Abstract
A review is given on the progress in the study of general solutions of elasticity and their applications since 1972. Apart from summarizing and remarking the development of the general solution method in literature, this review aims to present the readers with a systematic and constructive scheme to develop general solutions from given governing differential equations and then to prove their completeness and investigate their nonuniqueness features. The effectiveness of the constructive scheme manifests itself in the fact that almost all the classic solutions, including not just classic displacement potentials but also classic stress functions, can be rederived by using this scheme. Furthermore, thanks to the systematic features of the scheme, it produces a constructive approach to study the completeness and nonuniqueness of general solutions and possesses more flexibility, which facilitates the extension of elastic general solution methods to more general systems governed by elliptic differential equations. Under the framework of this scheme, a comprehensive review is presented on wide application of general solutions in a variety of research areas, ranging from problems with different materials, isotropic or anisotropic, to various coupling problems, such as thermoelasticity, magnetoelasticity, piezoelectric elasticity, porous elasticity, and quasicrystal elasticity, and to problems of different engineering structures, for instance, the refined theories for beams and plates. There are 213 references cited in this review article.
Issue Section:
Review Articles
References
1.
Muskhelishvili
, N.
I.
, 1963,
Some Basic Problems of the Mathematical Theory of
Elasticity
, Wolters-Noordhoff
,
Groningen
.2.
Sternberg
,
E.
,
1960, “On Some Recent
Development in the Linear Theory of Elasticity
,”
Structural Mechanics
,
Pergamon
,
Oxford
, pp.
48
–73
.3.
Teodorescu
, P.
P.
, 1964,
“One Hundred Years of Investigations in the Plane Problem of
the Theory of Elasticity
,” Appl. Mech. Rev.
0003-6900, 17
, pp.
175
–186
.4.
Teodorescu
, P.
P.
, 1956,
“On the General Three-Dimensional Solution to the Elastic
Problem
,” Ninth International Congress of
Mechanics
,
Brussels
.5.
Gurtin
, M.
E.
, 1972,
The Linear Theory of Elasticity
(Encyclopedia of
Physics
Vol. 6
a∕2), S.
Flugge
, ed.,
Springer-Verlag
, New
York
.6.
Love
, A. F.
H.
, 1927,
A Treatise on the Mathematical Theory of Elasticity
,
4th ed., Cambridge University
Press
,
Cambridge
.7.
Lur’e
, A.
I.
, 1937,
“On the Theory of the System of Linear Differential Equations
With the Constant Coefficients
,” Trudy Leningrad,
Industrial, in-ta
, 6
, pp.
31
–36
.8.
Neuber
,
H.
,
1964, “On the General
Solution of Linear-Elastic Problems in Isotropic and Anisotropic Cosserat
Continua
,” Proceedings of the International
Congress for Applied Mechanics
, pp.
153
–158
.9.
Neuber
,
H.
,
1972,
“Vollstandigkeistbeweis des Dreifunktionenansatzes der
Linearen Elastizitatstheorie
,” Ing.-Arch.
0020-1154,
41
, pp.
232
–234
.10.
Heki
,
K.
, and
Habara
,
T.
,
1965, “Introduction of
Parametric Functions Into Analysis of Elastic Thin Plate
,”
Proceedings of the Japanese National Congress for Applied
Mechanics
, pp.
1
–4
.11.
Zhang
, H.
Q.
, 1979,
“A United Theory on the General Solutions of Systems of
Elasticity Equations
,” J. Dalian Institute of
Tech.
, 18
, pp.
25
–47
.12.
Baida
, E.
N.
, 1990,
Several Spatial Problems of Theory of Elasticity
,
South-East University Press
,
Nanjing
, in Chinese.13.
Wang
, M.
Z.
, and Wang
,
W.
,
1995, “Completeness and
Nonuniqueness of General Solutions of Transversely Isotropic
Elasticity
,” Int. J. Solids Struct.
0020-7683, 32
, pp.
501
–513
.14.
Wang
, M.
Z.
, 2002,
Advanced Theory of Elasticity
, Peking
University Press
, Beijing
,
in Chinese.15.
Eubanks
, R.
A.
, and Sternberg
,
E.
,
1956, “On the
Completeness of the Boussinesq–Papkovich Stress Functions
,”
J. Rat. Mech. Anal.
, 5
, pp.
735
–746
.16.
Boussinesq
,
J.
,
1885, Application des
Potentiels a l’Equilibre et des Mouvements des Solides Elastiques
,
Gauthier-Villars
,
Paris
.17.
Galerkin
,
B.
, 1930,
“On an Investigation of Stresses and Deformations in Elastic Isotropic Solids,”
Dokl. Akad. Nauk SSSR, Ser. A, pp. 353–358.18.
Wang
, M.
Z.
, 1991,
“Constructivity and Completeness of the General Solutions in
Elasticity
,” Acta Scie. Natural. Universitatis
Pekinensis
, 27
, pp.
26
–29
.19.
Mindlin
,
R.
,
1936, “Note on the
Galerkin and Papkovich Stress Functions
,” Bull. Am.
Math. Soc.
0002-9904, 42
, pp.
373
–376
.20.
Sternberg
,
E.
, and
Gurtin
, M.
E.
, 1962,
“On the Completeness of Certain Stress Functions in the
Linear Theory of Elasticity
,” Proceedings of the
Fourth U.S. National Congress for Applied Mechanics
, pp.
793
–797
.21.
Wang
, M.
Z.
, and Xu
, X.
S.
, 1990,
“On Nonuniqueness of Boussinesq–Galerkin Solutions in
Elasticity
,” Chin. J. Appl. Mech.
,
7
, pp.
97
–100
.22.
Papkovich
, P.
