On nonlocal integral models for elastic nano-beams
TL;DR: In this paper, the applicability of the recently proposed stress-driven non-local elastic model is discussed and illustrated by description of a general solution procedure for nonlocal elastic beams.
About: This article is published in International Journal of Mechanical Sciences.The article was published on 2017-10-01. It has received 141 citations till now. The article focuses on the topics: Statically indeterminate.
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1,191 citations
TL;DR: In this article, the authors prove the equivalence between the nonlocal strain gradient integral model of elasticity and the differential problem with boundary conditions and provide a viable approach to study size-dependent phenomena in nano-beams of applicative interest.
136 citations
01 Jan 2016
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130 citations
TL;DR: In this article, a consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano-and microbeams is proposed, which is 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.
125 citations
Cites background from "On nonlocal integral models for ela..."
...Properties and merits of the stress-driven strategy in comparison with strain-driven formulations can be found in [26, 27]....
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TL;DR: In this paper, the size-dependent axial and flexural free vibrations of Bernoulli-Euler nano-beams are investigated by the modified nonlocal strain gradient elasticity model presented in (Barretta & Marotti de Sciarra, 2018).
121 citations
References
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TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.
Abstract: Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.
3,929 citations
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01 Jan 1988TL;DR: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 1.0 as mentioned in this paper, including 16 pages of full-color graphics.
Abstract: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 2.0. This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users of Mathematica will need this edition. Includes 16 pages of full-color graphics.
2,894 citations
Book•
01 Apr 1991TL;DR: This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users ofMathematica will need this edition.
Abstract: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 2.0. This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users of Mathematica will need this edition. Includes 16 pages of full-color graphics.
2,567 citations
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01 Jan 2002TL;DR: Memory-dependent nonlocal nonlocal Electromagnetic Elastic Solids as mentioned in this paper have been shown to be memory-dependent on nonlocal elasticity and nonlocal linear elasticity, as well as nonlocal Linear Elasticity and Nonlocal Fluid Dynamics.
Abstract: 1. Motion and Deformation.- 2. Stress.- 3. Constitutive Axioms.- 4. Nonlocal Electromagnetic Theory.- 5. Constitutive Equations of Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- 6. Nonlocal Linear Elasticity.- 7. Nonlocal Fluid Dynamics.- 8. Nonlocal Linear Electromagnetic Theory.- 9. Memory-Dependent Nonlocal Thermoelastic Solids.- 10. Memory-Dependent Nonlocal Fluids.- 11. Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- 12. Memory-Dependent Nonlocal Electromagnetic Thermofluids.- 13. Nonlocal Microcontinua.- 14. Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids.- 15. Nonlocal Continuum Theory of Liquid Crystals.
1,967 citations
TL;DR: In this paper, the authors proposed a nonlocal damage theory, which is based on the nonlocal treatment of damage from the local treatment of elastic behavior, and the only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of a material.
Abstract: In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh ...
1,672 citations