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Computational continua revisited
Author(s) -
Fish Jacob,
Filonova Vasilina,
Fafalis Dimitrios
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4793
Subject(s) - homogenization (climate) , tetrahedron , mathematics , hexahedron , boundary value problem , degrees of freedom (physics and chemistry) , mathematical optimization , finite element method , geometry , mathematical analysis , engineering , physics , structural engineering , biodiversity , ecology , quantum mechanics , biology
Summary In the recent paper, Fish and Kuznetsov introduced the so‐called computational continua (C 2 ) approach, which is a variant of the higher order computational homogenization that does not require higher order continuity, introduces no new degrees of freedom, and is free of higher order boundary conditions. In a follow‐up paper on reduced order computational continua, the C 2 formulation has been enhanced with a model reduction scheme based on construction of residual‐free fields to yield a computationally efficient framework coined as RC 2 . The original C 2 formulations were limited to rectangular and box elements. The primary objectives of the present manuscript is to revisit the original formulation in three respects: (i) consistent formulation of boundary conditions for unit cells subjected to higher order coarse scale fields, (ii) effective solution of the unit cell problem for lower order approximation of eigenstrains, and (iii) development of nonlocal quadrature schemes for general two‐dimensional (quad and triangle) and three‐dimensional (hexahedral and tetrahedral) elements. Copyright © 2014 John Wiley & Sons, Ltd.