F.
, 1932,
“The Representation of the General Integral of the
Fundamental Equations of the Theory of Elasticity in Terms of Harmonic
Functions
,” Izv. Akad. Nauk SSSR, Fiz. Mat.
Ser.
, 10
, pp.
1425
–1435
.23.
Neuber
,
H.
,
1934, “Ein Neuer Ansats
zur Losung Raumlicher Probleme der Elastizitatstheorie. Der Hohlkegel Unter
Einzellast als Beispiel
,” Z. Angew. Math.
Mech.
0044-2267, 14
, pp.
203
–212
.24.
Wang
, L.
S.
, and Wang
, B.
B.
, 1991,
“The Transformation of the Papkovich–Neuber (PN) General
Solution and Others
,” Acta Mech. Sin.
0459-1879, 23
, pp.
755
–758
.25.
Ter-Mkrtychan
, L.
N.
, 1947,
“On General Solutions of the Problems of the Theory of
Elasticity
,” Trudy Leningrad, Politekhn.
in-ta
, 4
, pp.
3
–38
.26.
Naghdi
, P.
M.
, and Hsu
, C.
S.
, 1961,
“On a Representation of Displacements in Linear Elasticity in
Terms of Three Stress Functions
,” J. Math.
Mech.
0095-9057, 10
, pp.
233
–245
.27.
Wang
, M.
Z.
, 1985,
“The Naghdi–Hsu Solution and the Naghdi–Hsu
Transformation
,” J. Elast.
0374-3535, 15
, pp.
103
–108
.28.
Ton
,
T.-C.
,
1989, “On the
Completeness of the Papkovich–Neuber Solution
,” Q.
Appl. Math.
0033-569X, 47
, pp.
645
–659
.29.
Sokolnikoff
, I.
S.
, 1956,
Mathematical Theory of Elasticity
, 2nd
ed., McGraw-Hill
,
New York
.30.
Stippes
,
M.
,
1969, “Completeness of
the Papkovich Potentials
,” Q. Appl. Math.
0033-569X, 26
, pp.
477
–483
.31.
Ton
,
T.-C.
,
1989, “On the
Completeness of the Papkovich–Neuber Solution
,” Q.
Appl. Math.
0033-569X, 47
, pp.
645
–659
.32.
Millar
, B.
F.
, 1984,
“On the Completeness of the Papkovich
Potentials
,” Q. Appl. Math.
0033-569X, 41
, pp.
385
–393
.33.
Slobodyansky
,
M. G.
, 1959,
“On the General and Complete Form of Solutions of the
Equations of Elasticity
,” Prikl. Mat. Mekh.
0032-8235, 23
, pp.
468
–482
; 34.
Golecki
, J.
J.
, 1974,
“Integral of Differential Equations in Elastostatics Through
Determination of the Mean Stress
,”
Ing.-Arch.
0020-1154,
43
, pp.
331
–344
.35.
Golecki
, J.
J.
, 1975,
“Mean Stress Approach to Integration of Differential
Equations in Elastostatics, and the Neuber–Papkovich and Galerkin
Representations
,” Ing.-Arch.
0020-1154,
44
, pp.
153
–160
.36.
Golecki
, J.
J.
, 1976,
“Uncoupled Solutions in Elastostatics
,”
Int. J. Eng. Sci.
0020-7225, 14
, pp.
177
–180
.37.
Piltner
,
R.
,
1987, “The Use of
Complex Valued Functions for the Solution of Three-Dimensional Elasticity
Problems
,” J. Elast.
0374-3535,
18
, pp.
191
–225
.38.
Piltner
,
R.
,
1989, “On the
Representation of Three-Dimensional Elasticity Solutions With the Aid of
Complex Valued Functions
,” J. Elast.
0374-3535,
22
, pp.
45
–55
.39.
Gurtin
, M.
E.
, 1962,
“On Helmholtz’s Theorem and the Completeness of the
Papkovich–Neuber Stress Functions for Infinite Domains
,”
Arch. Ration. Mech. Anal.
0003-9527,
9
, pp.
225
–233
.40.
Slobodyansky
, M.
C.
, 1938,
“Expression of the Solution of the Differential Equations of
Elasticity by Means of One, Two, and Three Functions and Proof of the
Generality of These Solutions
,” Uch. Zap. Gos.
Univ.
, 24
, pp.
191
–202
.41.
Lekhnitskii
, S.
G.
, 1940,
“Symmetrical Deformation and Torsion of a Body of Revolution
With Special Kind of Anisotropy
,” Prikl. Mat.
Mekh.
0032-8235, 4
, pp.
43
–60
.42.
Lekhnitskii
, S.
G.
, 1981,
Theory Elasticity of an Anisotropic Body
,
Mir
,
Moscow
.43.
Eubanks
, R.
A.
, and Sternberg
,
E.
,
1954, “On the
Axisymmetric Problems Elasticity Theory for a Medium With Transverse
Isotropy
,” J. Rat. Mech. Anal.
,
3
, pp.
89
–101
.44.
Hu
, H.
C.
, 1953,
“On the Three-Dimensional Problems of the Theory of a
Transversely Isotropic Body
,” Sci. Sin.
(Beijing)
, 2
, pp.
215
–217
.45.
Nowacki
,
W.
,
1954, “The Stress
Function in Three-Dimensional Problems Concerning an Elastic Body
Characterized by Transverse Isotropy
,” Bull. Acad.
Pol. Sci. [Biol]
2300-1917, 2
, pp.
21
–25
.46.
Elliott
, H.
A.
, 1948,
“Three-Dimensional Stress Distribution in Hexagonal
Aeolotropic Crystals
,” Proc. Cambridge Philos.
Soc.
