Modified nonlocal elasticity theory for functionally graded materials

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

“…Secondly, the closed-form solutions of the first-order shear deformable plate theory from Jung and Han [28] are compared with the present analytical results for the sigmoid law model as listed in Table 3. Finally, in Table 4 for exponential model, the present results are compared with those obtained from analytical solution according to the new modified nonlocal theory based on the first-order shear deformable plate theory and 3D elasticity theory [32]. It can be seen that all the obtained results are in an excellent agreement with other available solutions, thus the proposed formulation has accuracy and reliability for prediction about the free vibration response of FG nanoplates.…”

“…Salehipour et al [31] established the exact analytical solution of free vibration of FG micro/nanoplates by using three-dimensional theory of elasticity accounting small-scale effect. Salehipour et al [32] developed the modified nonlocal elasticity for examination of the natural frequency of FG micro/nanoplates. Ansari et al [33] analyzed the bending and vibration of FG nanoplates with three-dimension plate theory in conjunction with Eringen's nonlocal theory.…”

A unified integro-differential nonlocal model

“…provided the governing equations for bending of nonlocal Euler-Bernoulli and Timoshenko beam theories accounting for moderate rotations through modified von Kármán nonlinearity. Several studies have also applied Eringen nonlocal model to the study of functionally graded beams (Reddy, El-Borgi, & Romanoff, 2014;Rahmani & Pedram, 2014;Salehipour, Shahidi, & Nahvi, 2015). Studies on nonlocal beam theories based on the differential model are far more exhaustive to be reported here.…”

A non-local asymptotic theory for thin elastic plates

“…The general nonlocal theory is presented, for example, in the book by Eringen (2002), see also more recent papers by Arash and Wang (2012), Schwartz et al (2012), Benvenuti and Simone (2013), Abdollahi and Boroomand (2013), Abdollahi and Boroomand (2014), and Salehipour et al (2015). In addition, here we mention publications by Owen and Paroni (2000) and Owen and Paroni (2015) on the so-called 'structured deformations'.…”