A solenoidal part of displacement field appearing in a plate made of material with constraints has been determined. The semi-inverse method has been applied to description. The results being obtained together with the already known biharmonic representation (Jemielita, 1992) might be useful in a new micropolar plate theory formulation.
Issue Section:
Technical Papers
1.
Boggio
T.
1903
, “Sull integrazione di alcuna equationi linerari alle derivate parziale
,” Annali di Matematica Pura ed Applicata
, Ser. III, Vol. 8
, p. 181
181
.2.
Dougall
J.
1904
, “An Analytical Theory of the Equilibrium of an Isotropic Elastic Plate
,” Transaction of the Royal Society of Edinburgh
, Vol. 41
, Part 1, No. 8
, pp. 129
–228
.3.
Grioli
G.
1960
, “Elasticita` asimmetrica
,” Annali di Matematica Pura de Applicata
, Ser. IV, Vol. 50
, pp. 389
–417
.4.
Jemielita
G.
1992
, “Biharmonic Representation in the Analysis of Plates Made of the Grioli-Toupin Material
,” Journal of Theoretical and Applied Mechanics
, Vol. 30
, No. 1
, pp. 101
–107
.5.
Jemielita, G., 1993, “Exact Equations Theory of Plates (in Polish),” Prace Naukowe Politechniki Warszawskiej. Budownictwo, No. 124, pp. 1–153.
6.
Koiter
W. T.
1964
, “Couple Stresses in the Theory of Elasticity I-II
,” Proceedings Koninklijke Nederlandse Akademie van Wetenschappen
, Ser. B, Vol. 67
, No. 1
, pp. 17
–44
.7.
Le´vy
M.
1877
, “Me´moire sur la the´orie des plaques e´lastiques planes
,” Journal de Mathe´matiques Pures et Applique´es
, Ser. 3, Vol. 3
, pp. 219
–306
.8.
Lur’e
A. I.
1942
, “On the Theory of Thick Plates
,” Prikladnaya Matematika i Mekhanika
, Vol. 6
, Nos. 2–3
, pp. 151
–168
.9.
Nowacki, W., 1970, Theory of Elasticity (in Polish), PWN, Warszawa, pp. 757–759.
10.
Nowacki, W., 1970, Theory of Micropolar Elasticity, CISM, (Courses and Lectures), Springer-Verlag, Vienna.
11.
Nowacki, W., 1971, Theory of Asymmetric Elasticity, PWN, Warsaw (in Polish).
12.
Nowacki, W., 1981, Theory of Asymmetric Elasticity, 2nd ed., PWN, Warsaw (in Polish).
13.
Sokolowski, M., 1972, On the Theory of Couple Stresses in Media with Constrained Rotations, PWN, Warsaw (in Polish).
14.
Toupin
R. A.
1962
, “Elastic Materials with Couple-Stresses
,” Archive for Rational Mechanics and Analysis
, Vol. 11
, No. 5
, pp. 385
–414
.
This content is only available via PDF.
Copyright © 1995
by The American Society of Mechanical Engineers
You do not currently have access to this content.