0068-6735, 44
, pp.
522
–533
.47.
Lodge
, A.
S.
, 1955,
“The Transformation to Isotropic Form of the Equilibrium
Equations for a Class of Anisotropic Elastic Solids
,”
Q. J. Mech. Appl. Math.
0033-5614,
8
, pp.
211
–225
.48.
Wang
,
W.
, and
Shi
, M.
X.
, 1998,
“On the General Solutions of Transversely Isotropic
Elasticity
,” Int. J. Solids Struct.
0020-7683, 35
, pp.
3283
–3297
.49.
Wang
, M.
Z.
, 1981,
“On the Completeness of Hu Hai–Chang’s
Solution
,” Appl. Math. Mech.
0253-4827, 2
, pp.
43
–250
.50.
Ding
, H.
J.
, Chen
, W.
Q.
, and Zhang
, L.
C.
, 2005,
Elasticity of Transversely Isotropic Materials
,
Springer
,
Netherlands
.51.
Chen
, W.
T.
, 1966,
“On Some Problems in Transversely Isotropic Elastic
Materials
,” J. Appl. Mech.
0021-8936, 33
, pp.
347
–355
.52.
Alexandarov
, A.
Y.
, and Soloviev
,
I. I.
, 1978,
Three-Dimensional Problems of Theory of Elasticity
,
Nauka
,
Moscow
, in Russian.53.
Pan
, Y.
C.
, and Chou
, T.
W.
, 1976,
“Point Force Solution for an Infinite Transversely Isotropic
Solid
,” J. Appl. Mech.
0021-8936, 43
, pp.
608
–612
.54.
Pan
, Y.
C.
, and Chou
, T.
W.
, 1979,
“Green’s Function Solutions for Semi-Infinite Transversely
Isotropic Materials
,” Int. J. Eng. Sci.
0020-7225, 17
, pp.
543
–551
.55.
Pan
, Y.
C.
, and Chou
, T.
W.
, 1979,
“Green’s Functions for Two-Phase Transversely Isotropic
Materials
,” J. Appl. Mech.
0021-8936, 46
, pp.
551
–556
.56.
Okumura
, I.
A.
, 1987,
“Generalization of Elliott’s Solution to Transversely
Isotropic Solids and Its Application
,” Struct.
Eng./Earthquake Eng.
0289-8063, 4
, pp.
185
–195
.57.
Zureick
, A.
H.
, and Eubanks
, R.
A.
, 1988,
“Spheroidal Cavity With Prescribed Asymmetric Tractions in
Three-Dimensional Transverse Isotropy
,” J. Eng.
Mech.
0733-9399, 114
, pp.
24
–28
.58.
Ding
, H.
J.
, and Xu
, B.
H.
, 1988,
“General Solutions for Axisymmetric Problems in Transversely
Isotropic Body
,” Appl. Math. Mech.
0253-4827,
9
, pp.
143
–151
.59.
Horgan
, C.
O.
, and Simmonds
,
J. G.
, 1991,
“Asymptotic Analysis of an End-Loaded Transversely Isotropic
Elastic, Semi-Infinite Strip Weak in Shear
,” Int. J.
Solids Struct.
0020-7683, 27
, pp.
1895
–1914
.60.
Fabrikant
, V.
I.
, 1996,
“Complete Solution to the Problem of an External Circular
Crack in a Transvesely Isotropic Body Subjected to Arbitary Shear
Loading
,” Int. J. Solids Struct.
0020-7683, 27
, pp.
1895
–1914
.61.
Wang
, M.
Z.
, and He
, B.
C.
, 1991,
“A Note on the Completeness of Hu Hai–Chang’s
Solution
,” Appl. Math. Mech.
0253-4827,
10
, pp.
571
–576
.62.
Xu
, X.
S.
, and Wang
, M.
Z.
, 1993,
“The Equivalence Between Boussinesq–Galerkin Solution and Hu
Hai–Chang Solution in Elasticity
,” Acta Mech.
Sin.
0459-1879, 25
, pp.
237
–241
.63.
Chen
, W.
O.
, Lee
, K.
Y.
, and Ding
, H.
J.
, 2004,
“General Solution for Transversely Isotropic Magento-
Electro- Thermo- Elasticity and Potential Theory Method
,”
Int. J. Eng. Sci.
0020-7225, 42
, pp.
1361
–1379
.64.
Morteza
, E.
G.
, 2005,
“A Complete Solution of the Wave Equations for Transversely
Isotropic Media
,” J. Elast.
0374-3535, 81
, pp.
1
–19
.65.
Wang
, M.
Z.
, 1980,
“A Derivation of Complex Variable Formula in Plane
Elasticity
,” Acta Scientiarum Naturalium,
Universitatis Pekinensis
, 16
, pp.
43
–46
.66.
Nagatani
,
K.
,
1975, “Some Properties
of Displacement Functions of Problems of Two-Dimensional
Elasticity
,” Trans. Jpn. Soc. Mech. Eng.
0375-9466, 41
, pp.
3494
–3496
.67.
Golecki
, J.
J.
, 1974,
“On Many Valuedness of the Neuber–Papkovich in
Two-Dimensional Elasticity
,” Mech. Res.
Commun.
0093-6413, 1
, pp.
85
–74
.68.
Eshelby
, J.
D.
, Read
, W.
T.
, and Shockley
,
W.
,
1953, “Anisotropic
Elasticity With Applications to Dislocation Theory
,”
Acta Metall.
0001-6160, 1
, pp.
251
–259
.69.
Stroh
, A.
N.
, 1958,
“Dislocation and Cracks in Anisotropic
Elasticity
,” Philos. Mag.
0031-8086, 7
, pp.
625
–646
.70.
