A peridynamic model for non-Fourier heat transfer in orthotropic plate with uninsulated cracks

Wen, Zhuoxin; Chao-zhen, Hou; Zhao, Minghua; Wan, Xiaopeng

doi:10.1016/j.apm.2022.11.010

Cited by 13 publications

(4 citation statements)

References 48 publications

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“…The algorithm's approach can also be extended to solve more complex differential equations. Furthermore, given that the PDDO method can handle complex geometries [17,28] and discontinuity problems [31], it is anticipated that our method will find wider practical applications. and the amplification factor is:…”

Section: Two-dimensional Transient Heat Conduction Problem With Both ...mentioning

confidence: 99%

“…Currently, numerical methods for solving transient heat conduction equations are broadly classified into two categories: mesh-based methods, including finite difference method (FDM) [1,2], finite element method (FEM) [3,4], Finite Volume Method [5,6], and Boundary Element Method (BEM) [7]; and meshless methods, such as the generalized finite difference method [8,9], smoothed particle hydrodynamics method (SPH) [10], meshless local Petrov-Galerkin method (MLPG) [11][12][13][14], meshless local radial basis function-based differential quadrature (RBF-DQ) [15], peridynamics (PD) [16,17], and peridynamic differential operator (PDDO) [18,19]. Based on time discretization, these methods can be divided into explicit and implicit schemes.…”

Section: Introductionmentioning

confidence: 99%

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Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Ruan,

Dong,

Zhang

et al. 2024

CMES

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Transient heat conduction problems widely exist in engineering. In previous work on the peridynamic differential operator (PDDO) method for solving such problems, both time and spatial derivatives were discretized using the PDDO method, resulting in increased complexity and programming difficulty. In this work, the forward difference formula, the backward difference formula, and the centered difference formula are used to discretize the time derivative, while the PDDO method is used to discretize the spatial derivative. Three new schemes for solving transient heat conduction equations have been developed, namely, the forward-in-time and PDDO in space (FT-PDDO) scheme, the backward-in-time and PDDO in space (BT-PDDO) scheme, and the central-in-time and PDDO in space (CT-PDDO) scheme. The stability and convergence of these schemes are analyzed using the Fourier method and Taylor's theorem. Results show that the FT-PDDO scheme is conditionally stable, whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable. The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method. The convergence rate in space for these three methods is two. These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems. The accuracy and validity of the schemes are verified by comparison with analytical solutions.

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Section: Two-dimensional Transient Heat Conduction Problem With Both ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Ruan,

Dong,

Zhang

et al. 2024

CMES

View full text Add to dashboard Cite

show abstract

“…Consequently, there has been a notable upsurge in scholarly attention towards the numerical resolution of such problems in recent years. Several numerical techniques, encompassing but not confined to the finite difference method (FDM) [2,3], the finite element method (FEM) [4][5][6], the finite difference method, finite volume method (FVM) [7], the boundary element method (BEM) [8,9], the meshless methods [1,[10][11][12], and the lattice Boltzmann method [13,14], have been put forth to address these concerns.…”

Section: Introductionmentioning

confidence: 99%

A Reduced-Order FEM Based on POD for Solving Non-Fourier Heat Conduction Problems under Laser Heating

Kou,

Zhang,

Zheng

et al. 2024

Coatings

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The study presents a novel approach called FEM-POD, which aims to enhance the computational efficiency of the Finite Element Method (FEM) in solving problems related to non-Fourier heat conduction. The present method employs the Proper Orthogonal Decomposition (POD) technique. Firstly, spatial discretization of the second-order hyperbolic differential equation system is achieved through the Finite Element Method (FEM), followed by the application of the Newmark method to address the resultant ordinary differential equation system over time, with the resultant numerical solutions collected in snapshot form. Next, the Singular Value Decomposition (SVD) is employed to acquire the optimal proper orthogonal decomposition basis, which is subsequently combined with the FEM utilizing the Newmark scheme to construct a reduced-order model for non-Fourier heat conduction problems. To demonstrate the effectiveness of the suggested method, a range of numerical instances, including different laser heat sources and relaxation durations, are executed. The numerical results validate its enhanced computational accuracy and highlight significant time savings over addressing non-Fourier heat conduction problems using the full order FEM with the Newmark approach. Meanwhile, the numerical results show that when the number of elements or nodes is relatively large, the CPU running time of the FEM-POD method is even hundreds of times faster than that of classical FEM with the Newmark scheme.

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“…Materials 2024, 17, 2478 2 of 13 Fu et al [10] focused on non-Fourier heat conduction in a functionally graded cylinder containing a cylindrical crack, revealing that non-Fourier effects have a significant influence on heat flux and temperature fields, especially in materials with graded properties. Wen et al [11] presented a peridynamic model for non-Fourier heat transfer in orthotropic plates with uninsulated cracks. This innovative approach effectively captures complex heat transfer behaviors around cracks, offering valuable insights for predictive maintenance and the design of resilient materials.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Thermal Response of Multiple Interface Cracks between a Half-Plane and a Coating Layer under General Transient Temperature Loading

Nourazar,

Yang,

Chen

2024

Materials

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This paper explores the thermal behavior of multiple interface cracks situated between a half-plane and a thermal coating layer when subjected to transient thermal loading. The temperature distribution is analyzed using the hyperbolic heat conduction theory. In this model, cracks are represented as arrays of thermal dislocations, with densities calculated via Fourier and Laplace transformations. The methodology involves determining the temperature gradient within the uncracked region, and these calculations contribute to formulating a singular integral equation specific to the crack problem. This equation is subsequently utilized to ascertain the dislocation densities at the crack surface, which facilitates the estimation of temperature gradient intensity factors for the interface cracks experiencing transient thermal loading. This paper further explores how the relaxation time, loading parameters, and crack dimensions impact the temperature gradient intensity factors. The results can be used in fracture analysis of structures operating at high temperatures and can also assist in the selection and design of coating materials for specific applications, to minimize the damage caused by temperature loading.

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A peridynamic model for non-Fourier heat transfer in orthotropic plate with uninsulated cracks

Cited by 13 publications

References 48 publications

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

A Reduced-Order FEM Based on POD for Solving Non-Fourier Heat Conduction Problems under Laser Heating

Dynamic Thermal Response of Multiple Interface Cracks between a Half-Plane and a Coating Layer under General Transient Temperature Loading

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