Coupled phase field and nonlocal integral elasticity analysis of stress-induced martensitic transformations at the nanoscale: boundary effects, limitations and contradictions
Sign Up to like & getrecommendations! Published in 2021 at "Continuum Mechanics and Thermodynamics"
DOI: 10.1007/s00161-021-01042-y
Abstract: In this paper, the coupled phase field and local/nonlocal integral elasticity theories are used for stress-induced martensitic phase transformations (MPTs) at the nanoscale to investigate the limitations and contradictions of the nonlocal integral elasticity, which… read more here.
Keywords: phase kernel; integral elasticity; nonlocal integral; two phase ... See more keywords
A research into bi-Helmholtz type of nonlocal elasticity and a direct approach to Eringen’s nonlocal integral model in a finite body
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mechanica"
DOI: 10.1007/s00707-018-2180-9
Abstract: There are exhaustive reports revolving around the nonlocal differential beam models of micro- and nano-electromechanical systems (MEMS–NEMS), carbon nanotubes (CNTs), nanomaterials, etc., since the nonlocal continuum theory is considered a viable option for shedding light… read more here.
Keywords: helmholtz type; nonlocal integral; model; eringen nonlocal ... See more keywords
Existence results for $$(n-1,1)$$(n-1,1)-type nonlocal integral boundary value problems for coupled systems of fractional differential equations at resonance
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-016-1075-y
Abstract: In this paper, a coupled system of $$(n-1,1)$$(n-1,1)-type nonlinear fractional differential equations with nonlocal integral boundary conditions is considered. The existence of solutions is obtained by means of the coincidence degree theory due to Mawhin. read more here.
Keywords: nonlocal integral; integral boundary; fractional differential; differential equations ... See more keywords
On General Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions
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DOI: 10.1007/s12591-016-0319-5
Abstract: This paper investigates the existence of solutions for fractional differential inclusions involving Caputo fractional derivative of any order together with nonlocal integral boundary conditions. Our study includes the cases when the multivalued map involved in… read more here.
Keywords: fractional differential; general fractional; differential inclusions; integral boundary ... See more keywords
On Sequential Fractional Integro-Differential Equations with Nonlocal Integral Boundary Conditions
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-016-0421-4
Abstract: We study a boundary value problem of sequential fractional differential equations equipped with nonlocal integral boundary conditions (strip conditions of finite arbitrary size) involving the first-order derivative of the unknown function. As a variant problem,… read more here.
Keywords: boundary conditions; nonlocal integral; integral boundary; differential equations ... See more keywords
One-dimensional stress-driven nonlocal integral model with bi-Helmholtz kernel: Close form solution and consistent size effect
Sign Up to like & getrecommendations! Published in 2021 at "Applied Mathematical Modelling"
DOI: 10.1016/j.apm.2020.07.058
Abstract: Abstract In this paper, stress-driven nonlocal integral model with bi-Helmholtz kernel is applied to investigate the elastostatic tensile and free vibration analysis of microbar. The relation between nonlocal stress and strain is expressed as first… read more here.
Keywords: driven nonlocal; stress driven; nonlocal integral; model ... See more keywords
Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams
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DOI: 10.1016/j.compstruct.2019.111104
Abstract: Abstract An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be… read more here.
Keywords: integral thermoelasticity; functionally graded; nonlocal integral; framework functionally ... See more keywords
Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Mechanical Sciences"
DOI: 10.1016/j.ijmecsci.2017.09.030
Abstract: Abstract The size-dependent longitudinal and torsional dynamic problems for small-scaled rods are modeled by utilizing an integral formula of two-phase nonlocal theory. The energies diffused from surrounding particles in a reference domain can be taken… read more here.
Keywords: size dependent; two phase; phase nonlocal; longitudinal torsional ... See more keywords
Nonlinear flexure of Timoshenko–Ehrenfest nano-beams via nonlocal integral elasticity
Sign Up to like & getrecommendations! Published in 2020 at "European Physical Journal Plus"
DOI: 10.1140/epjp/s13360-020-00661-9
Abstract: Nonlinear flexural behavior of elastic nano-beams under static loads is investigated in the framework of the Eringen’s nonlocal integral elasticity. The integro-differential and boundary conditions of equilibrium for inflected Timoshenko–Ehrenfest elastic beams with von Karman… read more here.
Keywords: nonlinear flexure; timoshenko ehrenfest; integral elasticity; nonlocal integral ... See more keywords
Fractional Langevin Equations with Nonlocal Integral Boundary Conditions
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DOI: 10.3390/math7050402
Abstract: In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems,… read more here.
Keywords: fractional langevin; integral boundary; equations nonlocal; boundary conditions ... See more keywords
Existence and Uniqueness Results for Different Orders Coupled System of Fractional Integro-Differential Equations with Anti-Periodic Nonlocal Integral Boundary Conditions
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DOI: 10.3390/sym15010182
Abstract: This paper presents a new class of boundary value problems of integrodifferential fractional equations of different order equipped with coupled anti-periodic and nonlocal integral boundary conditions. We prove the existence and uniqueness criteria of the… read more here.
Keywords: nonlocal integral; integral boundary; existence uniqueness; boundary conditions ... See more keywords