Stroh
, A.
N.
, 1962,
“Steady State Problems in Anisotropic
Elasticity
,” J. Math. Phys.
0022-2488,
41
, pp.
77
–103
.71.
Barnett
, D.
M.
, and Lothe
,
J.
,
1973, “Synthesis of the
Sextic and the Integral Formalism for Dislocations, Green’s Functions, and
Surface Waves in Anisotropic Elastic Solids
,” Phys.
Norv.
0031-8930, 17
, pp.
13
–19
.72.
Ting
, T. C.
T.
, 1988,
“Some Identities and the Structure of Ni in the Stroh
Formalism of Anisotropic Elasticity
,” Q. Appl.
Math.
0033-569X, 46
, pp.
109
–120
.73.
Ting
, T. C.
T.
, 1991,
“The Stroh Formalism and Certain Invariances in
Two-Dimensional Anisotropic Elasticity
,” in Modern
Theory of Anisotropic Elasticity and Applications
(SIAM
Proceeding Series
), J. J.
Wu
, T. C.
T.
Ting
, and D.
M.
Barnett
, eds.,
SIAM
, Philadelphia,
PA
, pp. 3
–12
.74.
Suo
,
Z.
,
Kuo
, C.
M.
, Barnett
, D.
M.
, and Willis
, J.
R.
, 1992,
“Fracture Mechanics for Piezoelectric
Ceramics
,” J. Mech. Phys. Solids
0022-5096, 40
, pp.
739
–765
.75.
Ting
, T. C.
T.
, 1996,
Anisotropic Elasticity: Theory and Applications
,
Oxford University Press
,
Oxford
.76.
Ting
, T. C.
T.
, 2000,
“Recent Developments in Anisotropic
Elasticity
,” Int. J. Solids Struct.
0020-7683, 37
, pp.
401
–409
.77.
Gao
, C.
F.
, and Wang
, M.
Z.
, 2000,
“Collinear Permeable Cracks Between Dissimilar Piezoelectric
Materials
,” Int. J. Solids Struct.
0020-7683, 37
, pp.
4969
–4986
.78.
Gao
, C.
F.
, and Wang
, M.
Z.
, 2001,
“Green’s Functions of an Interfacial Crack Between Two
Dissimilar Piezoelectric Media
,” Int. J. Solids
Struct.
0020-7683, 38
, pp.
5323
–5334
.79.
Gao
, C.
F.
, Zhao
, Y.
T.
, and Wang
, M.
Z.
, 2000,
“An Exact and Explicit Treatment of an Elliptic Hole Problem
in Thermopiezoelectric Media
,” Int. J. Solids
Struct.
0020-7683, 39
, pp.
2665
–2685
.80.
Yin
, W.
L.
, 2000,
“Deconstructing Plane Anisotropic Elasticity, Part I: The
Latent Structure of Lekhnitskii’s Formalism
,” Int.
J. Solids Struct.
0020-7683, 37
, pp.
5257
–5276
.81.
Yin
, W.
L.
, 2000,
“Deconstructing Plane Anisotropic Elasticity, Part II:
Stroh’s Formalism
,” Int. J. Solids Struct.
0020-7683, 37
, pp.
5277
–5296
.82.
Guo
, F.
L.
, and Zheng
, Q.
S.
, 2003,
“The Completeness and a New Derivation of the Stroh Formalism
of Anisotropic Linear Elasticity
,” Acta Mech.
Sin.
0459-1879,
19
, pp.
270
–275
.83.
Lu
,
P.
,
1994, “Stroh Type
Formalism for Unsymmmetric Laminated Plate
,” Mech.
Res. Commun.
0093-6413, 21
, pp.
249
–254
.84.
Ding
, H.
J.
, Wang
, G.
Q.
, and Chen
, W.
Q.
, 1997,
“Green’s Functions for a Two-Phase Infinite Piezoelectric
Plane
,” Proc. R. Soc. London, Ser. A
1364-5021,
453
, pp.
2241
–2257
.85.
Ding
, H.
J.
, Wang
, G.
Q.
, and Chen
, W.
Q.
, 1997,
“General Solution of Plane Problem of Piezoelectric Media
Expressed by Harmonic Functions
,” Appl. Math.
Mech.
0253-4827,
18
, pp.
757
–764
.86.
Michell
, J.
H.
, 1900,
“The Uniform Torsion and Flexure of Incomplete Tores, With
Application to Helical Springs
,” Proc. London Math.
Soc.
0024-6115, 31
, pp.
130
–146
.87.
Timpe
,
A.
,
1924, “Achensymmetrische
Deformation von Under Hungsorpern
,” Z. Angew. Math.
Mech.
0044-2267, 4
, pp.
361
–376
.88.
Noll
,
W.
,
1957,
“Verschiebungsfunktionen Fuer Elastische
Schwingungsprobleme
,” Z. Angew. Math. Mech.
0044-2267, 37
, pp.
81
–87
.89.
Carlson
, D.
E.
, 1983,
“A Note on the Solutions of Boussinesq, Love, and Marguerre
in Axisymmetric Elasticity
,” J. Elast.
0374-3535,
13
, pp.
345
–349
.90.
Wang
, M.
Z.
, 1988,
“On the Completeness of Solutions of Boussinesq, Timpe, Love
and Michell in Axisymmetric Elasticity
,” J.
Elast.
0374-3535,
19
, pp.
85
–92
.91.
Ton
,
T.-C.
,
1995, “On the
Completeness and Uniqueness of the Papkovich–Neuber and the Nonaxisymmetric
Boussinesq, Love, and Burgatti solutions in General Cylindrical
Coordinates
,” J. Elast.
0374-3535,
36
, pp.
