Exact solutions of inflected functionally graded nano-beams in integral elasticity

Barretta, Raffaele; Čanađija, Marko; Feo, Luciano; Luciano, Raimondo; Sciarra, Francesco Marotti de; Penna, Rosa

doi:10.1016/j.compositesb.2017.12.022

Cited by 104 publications

(38 citation statements)

References 46 publications

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“…6. Such behaviour was not noticed in [3] in the isothermal statically indeterimine problems, where monotonic increase in the nanobeam stiffness with the increase in the nonlocal parameter was observed. The principal difference between these two cases is the fact that in the isothermal statically indetermine problems only prescribed displacement in a point (usually equal to zero) is given.…”

Section: Uniformly Heated Doubly Clamped Beammentioning

confidence: 79%

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Barretta

Čanađija

Sciarra

2018

International Journal of Engineering Science

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128

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A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano-and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward a number of difficulties. Following recent contributions within the isothermal setting, the developed model abandons the classical strain-driven methodology in favour of the modern stress-driven elasticity theory by G. Romano and R. Barretta. This effectively circumvents issues associated with strain-driven formulations. The new thermoelastic nonlocal integral model is proven to be equivalent to an adequate set of differential equations, accompanied by higher-order constitutive boundary conditions, when the special Helmholtz averaging kernel is adopted in the convolution.The example section provides several applications, thus enabling insight into performance of the formulation. Exact nonlocal solutions are established,

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Section: Uniformly Heated Doubly Clamped Beammentioning

confidence: 79%

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Barretta

Čanađija

Sciarra

2018

International Journal of Engineering Science

Self Cite

128

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“…Unfortunately, some strain-driven models suffer from the problem of fulfilling equilibrium conditions [6]. On the contrary, integral formulations of the stress-driven type [7] are able to properly address issues relating to the fulfilment of equilbrium conditions and paradoxes debated in the scientific community [8,9]. Moreover, it is pointed out that, at least for a certain class of kernel function, the stress-driven integral formulation can be made equivalent to differential problems [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Barretta

Čanađija

Sciarra

2019

Composite Structures

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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 governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.

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“…The stress-driven nonlocal integral model, conceived for nano-beams in [37] and recently extended to axisymmetric nano-plates in [38], yields instead a mathematically well-posed and effective nonlocal approach in structural applications of nanotechnology. Pure and two-phase stress-driven nonlocal elasticities have been applied in a series of papers to study elastostatic responses [28,29,[39][40][41][42][43], free vibrations [44][45][46][47][48] and stability of nano-beams [49].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

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Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation.The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest.Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS). KeywordsTorsion; nano-beams; nonlocal strain gradient model; strain gradient elasticity; integral elasticity; size effects; analytical modelling; NEMS. d J J dx J J dx J

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Exact solutions of inflected functionally graded nano-beams in integral elasticity

Cited by 104 publications

References 46 publications

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

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