Part 1. Three-dimensional theory 3 Outline 3 1.1. Notation, definitions, and some basic formulas 3 1.2. Equations of equilibrium 5 1.3. Constitutive equations of elastic materials 8 1.4. The equations of nonlinear and linearized three-dimensional elasticity 11 1.5. A fundamental lemma of J.L. Lions 13 1.6. Existence theory in linearized three-dimensional elasticity 14 1.7. Existence theory in n...

This study is the first report of numerical solution of nonlinear bending analysis for annular and circular plates based on 3D elasticity theory with asymmetric boundary conditions using semi-analytical polynomial method (SAPM). Orthotropic annular and circular plates are subjected to transverse loading and 3D bending analysis in the presence of symmetric and asymmetric boundary conditions is s...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

in this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. this strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. from the best knowledge of author, it is the first time that this theory is used for investigating wave pro...

Due to considerable stored energy in surfaces of nano-scales in comparison with the stored energy in their bulk, considering the surface energy is necessary for the analysis of various behaviors of nano-scales for more precise design and manufacturing. In this article, the longitudinal dynamic behavior of nanobars in the presence of the surface energy parameters is studied. To this end, the lon...