227
–255
.92.
Ton
,
T.-C.
,
1979, “On the
Equivalence Between Boussinesq and Timpe Approaches to the Torsion-Free
Axisymmetric Problems of Elasticity
,” J. Appl.
Phys.
0021-8979,
50
, pp.
3906
–3908
.93.
Simmonds
, J.
G.
, 2000,
“Love’s Stress Function for Torsionless Axisymmetric
Deformation of Elastically Isotropic Bodies With Body
Forces
,” J. Appl. Mech.
0021-8936,
67
, pp.
628
–629
.94.
Lou
, Y.
C.
, and Wang
, M.
Z.
, 2003,
“Michell’s General Solutions for Torsionless Axisymmetric
Problems With Body Forces in Elasticity
,” J. Appl.
Mech.
0021-8936,
70
, pp.
448
–449
.95.
Ding
, H.
J.
, 1987,
“On the Stress Function of Axisymmetric Deformation in a
Solid of Revolution
,” Shanghai J. Mech.
,
8
, pp.
42
–48
.96.
Thomson
,
W.
,
1848, “On the Equations
of Equilibrium of an Elastic Solid
,” Cambr. Dubl.
Math. J.
, 3
, pp.
87
–89
.97.
Sternberg
,
F.
, and
Eubanks
, R.
A.
, 1955,
“On the Concept of Concentrated Loads and an Extension of the
Uniqueness Theorem in the Linear Theory of Elasticity
,”
J. Ration. Mech. Anal.
, 4
, pp.
135
–168
.98.
Turteltaub
, M.
J.
, and Sternberg
,
E.
,
1968, “On Concentrated
Loads and Green’s Functions in Elastostatics
,” Arch.
Ration. Mech. Anal.
0003-9527,
29
, pp.
193
–240
.99.
Mura
,
T.
,
1987, Micromechanics of Defects
in Solids
, Martinus Nijhoff
,
Dordrecht
.100.
Eshelby
, J.
D.
, 1957,
“The Determination of the Elastic Field of an Ellipsoidal
Inclusion and Related Problems
,” Proc. R. Soc.
London, Ser. A
1364-5021,
241
, pp.
376
–396
.101.
Wang
, M.
Z.
, and Xu
, B.
X.
, 2004,
“The Arithmetic Mean Theorem of Eshelby Tensor for a
Rotational Symmetrical Inclusion
,” J.
Elast.
0374-3535, 77
, pp.
13
–23
.102.
Wang
, M.
Z.
, and Xu
, B.
X.
, 2006,
“The Arithmetic Mean Theorem of Eshelby Tensor for Exterior
Points Outside the Rotational Symmetrical Inclusion
,”
J. Appl. Mech.
0021-8936,
73
, pp.
672
–678
.103.
Xu
, B.
X.
, and Wang
, M.
Z.
, 2005,
“Special Properties of Eshelby Tensor for a Regular Polygonal
Inclusion
,” Acta Mech. Sin.
0459-1879, 21
, pp.
267
–271
.104.
Xu
, B.
X.
, and Wang
, M.
Z.
, 2005,
“The Quasi Eshelby Property for Rotational Symmetric
Inclusions of Uniform Eigencurvatures Within an Infinite
Plate
,” Proc. R. Soc. London, Ser. A
1364-5021,
461
, pp.
2899
–2910
.105.
Xu
, B.
X.
, and Wang
, M.
Z.
, 2007,
“The Arithmetic Mean Property for Rotational Symmetrical
Inclusions With Rotational Symmetrical Eigenstrains
,”
ZAMM
0044-2267,
87
(1
), pp.
59
–69
.106.
Franciosi
,
P.
,
2005, “On the Modified
Green Operator Integral for Polygonal, Polyhedral and Other Nonellipsoidal
Inclusions
,” Int. J. Solids Struct.
0020-7683,
42
(11–12
), pp.
3509
–3531
.107.
Zheng
, Q.
S.
, Zhao
, Z.
H.
, and Du
, D.
X.
, 2006,
“Irreducible Structure, Symmetry and Average of Eshelby’s
Tensor Fields in Isotropic Elasticity
,” J. Mech.
Phys. Solids
0022-5096, 54
, pp.
368
–393
.108.
Wang
, M.
Z.
, 1988,
“Brebbia’s Indirect Representation and the Completeness of
Papkovich–Neuber’s and Boussinesq–Galerkin’s Solutions in
Elasticity
,” Appl. Math. Model.
0307-904X, 12
, pp.
333
–335
.109.
Yan
, G.
P.
, and Wang
, M.
Z.
, 1988,
“Somigliana Formula and the Completeness of Papkovich–Neuber
and Boussinesq–Galerkin Solutions in Elasticity
,”
Mech. Res. Commun.
0093-6413, 15
, pp.
73
–77
.110.
Neuber
,
H.
,
1937,
Kerbspannungslehre
,
Springer
,
Berlin
.111.
Uflyand
, Y.
S.
, 1963,
Integral Transforms in the Theory of Elasticity
,
Academia Science SSSR
,
Leningrad
, in Russian.112.
Kassir
, M.
K.
, and Sih
, G.
C.
, 1973,
“Application of Papkovich–Neuber Potentials to a Crack
Problem
,” Int. J. Solids Struct.
0020-7683, 9
, pp.
643
–654
.113.
Kassir
, M.
K.
, and Sih
, G.
C.
, 1975,
Three-Dimensional Crack Problems, Mechanics of Fracture 2
,
Noordhoff International
,
Leyden
.114.
Meade
, K.
P.
, and Keer
, L.
M.
, 1984,
“On the Problem of a Pair of Point Forces Applied to the
Faces of a Semi-Infinite Plane Crack
,” J.
