Tipo
Artigos em Revista
Tipo de Documento
Artigo Completo
Título
Stress formulation and duality approach in periodic homogenization
Participantes na publicação
Cristian Barbarosie (Author)
Dep. Matemática
Anca-Maria Toader (Author)
Dep. Matemática
CMAFcIO
Resumo
This paper describes several different variational formulations of the so-called “cellular problem” which is a system of partial differential equations arising in the theory of homogenization, subject to periodicity boundary conditions. These variational formulations of the cellular problem, all of them equivalent, have as main unknown the displacement, the stress or the strain, respectively. For each of these three cases, an equivalent minimization problem is introduced. The variational formulation in stress proves to have a distinguished role and it gives rise to two dual formulations, one in displacementstress and another one in strain-stress. The corresponding Lagrangians may be used in numerical optimization for developing algorithms based on alternated directions, of Uzawa type.
Data de Submissão/Pedido
2023-11
Data de Publicação
2024-01
Suporte
Discrete and Continuous Dynamical Systems - B
Identificadores da Publicação
ISSN - 1531-3492
Editora
American Institute of Mathematical Sciences (AIMS)
Identificadores do Documento
DOI -
https://doi.org/10.3934/dcdsb.2024004
URL -
http://dx.doi.org/10.3934/dcdsb.2024004
Identificadores de Qualidade
SCIMAGO Q2 (2023) - 0.66 - Applied Mathematics
Keywords
periodic homogenization
cellular problem
formulation in stress
dual formulation
Lagrangian
displacement-stress formulation
strain-stress formulation