different problems. This paper investigates the performance of these methods in coupled hydro-mechanical (consolidation) analysis, by solution of some problems using a developed SFEM/FEM code. Biot's consolidation theory is reviewed, and after introduction of the idea and formulation of SFEMs, discretized form of equations is given. Requirements for creation of stable coupled hydro-mechanical models are discussed and based on them, two methods for creation of stable SFEM models are introduced. To investigate the effectiveness of the methods, a number of examples are solved and results are compared with the finite element and analytical ones.

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“…However, despite the spatial stability of NS‐FEM, it was pointed out that NS‐FEM has the disadvantage of spurious zero‐energy eigen modes and temporal instabilities, 27,54‐56 which could affect the result of time‐dependent mechanical problems, such as dynamics problems and geometric nonlinear problems 57 . In order to improve the temporal instabilities of NS‐FEM, many techniques have been developed, such as α S‐FEM, 58‐60 FbarES‐FEM, 61 SNS‐FEM, 62 and Selective S‐FEM 63‐66 . In this paper, we introduce the Selective S‐FEM in which shear deformation is handled by FS‐FEM or ES‐FEM, and volume deformation by NS‐FEM 65 .…”

Section: Introductionmentioning

confidence: 99%

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Jiang

et al. 2020

Numerical Meth Engineering

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Brain tissues are known for exhibiting complex nonlinear and time-dependent properties, which require visco-hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S-FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S-FEM deals with three-dimensional problems using four-node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco-hyperelastic constitutive model is developed within the framework of S-FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S-FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S-FEM with the visco-hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge-based S-FEM, and the volume deformation is calculated by NS-FEM. Numerical experiments show that Selective S-FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time-dependence behavior of bio-tissues.

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Steady and transient heat transfer analysis using a stable node-based smoothed finite element method

Cited by 69 publications

References 31 publications

Fast explicit dynamics finite element algorithm for transient heat transfer

Fast explicit dynamics finite element algorithm for transient heat transfer

Application of smoothed finite element method in coupled hydro-mechanical analyses

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

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