Elast.
0374-3535, 14
, pp.
3
–14
.115.
Huang
, K.
F.
, and Wang
, M.
Z.
, 1990,
“The Interface Crack Problem of the Bi-Material Elastic
Body
,” Acta Mech. Sin.
0459-1879, 22
, pp.
363
–365
.116.
Lur’e
, A.
I.
, 1964,
Three-Dimensional Problems of the Theory of Elasticity
,
Interscience
, New
York
.117.
Wang
, M.
Z.
, 1980,
“On the Solution for Several Boundary Value in Half-Space
Elasticity
,” Acta Scientiarum Naturalium,
Universitatis Pekinensis
, 16
, pp.
36
–42
.118.
Phan-Thien
,
N.
,
1983, “On the Image
System for the Kelvin State
,” J. Elast.
0374-3535, 13
, pp.
231
–235
.119.
Lorentz
, H.
A.
, 1907,
“Ein Allgemeiner Staz, Die Bewegung Einer Reibenden
Flssigkeit Betreffend, Nebst Einigen Anwendungen Desselben
,”
Abh. Theor. Phys. Leipzig
, 1
, pp.
23
–42
.120.
Mindlin
, R.
D.
, 1953,
“Force at a Point in the Interior of a Semi-Infinite
Solid
,” Proceedings of the First Midwest Conference
on Solid Mechanics
.121.
Huang
, K.
F.
, and Wang
, M.
Z.
1991, “Fundamental Solution
of Bimaterial Elastic Space
,” Sci. China, Ser. A:
Math., Phys., Astron. Technol. Sci.
1001-6511, 34
, pp.
309
–315
.122.
Panc
,
V.
,
1975, Theories of Elastic
Plates
, Noordhoff International
Publishing
, Leyden,
Czechoslovakia
.123.
Friedrichs
, K.
O.
, and Dressler
,
R. F.
, 1961,
“A Boundary-Layer Theory for Elastic Plates
,”
Commun. Pure Appl. Math.
0010-3640, 14
, pp.
2
–33
.124.
Naghdi
, P.
M.
, 1972,
The Theory of Shells and Plates
(Encyclopedia of
Physics
Vol. a∕2
), S.
Flugge
, ed.,
Springer-Verlag
, New
York
.125.
Piltner
,
R.
,
1992, “The Derivation of
a Thick and Thin Plate Formulation Without Ad Hoc
Assumptions
,” J. Elast.
0374-3535, 29
, pp.
133
–173
.126.
Ladevèze
,
P.
,
2002, “The Exact Theory
of Plate Bending
,” J. Elast.
0374-3535, 68
(1–3
), pp.
37
–71
.127.
Ladevèze
,
P.
, and
Simmonds
,
J.
,
1998, “New Concepts for
Linear Beam Theory With Arbitrary Geometry and Loading
,”
Eur. J. Mech. A/Solids
0997-7538,
17
(3
), pp.
377
–402
.128.
Ladevèze
,
P.
, and
Simmonds
,
J.
,
2001, “An Exact Theory
for Circular, End-Loaded, Anisotropic Beams of Narrow Rectangular Cross
Section
,” J. Elast.
0374-3535, 63
(2
), pp.
153
–170
.129.
Ladevèze
,
P.
, and
Simmonds
,
J.
,
2001, “The Exact
One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow
Rectangular Cross Section
,” Trans. ASME, J. Appl.
Mech.
0021-8936,
68
(6
), pp.
865
–868
.130.
Gregory
, R.
D.
, and Wan
, F. Y.
M.
, 1985,
“On Plate Theories and Saint Venant’s
Principle
,” Int. J. Solids Struct.
0020-7683, 21
, pp.
1005
–1024
.131.
Wan
, F. Y.
M.
, 2003,
“Stress Boundary Conditions for Plate
Bending
,” Int. J. Solids Struct.
0020-7683, 40
, pp.
4107
–4123
.132.
Cheng
,
S.
,
1979, “Elasticity Theory
of Plates and a Refined Theory
,” J. Appl.
Mech.
0021-8936, 46
, pp.
644
–650
.133.
Barrett
, K.
E.
, and Ellis
,
S.
,
1988, “An Exact Theory
of Elastic Plates
,” Int. J. Solids Struct.
0020-7683, 24
, pp.
859
–880
.134.
Wang
, F.
Y.
, 1990,
“Two-Dimensional Theories Deduced From Three-Dimensional
Theory for a Transversely Isotropic Body-I. Plate Problems
,”
Int. J. Solids Struct.
0020-7683, 26
, pp.
445
–470
.135.
Wang
, F.
Y.
, 1991,
“Two-Dimensional Theories Deduced From Three-Dimensional
Theory for a Transversely Isotropic Body-II. Plane
Problems
,” Int. J. Solids Struct.
0020-7683, 28
, pp.
161
–177
.136.
Wang
,
W.
, and
Shi
, M.
X.
, 1997,
“Thick Plate Theory Based on General Solutions of
Elasticity
,” Acta Mech.
0001-5970,
123
, pp.
27
–36
.137.
Gregory
, R.
D.
, 1979,
“Green’s Functions, Bilinear Forms, and Completeness of the
Eigenfunctions for the Elastostatic Strip and Wedge
,”
J. Elast.
0374-3535,
9
, pp.
283
–309
.138.
Gregory
, R.
D.
, 1980,
“The Traction Boundary Value Problem for the Elastostatic
Semi-Infinite Strip, Existence of Solution, and Completeness of the
Papkovich–Fadle Eigenfunctions
,” J. Elast.
0374-3535,
10
, pp.
295
–327
.139.
Gregory
, R.
D.
