Nonlocal steady-state thermoelastic analysis of functionally graded materials by using peridynamic differential operator

Li, Zhiyuan; Huang, Dan; Xu, Yepeng; Yan, Kanghao

doi:10.1016/j.apm.2020.12.004

Cited by 33 publications

(8 citation statements)

References 48 publications

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“…The PDDO method can be used to solve differential equations and derive smooth functions or scattered data from discontinuities or singular points. Thus, this method has been successfully applied to the study of stress analysis [26], heat and mass transfer [27], and thermodynamic problems [28]. Recently, Baryt et al [29] modified the weight function of the PDDO based on the characteristics of hyperbolic equations and obtained a generalized PDDO scheme to accurately solve these equations.…”

Section: Introductionmentioning

confidence: 99%

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Ruan,

Dong,

Liang

et al. 2024

CMES

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Using Euler's first-order explicit (EE) method and the peridynamic differential operator (PDDO) to discretize the time and internal crystal-size derivatives, respectively, the Euler's first-order explicit method-peridynamic differential operator (EE-PDDO) was obtained for solving the one-dimensional population balance equation in crystallization. Four different conditions during crystallization were studied: size-independent growth, sizedependent growth in a batch process, nucleation and size-independent growth, and nucleation and size-dependent growth in a continuous process. The high accuracy of the EE-PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods. The method is characterized by non-oscillation and high accuracy, especially in the discontinuous and sharp crystal size distribution. The stability of the EE-PDDO method, choice of weight function in the PDDO method, and optimal time step are also discussed.

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Section: Introductionmentioning

confidence: 99%

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Ruan,

Dong,

Liang

et al. 2024

CMES

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“…Capable of solving differential equations and calculating derivatives from smooth functions or scattered data amidst discontinuities or singular points [21], it also features time nonlocality and generalized space-time nonlocality, unrestricted by order of space and time partial derivatives, proving its efficacy in practical applications. For instance, Dorduncu devised a nonlocal stress analysis model for functionally graded sandwich panels using PDDO [22], Gao et al developed a nonlocal model for fluid flow and heat transfer coupling using PDDO [23], and Li et al introduced a nonlocal model for steady-state thermoelastic analysis of functionally graded materials with PDDO [24]. Additionally, Li et al compared the PDDO with the other nonlocal differential operators and proposed some improvements for PDDO [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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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“…Meanwhile, peridynamics includes the description of damage and fracture (Foster et al., 2011; Silling and Askari, 2005), which means that the crack could propagate spontaneously without any additional fracture criteria. Such a model has the natural theoretical advantages on analyzing dynamic crack growth (Gu et al., 2016; Wang et al., 2018; Zhou et al., 2021), impact ( Ren et al., 2017; Wang et al., 2019; Wu et al., 2020; Wu et al., 2021) and blast (Fan et al., 2016; Fan and Li, 2017; Zhu and Zhao, 2021) failure, and other discontinuous problems with non-local effects (He et al., 2021; Li et al., 2021; Ni et al., 2020; Wang et al., 2016, 2017; Zhang and Qiao, 2020).…”

Section: Introductionmentioning

confidence: 99%

Peridynamic modeling for impact failure of wet concrete considering the influence of saturation

Huang

et al. 2022

International Journal of Damage Mechanics

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In this paper, a modified intermediately homogenized peridynamic (IH-PD) model for analyzing impact failure of wet concrete has been presented under the configuration of ordinary state-based peridynamic theory. The meso-structural properties of concrete are linked to the macroscopic mechanical behavior in the IH-PD model, where the heterogeneity of concrete is taken into account, and the calculation cost does not increase. Simultaneously, the porosity of concrete is considered, which is implemented by deleting the bond between two material points, as well as the influence of porosity on the mechanical properties of concrete. Moreover, the effective bulk and shear modulus of cement mortar in wet concrete (saturated and unsaturated concrete) are calculated respectively. The dynamic model for wet concrete is described from three aspects: strength, dynamic increase factor, and equation of state. Validation of the proposed model is established through analyzing some benchmark tests and comparing with the corresponding experiment and other available numerical results.

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Nonlocal steady-state thermoelastic analysis of functionally graded materials by using peridynamic differential operator

Cited by 33 publications

References 48 publications

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

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

Peridynamic modeling for impact failure of wet concrete considering the influence of saturation

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