A boundary element method for solving 3D static gradient elastic problems with surface energy |
| |
Authors: | K G Tsepoura S Papargyri-Beskou D Polyzos |
| |
Affiliation: | (1) Department of Mechanical and Aeronautical Engineering, University of Patras, GR-26500 Patras, Greece e-mail: polyzos@mech.upatras.gr, GR;(2) General Department, School of Technology, Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece, GR |
| |
Abstract: | A boundary element methodology is developed for the static analysis of three-dimensional bodies exhibiting a linear elastic
material behavior coupled with microstructural effects. These microstructural effects are taken into account with the aid
of a simple strain gradient elastic theory with surface energy. A variational statement is established to determine all possible
classical and non-classical (due to gradient with surface energy terms) boundary conditions of the general boundary value
problem. The gradient elastic fundamental solution with surface energy is explicitly derived and used to construct the boundary
integral equations of the problem with the aid of the reciprocal theorem valid for the case of gradient elasticity with surface
energy. It turns out that for a well posed boundary value problem, in addition to a boundary integral representation for the
displacement, a second boundary integral representation for its normal derivative is also necessary. All the kernels in the
integral equations are explicitly provided. The numerical implementation and solution procedure are provided. Surface quadratic
quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. Advanced algorithms
are presented for the accurate and efficient numerical computation of the singular integrals involved. Two numerical examples
are presented to illustrate the method and demonstrate its merits.
Received: 9 November 2001 / Accepted: 20 June 2002
The first and third authors gratefully acknowledge the support of the Karatheodory program for basic research offered by
the University of Patras. |
| |
Keywords: | Gradient elasticity Surface energy Materials with microstructure Boundary Element Method Fundamental solutions Non-classical boundary conditions |
本文献已被 SpringerLink 等数据库收录! |
|