, 1992,
“The General Form of the Three-Dimensional Elastic Field
Inside an Isotropic Plate With Free Faces
,” J.
Elast.
0374-3535, 28
, pp.
1
–28
.140.
Zhao
, B.
S.
, and Wang
, M.
Z.
, 2003,
“The Decomposed Form of the Three-Dimensional Elastic
Plate
,” Acta Mech.
0001-5970, 166
, pp.
207
–216
.141.
Zhao
, B.
S.
, and Wang
, M.
Z.
, 2005,
“Equivalence of the Refined Theory and the Decomposed Theorem
of an Elastic Plate
,” Appl. Math. Mech.
0253-4827,
26
(4
), pp.
486
–494
.142.
Lo
, K.
H.
, Christensen
, R.
M.
, and Wu
, E.
M.
, 1977,
“A Higher Order Theory for Plate Deformations, Part 2:
Laminated Plates
,” ASME J. Appl. Mech.
0021-8936, 44
, pp.
669
–676
.143.
Levinson
,
M.
,
1981, “A New Rectangular
Beam Theory
,” J. Sound Vib.
0022-460X, 74
, pp.
81
–87
.144.
Levinson
,
M.
,
1981, “Further Results
of a New Beam Theory
,” J. Sound Vib.
0022-460X, 77
, pp.
440
–444
.145.
Levinson
,
M.
,
1986, “Consistent and
Inconsistent Higher Order Beam and Plate Theories: Some Surprising
Comparisons
,” Proceedings of Euromech Colloquium 219
on Refined Dynamical Theories of Beams, Plates and Shells and Their
Applications
, Kassel FR, Germany
,
pp. 122
–130
.146.
Fan
,
H.
, and
Widera
, G. E.
O.
, 1992,
“Refined Engineering Beam Theory Based on the Asymptotic
Expansion Approach
,” AIAA J.
0001-1452, 29
, pp.
444
–449
.147.
Kathnelson
, A.
N.
, 1996,
“Improved Engineering Theory for Uniform
Beams
,” Acta Mech.
0001-5970,
114
, pp.
225
–229
.148.
Reddy
, J.
N.
, Wang
, C.
M.
, Lim
, C.
T.
, and Ng
, K.
H.
, 2001,
“Bending Solutions of Levison Beams and Plates in Terms of
the Classical Theories
,” Int. J. Solids
Struct.
0020-7683, 38
, pp.
4701
–4720
.149.
Gao
,
Y.
, and
Wang
, M.
Z.
, 2004,
“The Refined Theory of Magnetoelastic Beams
,”
Acta Mech.
0001-5970, 173
, pp.
147
–161
.150.
Gao
,
Y.
, and
Wang
, M.
Z.
, 2005,
“Equivalence of Refined Theory and Decomposed Theory of
Thermoelastic Beams Under Steady Temperature
,” Chin.
J. Appl. Mech.
, 22
, pp.
164
–168
.151.
Gao
,
Y.
, and
Wang
, M.
Z.
, 2005,
“The Refined Beam Theory Based on the Refined Beam
Plate
,” Acta Mech.
0001-5970, 177
, pp.
191
–206
.152.
Gao
,
Y.
, and
Wang
, M.
Z.
, 2007,
“The Equivalence of the Refined Theory and the Decomposed
Theorem of Rectangular Beams
,” Appl. Math.
Model.
0307-904X, 31
(3
),
pp. 551
–563
.153.
Schaefer
,
H.
,
1953, “Die
Spannungsfunktionen des Dreidimensionalen Kontinuums und des Elastischen
Krpers
,” Z. Angew. Math. Mech.
0044-2267, 33
, pp.
356
–362
.154.
Gurtin
, M.
E.
, 1963,
“A Generalization of the Beltrami Stress Functions in
Continuum Mechanics
,” Arch. Ration. Mech.
Anal.
0003-9527,
13
, pp.
321
–329
.155.
Wang
, M.
Z.
, 1995,
“Generalized Inverse of Matrices and Stress
Function
,” Proceedings of Modern Mathematical
Mechanics of China
, Vol. 16
, pp.
139
–145
.156.
Yin
, H.
M.
, and Wang
, M.
Z.
, 1998,
“Stress Functions in Two-Dimensional, Three-Dimensional, and
n-Dimensional Elasticity
,” Acta Scientiarum
Naturalium, Universitatis Pekinensis
, 34
, pp.
21
–26
.157.
Rao
, C.
R.
, and Mitra
, S.
K.
, 1974,
Generalized Inverse of Matrices and Its Applications
,
Wiley
, New
York
.158.
Rostamian
,
R.
,
1979, “The Completeness
of Maxwell’s Stress Function Representation
,” J.
Elast.
0374-3535,
9
, pp.
349
–356
.159.
Shen
, H.
C.
, 1982,
“Dynamic Stress Function Tensor
,”
Appl. Math. Mech.
0253-4827, 3
, pp.
829
–834
.160.
Hackl
,
K.
, and
Zastrow
,
V.
,
1988, “On the Existence,
Uniqueness and Completeness of Displacements and Stress Functions in Linear
Elasticity
,” J. Elast.
0374-3535,
19
, pp.
3
–23
.161.
Pobedria
,
B. E.
, 1980,
“A New Formulation of the Problem of the Mechanics of a
Deformable Solid in Stresses
,” Dokl. Akad. Nauk
SSSR
0002-3264, 253
, pp.
295
–297
; Pobedria
,
B. E.
, 1980,
Sov. Math. Dokl.
0197-6788, 22
, pp.
88
–91
.162.
Pobedria
, B.
E.
, 1979,
“Some General Theorems of the Mechanics of a Deformable
Solid
,” Prikl. Mat. Mekh.
