Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates

By J. Reddy. 2010

561 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b4d264a1d5d2bcddc426c792cdae161990ba626c

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Nonlocal nonlinear free vibration of functionally graded nanobeams (2014, methodology): “Table 1 gives a comparison between the present results with those obtained by Reddy [8] for a simply supported nonlocal Euler–Bernoulli nanobeam.”
Nonlocal elasticity in nanobeams: the stress-driven integral model (2017, methodology): “This differential formulation was later adopted to analyse simple beam models with standard boundary constraints of structural mechanics ( Aydogdu, 2009; Peddieson, Buchanan, & McNitt, 2003; Reddy, 2007; 2010; Reddy & El-Borgi, 2014; Reddy, El-Borgi, & Romanoff, 2014; Reddy & Pang, 2008 ).”
A general third-order theory of functionally graded plates with modified couple stress effect and the von Kármán nonlinearity: theory and finite element analysis (2015, methodology): “[16] and Reddy [32] developed classical and first-order shear deformation plate models using the nonlocal differential constitutive relations of Eringen.”
On nonconservativeness of Eringen’s nonlocal elasticity in beam mechanics: correction from a discrete-based approach (2014, background): “In a seminal paper dated from 2007, Reddy [5] mentioned the possible nonself-adjointness of Eringen’s model and the impossibility to build the underlying quadratic functional for such nonlocal beam models (see, also [6]).”
Geometrically nonlinear isogeometric analysis of functionally graded microplates with the modified couple stress theory (2017, background): “The accuracy of the proposed approach is further demonstrated for circular plates in Figure 9 where the proposed solutions are almost coincident with the results published by Reddy et al. [28] for various boundary conditions and material parameters.”
Bending relationships between the modified couple stress-based functionally graded Timoshenko beams and homogeneous Bernoulli–Euler beams (2012, methodology): “[8], Reddy [17, 19], Reddy and Pang [20], and Aghababei and Reddy [1] have used the Eringen’s differential model to bring out the effect of the internal characteristic parameter on the bending, buckling, and vibration characteristics of beams and plates.”