A simple solution method to 3D integral nonlocal elasticity: Isotropic-BEM coupled with strong form local radial point interpolation

Schwartz, M.; Niane, Ngadia Taha; Njiwa, Richard Kouitat

doi:10.1016/j.enganabound.2011.10.004

Cited by 16 publications

(7 citation statements)

References 26 publications

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“…Among other recent publications on the subject, we mention papers by Di Paola & Zingales [14], Di Paola et al [15], Zingales [16], Schwartz et al [17], Benvenuti & Simone [18], Abdollahi & Boroomand [19,20], dealing with various analytical and numerical aspects of non-local elasticity. Here, we also cite publications developing novel micromechanical approaches known as 'structured deformations' (e.g.…”

Section: Introductionmentioning

confidence: 99%

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

Chebakov¹,

Kaplunov²,

Rogerson³

2016

Proc. R. Soc. A.

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The dynamic response of a homogeneous halfspace, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the 'local' problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of nonlocal elastic phenomena on the Rayleigh wave speed is investigated.

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Section: Introductionmentioning

confidence: 99%

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

Chebakov¹,

Kaplunov²,

Rogerson³

2016

Proc. R. Soc. A.

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“…where 𝑅 = 9𝑙, |𝑥 ′ − 𝑥| ≥ 𝑅 (see Polizzotto et al [38]). According to Polizzotto et al [38] a stress-strain relation can be expressed as 𝜎 ̿ 𝑖𝑗 (𝑥) = 𝐶 𝑖𝑗𝑘𝑙 𝑅 𝑘𝑙 (𝜀) (40) where…”

Section: Nonlinear Nonlocal Elasticity Solution (Nnes)mentioning

confidence: 99%

“…( 43). In addition, Schwartz et al [40] presented the strong form local radial point interpolation method for solving Eq. ( 43).…”

Section: Nonlinear Nonlocal Elasticity Solution (Nnes)mentioning

confidence: 99%

Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials

Fahmy,

Toujani

2024

Preprint

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Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.

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“…(see [1][2][3][4][5] and references therein). The general non-local theory is presented, for example, in the book by Eringen [6], see also more recent papers [7][8][9][10][11][12]. In addition, here we mention publications by Owen & Paroni [13,14] on the so-called 'structured deformations'.…”

Section: Introductionmentioning

confidence: 99%

“…The general nonlocal theory is presented, for example, in the book by Eringen (2002), see also more recent papers by Arash and Wang (2012), Schwartz et al (2012), Benvenuti and Simone (2013), Abdollahi and Boroomand (2013), Abdollahi and Boroomand (2014), and Salehipour et al (2015). In addition, here we mention publications by Owen and Paroni (2000) and Owen and Paroni (2015) on the so-called 'structured deformations'.…”

Section: Introductionmentioning

confidence: 99%

A non-local asymptotic theory for thin elastic plates

2017

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The 3D dynamic nonlocal elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size. The integral constitutive relations, incorporating the variation of an exponential nonlocal kernel across the thickness, are adopted. Long-wave low-frequency approximations are derived for both bending and extensional motions. Boundary layers specific for nonlocal behaviour are revealed near the plate faces. It is established that the effect of the boundary layers leads to first-order corrections to the bending and extensional stiffness in the classical 2D plate equations.

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A simple solution method to 3D integral nonlocal elasticity: Isotropic-BEM coupled with strong form local radial point interpolation

Cited by 16 publications

References 26 publications

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials

A non-local asymptotic theory for thin elastic plates

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