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Computational continua for linear elastic heterogeneous solids on unstructured finite element meshes
Author(s) -
Fafalis Dimitrios,
Fish Jacob
Publication year - 2018
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.5814
Subject(s) - homogenization (climate) , polygon mesh , finite element method , quadrature (astronomy) , gaussian quadrature , mathematics , boundary value problem , mathematical analysis , geometry , nyström method , physics , biodiversity , ecology , optics , biology , thermodynamics
Summary The computational continua framework, which is a variant of higher‐order computational homogenization theories that is free of scale separation, does not require higher‐order finite element continuity, and is free of higher‐order boundary conditions, has been generalized to unstructured meshes. The salient features of the proposed generalization are (i) a nonlocal quadrature scheme for distorted elements that accounts for unit cell distortion in the parent element domain and (ii) an approximate variant of the nonlocal quadrature that eliminates the cost of computing positions of the quadrature points in the preprocessing stage. The performance of the computational continua framework on unstructured meshes has been compared to the first‐order homogenization theory and the direct numerical simulation.