Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Computational Mechanics
Published in: Computational Mechanics 3/2020

07-11-2019 | Original Paper

Homogenization assumptions for coupled multiscale analysis of structural elements: beam kinematics

Authors: Simon Klarmann, Friedrich Gruttmann, Sven Klinkel

Published in: Computational Mechanics | Issue 3/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This contribution proposes a multiscale scheme for structural elements considering beam kinematics. The scheme is based on a first-order homogenization approach fulfilling the Hill–Mandel condition. Within this paper, special focus is given to the transverse shear stiffness. Using basic boundary conditions, the transverse shear stiffness drastically depends on the size of the representative volume element (RVE). The reason for this size dependency is identified. As a consequence, additional internal constraints are proposed. With these new constraints, the homogenization scheme leads to cross-sectional values independent of the size of the RVE. As they are based on the beam assumptions, a homogeneous material distribution in the length direction yields optimal results. Furthermore, outcomes of the scheme are verified with simple linear elastic benchmark tests as well as nonlinear computations involving plasticity and cross-sectional deformations.
previous article The dynamic analysis of stochastic thin-walled structures under thermal–structural–acoustic coupling
next article Solving primal plasticity increment problems in the time of a single predictor–corrector iteration

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Buannic N, Cartraud P (2001) Higher-order effective modeling of periodic heterogeneous beams. II. Derivation of the proper boundary conditions for the interior asymptotic solution. Int J Solids Struct 38(40–41):7163–7180MathSciNetCrossRef
2.
Carrera E, Giunta G, Nali P, Petrolo M (2010) Refined beam elements with arbitrary cross-section geometries. Comput Struct 88(5–6):283–293CrossRef
3.
Cartraud P, Messager T (2006) Computational homogenization of periodic beam-like structures. Int J Solids Struct 43(3):686–696MathSciNetCrossRef
4.
Coenen EWC, Kouznetsova VG, Geers MGD (2010) Computational homogenization for heterogeneous thin sheets. Int J Numer Methods Eng 83(8–9):1180–1205CrossRef
5.
Feyel F (1998) Application du calcul parallèle aux modéles á grand nombre de variables internes, PhD Thesis. ONERA
6.
Feyel F, Chaboche JL (2000) FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Comput Methods Appl Mech Eng 183(3–4):309–330CrossRef
7.
Geers MGD, Coenen EWC, Kouznetsova VG (2007) Multi-scale computational homogenization of structured thin sheets. Model Simul Mater Sci Eng 15(4):S393–S404CrossRef
8.
Gruttmann F, Wagner W (2001) Shear correction factors in Timoshenko’s beam theory for arbitrary shaped cross-sections. Comput Mech 27(3):199–207CrossRef
9.
Gruttmann F, Wagner W (2013) A coupled two-scale shell model with applications to layered structures. Int J Numer Methods Eng 94(13):1233–1254MathSciNetCrossRef
10.
11.
Gruttmann F, Sauer R, Wagner W (1998) A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections. Comput Methods Appl Mech Eng 160(3–4):383–400CrossRef
12.
Gruttmann F, Wagner W, Sauer R (1998) Zur Berechnung von Wölbfunktion und Torsionskennwerten beliebiger Stabquerschnitte mit der Methode der finiten Elemente. Bauingenieur 73:138–143
13.
Gruttmann F, Knust G, Wagner W (2017) Theory and numerics of layered shells with variationally embedded interlaminar stresses. Comput Methods Appl Mech Eng 326:713–738MathSciNetCrossRef
14.
Heller D, Gruttmann F (2016) Nonlinear two-scale shell modeling of sandwiches with a comb-like core. Compos Struct 144:147–155CrossRef
15.
Hill R (1952) The elastic behaviour of a crystalline aggregate. Proc Phys Soc London Sect A 65(5):349–354CrossRef
16.
Hodges DH (2006) Nonlinear composite beam theory, vol 213. Progress in astronautics and aeronautics. American Institute of Aeronautics and Astronautics, RestonCrossRef
17.
Klinkel S, Govindjee S (2002) Using finite strain 3D-material models in beam and shell elements. Eng Comput 19(3):254–271CrossRef
18.
Kollbrunner CF, Meister M (1961) Knicken, Biegedrillknicken, Kippen. Springer, BerlinCrossRef
19.
Markovič D, Ibrahimbegović A (2004) On micro-macro interface conditions for micro scale based fem for inelastic behavior of heterogeneous materials. Comput Methods Appl Mech Eng 193(48–51):5503–5523CrossRef
20.
Saeb S, Steinmann P, Javili A (2016) Aspects of computational homogenization at finite deformations: a unifying review from Reuss’ to Voigt’s bound. Appl Mech Rev 68(5):050801CrossRef
21.
Sayyad AS (2011) Comparison of various refined beam theories for the bending and free vibration analysis of thick beams. Appl Comput Mech 5:217–230
22.
Schröder J (2000) Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen. Habilitation, Bericht Nr I-7 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart
23.
Simo JC, Vu-Quoc L (1991) A geometrically-exact rod model incorporating shear and torsion-warping deformation. Int J Solids Struct 27(3):371–393MathSciNetCrossRef
24.
Timoshenko SP, Goodier JN (1951) Theory of elasticity. McGraw-Hill, New YorkMATH
25.
Vlachoutsis S (1992) Shear correction factors for plates and shells. Int J Numer Methods Eng 33(7):1537–1552CrossRef
26.
Wackerfuß J, Gruttmann F (2009) A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models. Comput Methods Appl Mech Eng 198(27):2053–2066MathSciNetCrossRef
27.
Wackerfuß J, Gruttmann F (2011) A nonlinear Hu-Washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sections. Comput Methods Appl Mech Eng 200(17–20):1671–1690MathSciNetCrossRef
28.
Wagner W, Gruttmann F (2001) Finite element analysis of Saint–Venant torsion problem with exact integration of the elastic–plastic constitutive equations. Comput Methods Appl Mech Eng 190(29–30):3831–3848CrossRef
29.
Wagner W, Gruttmann F (2013) A consistently linearized multiscale model for shell structures. In: Pietraszkiewicz W (ed) Shell structures. CRC Press, Boca RatonMATH
30.
Xu L, Cheng G, Yi S (2016) A new method of shear stiffness prediction of periodic Timoshenko beams. Mech Adv Mater Struct 23(6):670–680CrossRef
31.
Yu W, Hodges DH (2005) Generalized Timoshenko theory of the variational asymptotic beam sectional analysis. J Am Helicopter Soc 50(1):46–55CrossRef
Metadata
Title
Homogenization assumptions for coupled multiscale analysis of structural elements: beam kinematics
Authors
Simon Klarmann
Friedrich Gruttmann
Sven Klinkel
Publication date
07-11-2019
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 3/2020
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-019-01787-z

Other articles of this Issue 3/2020

Computational Mechanics 3/2020 Go to the issue

Original Paper

Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities

Original Paper

Effective floating volume: a highly parallelizable mesh-free approach for solving transient multiphysics problems in multi-scale geometries with non-linear material properties

Original Paper

On the local identifiability of constituent stress–strain laws for hyperelastic composite materials

Original Paper

Hydrodynamic effects of mucus on swimming performance of an undulatory foil by using the DSD/SST method

Original Paper

The dynamic analysis of stochastic thin-walled structures under thermal–structural–acoustic coupling

Original Paper

A reproducing kernel particle method for solving generalized probability density evolution equation in stochastic dynamic analysis