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Mathematics and Mechanics of Solids, 2021
Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. However, due to the different nonlocal averaging processes, they are expected to yield different results in their nonlocal forms. In the present work, the free vibration behavior of nonlocal nanobeams is studied using the nonlocal integral Timoshenko beam ...
Hooman Danesh, Mahdi Javanbakht
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Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. However, due to the different nonlocal averaging processes, they are expected to yield different results in their nonlocal forms. In the present work, the free vibration behavior of nonlocal nanobeams is studied using the nonlocal integral Timoshenko beam ...
Hooman Danesh, Mahdi Javanbakht
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Eringen’s Nonlocal Integral Elasticity and Applications for Structural Models
2021The requirement of studying the unsolved problems of continuum mechanics in the context of micro- and nano-dimensions imperatively arose during the second half of the 20th century. For instance, the concentration of stresses at the tip of a crack and the wave dispersion at atomic dimensions were some of the problems that concerned the scientific ...
Constantinos Chr. Koutsoumaris +1 more
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Benchmarks in nonlocal elasticity defined by Eringen’s integral model
International Journal of Solids and Structures, 2013 AbstractIn this paper we present low-residual approximate solutions for nonlocal 1D and 2D elasticity problems defined according to Eringen’s integral model. The benchmarks in the 1D cases are defined by prescribing the stress field while the unknown fields are the strains or the displacements.
Abdollahi, R., Boroomand, B.
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On nonlocal integral models for elastic nano-beams
International Journal of Mechanical Sciences, 2017Abstract Nonlocal integral constitutive laws, for application to nano-beams, are investigated in a general setting. Both purely nonlocal and mixture models involving convolutions with averaging kernels are taken into account. Evidence of boundary effects is enlightened by theoretical analysis and numerical computations.
Romano, Giovanni +2 more
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Acta Mechanica, 2020
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Eptaimeros, K. G. +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eptaimeros, K. G. +2 more
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Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity
International Journal of Mechanical Sciences, 2017Abstract 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 into account in the rod model by using the two-phase nonlocal theory, which depends on the internal
Li Li
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Nonlocal integral elasticity analysis of beam bending by using finite element method
Structural Engineering and Mechanics, 2015In this study, a 2-D finite element formulation in the frame of nonlocal integral elasticity is presented. Subsequently, the bending problem of a nanobeam under different types of loadings and boundary conditions is solved based on classical beam theory and also 3-D elasticity theory using nonlocal finite elements (NL-FEM).
H R Ovesy, S A M Ghannadpour
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Beam Buckling Analysis by Nonlocal Integral Elasticity Finite Element Method
International Journal of Structural Stability and Dynamics, 2016In this study, a finite element method (FEM) based on the size dependent nonlocal integral elasticity theory is implemented for buckling analysis of nanoscaled beams with various boundary conditions. The method is based on the principle of total potential energy.
Taghizadeh, M. +2 more
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Contribution of nonlocal integral elasticity to modified strain gradient theory
The European Physical Journal Plus, 2021The nonlocal integral elasticity and the modified strain gradient theory are consistently integrated in the framework of the nonlocal modified gradient theory of elasticity. The equivalent differential formulation of the constitutive law, equipped with appropriate nonstandard boundary conditions, is introduced.
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ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2021
AbstractThe Eringen's fully nonlocal elasticity model is known to lead to ill‐posed boundary‐value problems and to suffer some boundary effects arising from particle interactions impeded by the body's boundary surface. An enhanced model is derived from the original fully nonlocal one by the addition of a regularizing non‐homogeneous local phase which ...
Aurora Angela Pisano
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AbstractThe Eringen's fully nonlocal elasticity model is known to lead to ill‐posed boundary‐value problems and to suffer some boundary effects arising from particle interactions impeded by the body's boundary surface. An enhanced model is derived from the original fully nonlocal one by the addition of a regularizing non‐homogeneous local phase which ...
Aurora Angela Pisano
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