A multiscale virtual element method for the analysis of heterogeneous media

被引：8

作者：

Sreekumar, Abhilash ^{[1
]}

Triantafyllou, Savvas P. ^{[2
]}

Becot, Francois-Xavier ^{[3
]}

Chevillotte, Fabien ^{[3
]}

机构：

[1] Univ Nottingham, Fac Engn, Ctr Struct Engn & Informat, Nottingham, England

[2] Natl Tech Univ Athens, Sch Civil Engn, Inst Struct Anal & Aseism Res, 9 Heroon Polytechniou,Zografou Campus, GR-15780 Athens, Greece

[3] Matelys Res Lab, 7 Rue Maraichers Bailment B, F-69120 Vaulx En Velin, France

来源：

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2020年 / 121卷 / 08期

基金：

欧盟地平线“2020”;

关键词：

heterogeneous domains; multiscale; virtual elements; POLYGONAL FINITE-ELEMENTS; MIMETIC DISCRETIZATIONS; TOPOLOGY OPTIMIZATION; ELLIPTIC PROBLEMS; HOMOGENIZATION; COMPOSITES; CONVERGENCE; FORMULATION; SIMULATION; PRINCIPLES;

D O I：

10.1002/nme.6287

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We introduce a novel heterogeneous multiscale method for the elastic analysis of two-dimensional domains with a complex microstructure. To this end, the multiscale finite element method is revisited and originally upgraded by introducing virtual element discretizations at the microscale, hence allowing for generalized polygonal and nonconvex elements. The microscale is upscaled through the numerical evaluation of a set of multiscale basis functions. The solution of the equilibrium equations is performed at the coarse scale at a reduced computational cost. We discuss the computation of the multiscale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples.

引用

页码：1791 / 1821

页数：31

共 69 条

[1] Micro-mechanics of off-axis loading of metal matrix composites using finite element analysis [J].

Aghdam, MM ;

Pavier, MJ ;

Smith, DJ .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2001, 38 (22-23) :3905-3925

[2] Equivalent projectors for virtual element methods [J].

Ahmad, B. ;

Alsaedi, A. ;

Brezzi, F. ;

Marini, L. D. ;

Russo, A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (03) :376-391

[3] Multiscale framework for behavior prediction in granular media [J].

Andrade, Jose E. ;

Tu, Xuxin .

MECHANICS OF MATERIALS, 2009, 41 (06) :652-669

[4] Local maximum-entropy approximation schemes:: a seamless bridge between finite elements and meshfree methods [J].

Arroyo, M ;

Ortiz, M .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2006, 65 (13) :2167-2202

[5] High-order virtual element method for the homogenization of long fiber nonlinear composites [J].

Artioli, E. ;

Marfia, S. ;

Sacco, E. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 341 :571-585

[6] The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis [J].

Augarde, Charles E. ;

Deeks, Andrew J. .

FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2008, 44 (9-10) :595-601

[7] Size-effects on yield surfaces for micro reinforced composites [J].

Azizi, Reza ;

Niordson, Christian F. ;

Legarth, Brian Nyvang .

INTERNATIONAL JOURNAL OF PLASTICITY, 2011, 27 (11) :1817-1832

[8]

Babuska I., 1975, LECT NOTES EC MATH S, P137, DOI [10.1007/978-3-642-85972-4_8, DOI 10.1007/978-3-642-85972-4_8]

[9]

BEIRAODAVEIGA L, 2017, COMPUT MATH APPL, V74, P1110

[10] Polygonal finite element methods for contact-impact problems on non-conformal meshes [J].

Biabanaki, S. O. R. ;

Khoei, A. R. ;

Wriggers, P. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 269 :198-221

← 1 2 3 4 5 6 7 →