Doctoral Thesis
DOI
10.11606/T.18.2008.tde-10092008-102729
Document
Author
Full name
Leandro Waidemam
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2008
Supervisor
Committee
Paiva, João Batista de (President)
Coda, Humberto Breves
Laier, José Elias
Lindenberg Neto, Henrique
Palermo Junior, Leandro
Title in Portuguese
Formulação do método dos elementos de contorno para placas enrijecidas considerando-se não-linearidades física e geométrica
Keywords in Portuguese
Enrijecedores
Método dos elementos de contorno
Placas
Abstract in Portuguese
Title in English
Boundary element method formulation for reinforced plates with combined geometrical and material nonlinearities
Keywords in English
Boundary element method
Geometrical nonlinearity
Material nonlinearity
Plates
Reinforcements
Abstract in English
In this work a boundary element method formulation to analyse plates with combined geometrical and material nonlinearities was presented. Additionally an alternative boundary element method formulation was presented to analyse material nonlinear reinforced plates. The boundary integral equations are derived based on Kirchhoff's theory. An initial stress field and von Kármán hypothesis are considered to take into account the material and geometrical nonlinearities, respectively. The elastoplastic von Mises criterion with linear isotropic hardening and particularized to the plane stress condition is considered to evaluate the plastic zone. The effects of the reinforcements are taken into account by using a simplified scheme based on applying an initial stress field to correct locally the bending and stretching stiffness of the reinforcement regions. Only bending and stretching rigidities in the direction of the reinforcements are considered. Isoparametric linear elements are used to approximate the boundary unknown values and triangular internal cells with linear shape functions are used to evaluate the plate domain value influences. The domain integrals due to the presence of the reinforcements are transformed to the reinforcement/plate interface. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator presented along this paper. Finally, several examples are presented to confirm the correct development of the proposed formulations.