In this contribution, the variational problem for Kirchhoff plate based on modified strain gradient theory (MSGT) is derived, and Euler-Lagrange equations governing equation of motion are obtained. The Galerkin-type weak form, upon which finite element method constructed, derived from problem. shape functions satisfy homogeneous partial differential as extensions Adini-Clough-Melosh (ACM) Bogne...

A meshless numerical implementation is reported of the 2-D Fleck-Hutchinson phenomenological strain-gradient theory, which fits within the framework of the Toupin-Mindlin theories and deals with firstorder strain gradients and the associated work-conjugate higher-order stresses. From a mathematical point of view, the two-dimensional Toupin-Mindlin strain gradient theory is a generalization of t...

Nonlinear plate bending within Mindlin's strain gradient elasticity theory (SGT) is investigated by employing somewhat non-standard finite element methods. The main goal to compare the results provided geometrically nonlinear three-dimensional (3D) and Reissner–Mindlin theory, i.e., first-order shear deformation (FSDT), SGT. For 3D Green–Lagrange relations are adopted, while von Kármán strains ...

The multi-mode propagation and diffusion properties are crucial informations when studying complex waveguides. In this paper, firstly, the three-dimensional modeling of micro-sized structures is introduced by using second strain gradient theory. constitutive relation deduced while six quintic Hermite polynomial shape functions employed for displacement field. weak formulations including element...