On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models

被引：47

作者：

Arnold, DN ^{[1
]}

Madureira, AL

Zhang, S

机构：

[1] Univ Minnesota, IMA, Minneapolis, MN 55455 USA

[2] DMA, LNCC, BR-25651070 Petropolis, RJ, Brazil

[3] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

JOURNAL OF ELASTICITY | 2002年 / 67卷 / 03期

基金：

美国国家科学基金会;

关键词：

plate; Kirchhoff-Love; Reissner-Mindlin;

D O I：

10.1023/A:1024986427134

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We show that the Reissner-Mindlin plate bending model has a wider range of applicability than the Kirchhoff-Love model for the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the transverse direction, the Reissner-Mindlin model solution converges to the three- dimensional linear elasticity solution in the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear effect, the Kirchhoff - Love model fails.

引用

页码：171 / 185

页数：15

共 10 条

[1]

ALESSANDRINI SM, 1999, CRM P LECT NOTES

[2]

[Anonymous], 1997, STUD MATH APPL

[3] Asymptotic analysis of the boundary layer for the reissner-mindlin plate model [J].

Arnold, DN ;

Falk, RS .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (02) :486-514

[4]

ARNOLD DN, 1997, RAIRO-MATH MODEL NUM, V31, P517

[5]

Dauge M, 1996, ASYMPTOTIC ANAL, V13, P167

[6] Explicit error bounds for the Kirchhoff-Love and Reissner-Mindlin plate models [J].

Destuynder, P .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (02) :233-238

[7]

Hughes T. J. R., 2012, The finite element method: linear static and dynamic finite element analysis

[8] HERLEITUNG DER PLATTENTHEORIE AUS DER DREIDIMENSIONALEN ELASTIZITATSTHEORIE [J].

MORGENSTERN, D .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1959, 4 (02) :145-152

[9] CONSTRUCTION OF A MODEL ON THE EVOLUTION OF PLATES WITH ROTATIONAL INERT TERM [J].

RAOULT, A .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1985, 139 :361-400

[10]

Reissner E., 1985, Appl. Mech. Rev, V38, P1453, DOI [10.1115/1.3143699, DOI 10.1115/1.3143699]

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