A mixed finite volume formulation for the solution of gradient elasticity problems

Abstract

The present works aims at solving the equations of dipolar gradient elasticity via the finite volume method. Initially, a general, mixed, finite volume formulation is stated. As a first approach, the equations of 1D and 2D gradient elasticity are solved via the proposed method. Numerical implementation shows that the suggested model is in excellent agreement with analytic solutions. The approach seems to be promising for extension to 3D problems also.

Interior penalty discontinuous Galerkin and continuous interior penalty finite element methods for boundary value problems of strain gradient elasticity as well as of plate theory

“…In keeping with these developments, Markolefas et al, additionally presented mixed weak formulations for general multi-dimensional DGE boundary value problems [153]. Three years later in 2010, Tsamasphyros and Vrettos [196] developed a mixed finite volume formulation for the solution of 1D as well as 2D equations in strain gradient elasticity while Filopoulos et al, proposed a dynamic finite element analysis for a gradient elastic bar by including the micro-inertia [100].…”

Χρήση Γενικευμένων Μη Τοπικών Θεωριών Για Την Επίλυση Προβλημάτων Ελαστικότητας

“…Στον τομέα αυτό, σημαντική είναι η παρουσία των (Tsamasphyros, Markolefas et al 2007;Tsamasphyros and Vrettos 2010), (Markolefas, Tsouvalas et al 2007;Markolefas, Tsouvalas et al 2008;Markolefas, Tsouvalas et al 2009), (Amanatidou and Aravas 2002), (Tsepoura, Papargyri-Beskou et al 2003;Tsepoura and Pavlou 2006;Pegios, Papargyri-Beskou et al 2015).…”