A Trigonometric Shear Deformation Theory (TSDT) for the analysis of isotropic plate, taking into account transverse shear deformation effect as well as transverse normal strain effect, is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, trigonometric shear deformation theory, the in-plane displacement field uses sinusoidal function in ...

In this article, the Second Strain Gradient (SSG) theory proposed by Mindlin is used within a Wave Finite Element Method (WFEM) framework for dynamic analysis of one-dimensional Euler–Bernoulli bending beam and torsional bar. Firstly, strong forms continuum models including governing equations boundary conditions torsion cases, respectively, are derived using Hamilton’s principle. New “non-loca...

Abstract In this paper, the reduced strain gradient elasticity model with two characteristic lengths is proposed and presented. The a particular case of Mindlin’s first theory number material parameters generalization simplified to include different length scale parameters. have physical meaning longitudinal transverse scales. used study screw edge dislocations derive analytical solutions dislo...

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical so...

Launched before the atomic hypothesis took hold, elasticity theory is a spectacular achievement. A continuum-level description, it provides a powerful toolkit for determining how architecturally simple solids such as crystals respond macroscopically to stress, whilst encoding microscopic, atomic-realm details parsimoniously, via a few parameters. Solids that are architecturally complex at the a...