Um novo método de elementos finitos hibrido-misto aplicado a problemas de elasticidade

• Autor(a) principal: Santos, Geraldo José Belmonte dos
• Data de Publicação: 2016
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/264
• topic: Método dos elementos finitos; Método misto; Hibridização; Finite element methods; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::ANALISE NUMERICA

A new finite element method is proposed for mixed variational formulation by use of the hybridization technique and of the adding of several stabilization mechanisms to the classical Galerkin methods applied to the elasticity problems. The method is designed by hibridization technique of the classical dual mixed formulation applied to the element level, adding various least-squares residual terms of the locally governing equations and of the interelement continuity conditions of the fields. The residual terms are added without violating the consistency condition of the methods and include mesh-parameter dependent coefficients. The method is designed to enhance stability in a better norm, adding features such as: flexibility in the choice of the approximation spaces, including equal-order interpolation, by adding residual stabilization terms; improvement of the convergence rate of the dual variables, using mixed formulation; very efficient solver with global system assembled with Lagrange multiplier (hybridized variable) only via static condensation; robustness to solver problems with non smooth fields and internal limits, including discontinuous fields (e.g. cracks), typical features of Galerkin discontinuous; possibility of easily handling local enrichment with polynomial (p-adaptivity) and non polynomial functions in different elements; and under certain conditions we have local conservation. The stability of the methods is proved and various numerical experiments are provided to show the features listed above, including convergence rates, stability and accuracy. The method is applied the several problems of plane stress, plane strain and axisymmetric solid, including the cases of compressible elasticity, Girkmann problem and linear elastic fracture.