Buckling analysis of cracked plates using peridynamics

Heo, Jeeyeon; Yang, Zhenghao; Xia, Wenxuan; Oterkus, Selda; Öterkuş, Erkan

doi:10.1016/j.oceaneng.2020.107817

Cited by 16 publications

(5 citation statements)

References 27 publications

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“…It consists in a second order in time partial integro‐differential equation, where the motion of a material body depends on the interactions among its infinitesimal units with other units in their neighborhood directly across finite distance called horizon (see, e.g., Reference 2). The use of integro‐differential equations instead of the spatial differential equations allow the displacement and internal forces to develop singularities (see References 3‐8). Thus, such theory is suitable for modeling the dynamic of discontinuous phenomena, such as cracks and defects (see References 9‐14).…”

Section: Introductionmentioning

confidence: 99%

A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

Lopez

Pellegrino²

2022

Numerical Meth Engineering

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In the framework of elastodynamics, peridynamics is a nonlocal theory able to capture singularities without using partial derivatives. The governing equation is a second order in time partial integro-differential equation. In this article, we focus on a one-dimensional nonlinear model of peridynamics and propose a spectral method based on the Chebyshev polynomials to discretize in space.The main capability of the method is that it avoids the assumption of periodic boundary condition in the solution and can benefit of the use of the fast Fourier transform. We show its convergence and find that the method results to be very efficient in terms of accuracy and execution time with respect to spectral methods based on the Fourier trigonometric polynomials associated to a volume penalization technique.

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Section: Introductionmentioning

confidence: 99%

A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

Lopez

Pellegrino²

2022

Numerical Meth Engineering

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“…al. [28] performed topology optimisation analysis and buckling analysis of cracked structures, respectively. Vazic et.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of the Peridynamic Equation of Motion for a 2-Dimensional Rectangular Membrane

Yang

Öterkuş

et al. 2022

J Peridyn Nonlocal Model

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In order to analyse the deformation response of materials and structures, various continuum mechanics theories have been proposed. Peridynamics is a new non-local continuum mechanics formulation which has governing equations in integro-differential equation form. Analytical solution of these integro-differential equations is limited in the literature. In this study, analytical solution of the peridynamic equation of motion for a 2-dimensional membrane is presented. Analytical solutions are obtained for both static and dynamic conditions. Various numerical cases are considered to validate the derived analytical solution by comparing peridynamic results against classical continuum mechanics results. For both static and dynamic cases, both solutions agree very well with each other. Moreover, the influence of the size of the length scale parameter in peridynamics, horizon, is investigated. According to the numerical results, it is concluded that as the horizon size becomes larger, peridynamic solution captures nonlocal characteristics and peridynamic results deviate from classical continuum mechanics results.

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“…Moreover, PD formulations are also available for simplified structures such as beams [17,18], plates [19][20][21] and shells [22]. PD has also been utilised for the investigation of fatigue damage [23,24], buckling [25], topology optimisation [26], dynamic crack arrest [27], macro crack and micro crack interactions [28]. PD has also been used for the analysis of moisture diffusion [29] and corrosion damage [30,31].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of 1-Dimensional Peridynamic Equation of Motion

Yang

Ma²,

Öterkuş³

et al. 2022

J Peridyn Nonlocal Model

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Peridynamics has been introduced to overcome limitations of classical continuum mechanics. Peridynamic equations of motion are in the form of integro-differential equations and analytical solutions of these equations are limited in the literature. In this study, a new analytical solution methodology for 1-Dimensional peridynamic equation of motion is presented by utilising inverse Fourier Transform. Analytical solutions for both static and dynamic conditions are obtained. Moreover, different boundary conditions including fixedfixed and fixed-free are considered. Several numerical cases are demonstrated to show the capability of the presented methodology and peridynamic results are compared against results obtained from classical continuum mechanics. A very good agreement between these two different approaches is observed which shows the capability of the current approach.

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Buckling analysis of cracked plates using peridynamics

Cited by 16 publications

References 27 publications

A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

Analytical Solution of the Peridynamic Equation of Motion for a 2-Dimensional Rectangular Membrane

Analytical Solution of 1-Dimensional Peridynamic Equation of Motion

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