Nonlinear bending of microarchitectural thin beams within strain gradient elasticity

Loc Tran; Jarkko Niiranen

Nonlinear bending of microarchitectural thin beams within strain gradient elasticity

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific

Abstract

This paper investigates the bending behaviour of beams by taking into account (1)material length scales according to Mindlin’s strain gradient elasticity theory of form II, (2) small strains but moderate displacements based on the von Kármán strain assumptions. The principle of virtual work is used to derive the nonlinear governing equations in form of a sixth-order partial differential equation. Thereafter, a conforming Galerkin method based on an isogeometric approach is adopted to naturally fulfill the stringent C2-continuity required by the beam model. Through numerical benchmarks, the accuracy and validity of the present theoretical formulations at linear and nonlinear regimes are confirmed.

Original language	English
Title of host publication	Proceedings of the 32nd Nordic Seminar on Computational Mechanics
Editors	A.H. Niemi, H. Koivurova
Publisher	Oulun yliopisto
Pages	158-159
ISBN (Electronic)	978-952-62-2420-6
Publication status	Published - 2019
MoE publication type	B3 Non-refereed conference publication
Event	Nordic Seminar on Computational Mechanics - Oulu, Finland Duration: 24 Oct 2019 → 25 Oct 2019 Conference number: 32 https://www.oulu.fi/construction/nscm32

Publication series

Name	Raportti / Oulun yliopisto, Konetekniikka
Publisher	Oulun yliopisto
Number	9
ISSN (Print)	2342-2599

Seminar

Seminar	Nordic Seminar on Computational Mechanics
Abbreviated title	NSCM
Country/Territory	Finland
City	Oulu
Period	24/10/2019 → 25/10/2019
Internet address	https://www.oulu.fi/construction/nscm32

Keywords

beam
strain gradient elasticity
isogeometric analysis
geometrical nonlinearity

Cite this

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title = "Nonlinear bending of microarchitectural thin beams within strain gradient elasticity",

abstract = "This paper investigates the bending behaviour of beams by taking into account (1)material length scales according to Mindlin{\textquoteright}s strain gradient elasticity theory of form II, (2) small strains but moderate displacements based on the von K{\'a}rm{\'a}n strain assumptions. The principle of virtual work is used to derive the nonlinear governing equations in form of a sixth-order partial differential equation. Thereafter, a conforming Galerkin method based on an isogeometric approach is adopted to naturally fulfill the stringent C2-continuity required by the beam model. Through numerical benchmarks, the accuracy and validity of the present theoretical formulations at linear and nonlinear regimes are confirmed.",

keywords = "beam, strain gradient elasticity, isogeometric analysis, geometrical nonlinearity",

author = "Loc Tran and Jarkko Niiranen",

year = "2019",

language = "English",

series = "Raportti / Oulun yliopisto, Konetekniikka ",

publisher = "Oulun yliopisto",

number = "9",

pages = "158--159",

editor = "A.H. Niemi and H. Koivurova",

booktitle = "Proceedings of the 32nd Nordic Seminar on Computational Mechanics",

address = "Finland",

note = "Nordic Seminar on Computational Mechanics, NSCM ; Conference date: 24-10-2019 Through 25-10-2019",

url = "https://www.oulu.fi/construction/nscm32",

}

Nonlinear bending of microarchitectural thin beams within strain gradient elasticity. / Tran, Loc; Niiranen, Jarkko.
Proceedings of the 32nd Nordic Seminar on Computational Mechanics. ed. / A.H. Niemi; H. Koivurova. Oulun yliopisto, 2019. p. 158-159 (Raportti / Oulun yliopisto, Konetekniikka ; No. 9).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific

TY - GEN

T1 - Nonlinear bending of microarchitectural thin beams within strain gradient elasticity

AU - Tran, Loc

AU - Niiranen, Jarkko

N1 - Conference code: 32

PY - 2019

Y1 - 2019

N2 - This paper investigates the bending behaviour of beams by taking into account (1)material length scales according to Mindlin’s strain gradient elasticity theory of form II, (2) small strains but moderate displacements based on the von Kármán strain assumptions. The principle of virtual work is used to derive the nonlinear governing equations in form of a sixth-order partial differential equation. Thereafter, a conforming Galerkin method based on an isogeometric approach is adopted to naturally fulfill the stringent C2-continuity required by the beam model. Through numerical benchmarks, the accuracy and validity of the present theoretical formulations at linear and nonlinear regimes are confirmed.

AB - This paper investigates the bending behaviour of beams by taking into account (1)material length scales according to Mindlin’s strain gradient elasticity theory of form II, (2) small strains but moderate displacements based on the von Kármán strain assumptions. The principle of virtual work is used to derive the nonlinear governing equations in form of a sixth-order partial differential equation. Thereafter, a conforming Galerkin method based on an isogeometric approach is adopted to naturally fulfill the stringent C2-continuity required by the beam model. Through numerical benchmarks, the accuracy and validity of the present theoretical formulations at linear and nonlinear regimes are confirmed.

KW - beam

KW - strain gradient elasticity

KW - isogeometric analysis

KW - geometrical nonlinearity

UR - https://www.oulu.fi/sites/default/files/content/NSCM32_Proceedings_not_archived_0.pdf

M3 - Conference article in proceedings

T3 - Raportti / Oulun yliopisto, Konetekniikka

SP - 158

EP - 159

BT - Proceedings of the 32nd Nordic Seminar on Computational Mechanics

A2 - Niemi, A.H.

A2 - Koivurova, H.

PB - Oulun yliopisto

T2 - Nordic Seminar on Computational Mechanics

Y2 - 24 October 2019 through 25 October 2019

ER -

Nonlinear bending of microarchitectural thin beams within strain gradient elasticity

Abstract

Publication series

Seminar

Keywords

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