کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6915743 1447406 2018 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The heterogeneous multiscale finite element method for the homogenization of linear elastic solids and a comparison with the FE2 method
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
The heterogeneous multiscale finite element method for the homogenization of linear elastic solids and a comparison with the FE2 method
چکیده انگلیسی
The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E, B. Engquist, Commun. Math. Sci. 1 (2003) 87-132]. The objective of the present work is an FE-HMM formulation for the homogenization of linear elastic solids in a geometrical linear frame, and doing so, of a vector-valued field problem. A key ingredient of FE-HMM is that macrostiffness is estimated by stiffness sampling on heterogeneous microdomains in terms of a modified quadrature formula, which implies an equivalence of energy densities of the microscale with the macroscale. Beyond this coincidence with the Hill-Mandel condition, which is the cornerstone of the FE2 method, we elaborate a conceptual comparison with the latter method. After developing an algorithmic framework we (i) assess the existing a priori convergence estimates for the micro- and macro-errors in various norms, (ii) verify optimal strategies in uniform micro-macromesh refinements based on the estimates, (iii) analyze superconvergence properties of FE-HMM, and (iv) compare FE-HMM with FE2 by numerical results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 329, 1 February 2018, Pages 332-368
نویسندگان
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