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.

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
.
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