Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory
TL;DR: In this paper, the bending, buckling and vibration problems of axially functionally graded (FG) beams are solved by a generalized differential quadrature method, and the influence of power-law variation and size-dependent parameters on the axially FG beam behavior is investigated.
About: This article is published in Composite Structures.The article was published on 2017-04-01. It has received 245 citations till now. The article focuses on the topics: Timoshenko beam theory & Beam (structure).
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TL;DR: In this paper, the size-dependent nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets and subjected to the uniform distributed load together with an axial compressive load was investigated.
213 citations
TL;DR: In this article, a review of the mechanical properties of functionally graded nanoscale and micro-scale structures is presented, where various scale-dependent theories of elasticity for FG nanostructures such as FG nanobeams and nanoplates are explained.
199 citations
TL;DR: In this paper, the nonlocal elasticity and nonlocal strain gradient elasticity have been employed to estimate the mechanical behavior of nanostructures, and the results of size-dependent wave propagation analyses are discussed.
174 citations
TL;DR: In this article, a size-dependent integral elasticity model is developed for a small-scaled rod in tension based on the nonlocal strain gradient theory, which contains a nonlocal parameter and a material length scale parameter to incorporate the scaling effects of nonlocal stress and microstructure-dependent strain gradient.
165 citations
TL;DR: In this paper, the size dependency in nonlinear large-amplitude vibrational response of functionally graded porous micro/nano-plates reinforced with graphene platelets (GPLs) was explored.
151 citations
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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
3,323 citations
TL;DR: In this paper, an equilibrium relation is developed to govern the behavior of the couples, which constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system.
2,725 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 article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.
1,519 citations