Peridynamics for bending of beams and plates with transverse shear deformation

Diyaroglu, Cagan; Öterkuş, Erkan; Oterkus, Selda; Madenci, Erdogan

doi:10.1016/j.ijsolstr.2015.04.040

Cited by 120 publications

(88 citation statements)

References 13 publications

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“…, ∞), and is associated with an incremental volume, V (k) , and a mass density of ρ(x (k) ). In this section, peridynamic Timoshenko beam and Mindlin plate formulations will be briefly presented based on the study by Diyaroglu et al [11].…”

Section: Peridynamic Timoshenko Beam and Mindlin Plate Formulationmentioning

confidence: 99%

“…(1, 2) for a Timoshenko beam and utilizing the definitions given in Eqs. (8)(9)(10)(11), the peridynamic equations of motion for a Mindlin plate can be written as…”

Section: Peridynamic Mindlin Plate Formulationmentioning

confidence: 99%

“…al. [11]. In order to include failure in the material response, the response functions in the equations of motion for the beam and plate can be modified through a history-dependent scalar value function,…”

Section: Peridynamic Mindlin Plate Formulationmentioning

confidence: 99%

“…Moreover, O'Grady and Foster [25,26] developed a non-ordinary statebased peridynamic model for Euler-Bernoulli beam and Kirchhoff-Love plate formulations by disregarding the transverse shear deformations. For thick beams and plates, Diyaroglu et al [11] introduced peridynamic Timoshenko beam and Mindlin plate formulations considering transverse shear deformations, which will also be the foundation of the current study.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Implementation of peridynamic beam and plate formulations in finite element framework

Yang

Öterkuş

Nguyen

et al. 2018

Continuum Mech. Thermodyn.

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Peridynamic (PD) theory is a new continuum mechanics formulation introduced to overcome the limitations of classical continuum mechanics such as predicting crack initiation and propagation, and capturing nonlocal effects. PD theory is based on integro-differential equations and these equations are generally difficult to be solved by using analytical techniques. Therefore, numerical approximations, especially with meshless method, have been widely used. Numerical solution of three-dimensional models is usually computationally expensive and structural idealization can be utilized to reduce the computational time significantly. In this study, two of such structural idealization types are considered, namely Timoshenko beam and Mindlin plate, and their peridynamic formulations are briefly explained. Moreover, the implementation of these formulations in finite element framework is presented. To demonstrate the capability of the present approach, several case studies are considered including beam and plate bending due to transverse loading, buckling analysis and propagation of an initial crack in a plate under bending loading.

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Section: Peridynamic Timoshenko Beam and Mindlin Plate Formulationmentioning

confidence: 99%

“…(1, 2) for a Timoshenko beam and utilizing the definitions given in Eqs. (8)(9)(10)(11), the peridynamic equations of motion for a Mindlin plate can be written as…”

Section: Peridynamic Mindlin Plate Formulationmentioning

confidence: 99%

Section: Peridynamic Mindlin Plate Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Implementation of peridynamic beam and plate formulations in finite element framework

Yang

Öterkuş

Nguyen

et al. 2018

Continuum Mech. Thermodyn.

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show abstract

“…As explained in Oterkus et al (2015) and Madenci and Oterkus (2016), the displacement boundary conditions in PD theory can be imposed through a nonzero volume of fictitious boundary layer, c R , as shown in Figure 4. The size of this layer is equivalent to the horizon.…”

Section: Boundary Conditionsmentioning

confidence: 99%

An Euler–Bernoulli beam formulation in an ordinary state-based peridynamic framework

Diyaroglu

Öterkuş

Oterkus

2017

Mathematics and Mechanics of Solids

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Every object in the world has a 3-Dimensional geometrical shape and it is usually possible to model structures in a 3-Dimensional fashion although this approach can be computationally expensive. In order to reduce computational time, the 3-Dimensional geometry can be simplified as a beam, plate or shell type of structure depending on the geometry and loading.This simplification should also be accurately reflected in the formulation which is used for the analysis. In this study, such an approach is presented by developing an Euler-Bernoulli beam formulation within ordinary-state based peridynamic framework. The equation of motion is obtained by utilizing Euler-Lagrange equations. The accuracy of the formulation is validated by considering various benchmark problems subjected to different loading and displacement/rotation boundary conditions.

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A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

Turco

Dell’Isola²,

Misra

2019

Num Anal Meth Geomechanics

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Summary We formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model.

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Peridynamics for bending of beams and plates with transverse shear deformation

Cited by 120 publications

References 13 publications

Implementation of peridynamic beam and plate formulations in finite element framework

Implementation of peridynamic beam and plate formulations in finite element framework

An Euler–Bernoulli beam formulation in an ordinary state-based peridynamic framework

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

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