The Euler-Bernoulli Limit of Thin Brittle Linearized Elastic Beams

被引：0

作者：

Ginster, Janusz ^{[1
]}

Gladbach, Peter ^{[2
]}

机构：

[1] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany

[2] Univ Bonn, Inst Angew Math, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

JOURNAL OF ELASTICITY | 2024年 / 156卷 / 01期

关键词：

Dimension reduction; Brittle fracture; Gamma-Convergence; Euler-Bernoulli beam; NONLINEAR MEMBRANE ENERGY; VARIATIONAL DERIVATION; GAMMA-LIMIT; MODEL; FRACTURE; BLAKE; FILMS;

D O I：

10.1007/s10659-023-10040-x

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We show that the linear brittle Griffith energy on a thin rectangle Gamma-converges after rescaling to the linear one-dimensional brittle Euler-Bernoulli beam energy.In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy.

引用

页码：125 / 155

页数：31

共 50 条

[41] Bending Solutions of FGM Reddy-Bickford Beams in Terms of Those of the Homogenous Euler-Bernoulli Beams
Xia, You-Ming
Li, Shi-Rong
Wan, Ze-Qing
ACTA MECHANICA SOLIDA SINICA, 2019, 32 (04) : 499 - 516
[42] RESONANT GREEN'S FUNCTION FOR EULER-BERNOULLI BEAMS BY MEANS OF THE FREDHOLM ALTERNATIVE THEOREM
Hozhabrossadati, Seyed Mojtaba
Sani, Ahmad Aftabi
Mofid, Masood
JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, 2013, 12 (03) : 55 - 67
[43] Nondeterministic dynamic stability assessment of Euler-Bernoulli beams using Chebyshev surrogate model
Gao, Kang
Gao, Wei
Wu, Binhua
Song, Chongmin
APPLIED MATHEMATICAL MODELLING, 2019, 66 : 1 - 25
[44] Bending of Euler-Bernoulli beams using Eringen's integral formulation: A paradox resolved
Fernandez-Saez, J.
Zaera, R.
Loya, J. A.
Reddy, J. N.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2016, 99 : 107 - 116
[45] Moving load identification on Euler-Bernoulli beams with viscoelastic boundary conditions by Tikhonov regularization
Qiao, Guandong
Rahmatalla, Salam
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2021, 29 (08) : 1070 - 1107
[46] Exponential stability of uniform Euler-Bernoulli beams with non-collocated boundary controllers
Chen, Yun Lan
Xu, Gen Qi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (02) : 851 - 867
[47] Formulation of the Green's functions stiffness method for Euler-Bernoulli beams on elastic Winkler foundation with semi-rigid connections
Molina-Villegas, Juan Camilo
Ortega, Jorge Eliecer Ballesteros
Cardona, David Ruiz
ENGINEERING STRUCTURES, 2022, 266
[48] Tensile fracture analysis of a thin Euler-Bernoulli beam and the transition to the voussoir model
Newman, D.
Hutchinson, A. J.
Mason, D. P.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, 2018, 102 : 78 - 88
[49] Application of iteration perturbation method and Hamiltonian approach for nonlinear vibration of Euler-Bernoulli beams
Ahmadi, Morteza
Hashemi, Gholamreza
Asghari, Ali
LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES, 2014, 11 (06): : 1049 - 1062
[50] A generally modified cuckoo optimization algorithm for crack detection in cantilever Euler-Bernoulli beams
Moezi, Seyed Alireza
Zakeri, Ehsan
Zare, Amin
PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY, 2018, 52 : 227 - 241

← 1 2 3 4 5 →