Simplified theories governing behavior of beams and plates keeping the fundamental characteristics of the being modeled objects are proposed and discussed. By simplification, we mean decrease of order of partial differential equations (PDEs) with respect to spatial coordinates. Our approach is used for both discrete and continuous models. An advantage of Padé approximation is addressed. First p...

The geometrically rigorous nonlinear analysis of elastic shells is considered in the context finite, but small, strain theory. research focused on introduction full shell metric and examination its influence structural response. exact relation between reference equidistant strains employed complete analytic constitutive energetically conjugated forces derived. Utilizing these strict relations, ...

The effects of flexoelectricity on thermo-electro-mechanical behavior of a functionally graded electro-piezo-flexoelectric nano-plate are investigated in this paper using flexoelectric modified and the Kirchhoff classic theories. Moreover, using the variation method and the principle of minimum potential energy for the first time, the coupled governing nonlinear differential equations of the na...

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...