0032-8235, 43
, pp.
531
–541
.163.
Pobedria
,
B. E.
, 1994,
“A Problem in Stresses for an Anisotropic
Medium
,” Prikl. Mat. Mekh.
0032-8235, 58
, pp.
77
–85
; 164.
Kucher
, V.
A.
, Markenscoff
,
X.
, and
Paukshto
, M.
V.
, 2004,
“Some Properties of the Boundary Value Problem of Linear
Elasticity in Terms of Stresses
,” J. Elast.
0374-3535, 74
, pp.
135
–145
.165.
Teodorescu
, P.
P.
, 1972,
“Stress Functions in Three-Dimensional
Elastodynamics
,” Acta Mech.
0001-5970,
14
(2–3
), pp.
103
–118
.166.
Sternberg
,
E.
, and
Eubanks
, R.
A.
, 1957,
“On Stress Functions for Elastokinetics and the Integration
of the Repeated Wave Equation
,” Q. Appl.
Math.
0033-569X, 15
(2
), pp.
149
–153
.167.
Payne
, L.
E.
, 1959,
“Representation Formulas for Solutions of a Class of Partial
Differential Equations
,” J. Math. Phys.
0022-2488, 83
, pp.
145
–149
.168.
Aderogba
,
K.
,
1976, “On Stokelets in a
Two-Fluid Space
,” J. Eng. Math.
0022-0833,
10
, pp.
143
–151
.169.
Ton
,
T.-C.
, and
Blake
, J.
B.
, 1982,
“General Solutions of the Stokes’ Flow
Equations
,” J. Math. Anal. Appl.
0022-247X, 90
, pp.
72
–84
.170.
Wang
, L.
N.
, and Wang
, M.
Z.
, 1990,
“On the Stokes Entry Flow Into a Semi-Infinite Circular
Cylindrical Tube
,” Appl. Math. Mech.
0253-4827,
11
, pp.
479
–487
.171.
Xu
, X.
S.
, and Wang
, M.
Z.
, 1991,
“The Use of Complex Valued Functions for the Solution of
Spatial Stokes Flow
,” Acta Scientiarum Naturalium,
Universitatis Pekinensis
, 27
, pp.
22
–25
.172.
Xu
, X.
S.
, and Wang
, M.
Z.
, 1991,
“General Complete Solutions of the Equations of Spatial and
Axisymmetric Stokes Flow
,” Q. J. Mech. Appl.
Math.
0033-5614,
44
, pp.
537
–548
.173.
Xu
, X.
S.
, and Wang
, M.
Z.
, 1992,
“The Axisymmetric Solutions of Stokes and Ideal Flows With
the Aid of the Analytic Functions
,” Appl. Math.
(Germany)
0862-7940, 5
, pp.
90
–94
.174.
Shen
, H.
C.
, 1985,
“General Solution of Elastodynamics
,”
Appl. Math. Mech.
0253-4827,
6
, pp.
791
–796
.175.
Poruchikov
, V.
B.
, 1986,
Method of Elastodynamics
,
Nauka
,
Moscow
, in Russian.176.
Wang
,
W.
, and
Wang
, M.
Z.
, 1992,
“Constructivity and Completeness of the General Solutions in
Elastodynamics
,” Acta Mech.
0001-5970,
91
, pp.
209
–214
.177.
Biot
, M.
A.
, 1956,
“Thermoelasticity and Irreversible
Thermodynamics
,” J. Appl. Phys.
0021-8979,
27
, pp.
240
–253
.178.
Verruijt
,
A.
,
1969, “The Completeness
of Biot’s Solution of the Coupled Thermoelastic Problem
,”
Q. Appl. Math.
0033-569X, 26
, pp.
485
–490
.179.
Qing
, C.
B.
, and Wang
, M.
Z.
, 1989,
“A New Proof of Completeness of General Solutions in
Thermoelasticity
,” Chin. J. Appl. Mech.
,
6
, pp.
80
–82
.180.
Wang
, M.
Z.
, and Huang
, K.
F.
, 1991,
“Thermoelastic Problem in the Half Space u an Application of
the General Solution in Elasticity
,” Appl. Math.
Mech.
0253-4827,
12
, pp.
849
–862
.181.
Ding
, H.
J.
, Guo
, F.
L.
, and Hou
, P.
F.
, 2000,
“General Solution of Coupled Thermoelastic
Problem
,” Appl. Math. Mech.
0253-4827,
21
, pp.
631
–636
.182.
McName
,
J.
, and
Gibson
, R.
E.
, 1960,
“Plane Strain and Axially Symmetric Problems of the
Consolidation of Semi-Infinite Clay Stratum
,” Q. J.
Mech. Appl. Math.
0033-5614, 13
, pp.
210
–227
.183.
Biot
, M.
A.
, 1940,
“General Theory of Three-Dimensional
Consolidation
,” J. Appl. Phys.
0021-8979,
12
, pp.
155
–164
.184.
Aifantis
, E.
C.
, 1980,
“On the Problem of Diffusion in Solid
,”
Acta Mech.
0001-5970,
37
, pp.
265
–296
.185.
Unger
, D.
J.
, 1988,
“Completeness of Solutions in the Double Porosity
Theory
,” Acta Mech.
0001-5970,
75
, pp.
269
–274
.186.
Chandrasekharaiah
, D.
S.
, 1987,
“Complete Solutions in the Theory of Elastic Materials With
Voids
,” Q. J. Mech. Appl. Math.
0033-5614,
40
, pp.
401
–414
.187.
Chandrasekharaiah
, D.
S.
, and Cowin
, S.
C.
, 1989,
“Unified Complete Solutions for the Theories of
Thermoelasticity and Poroelasticity
,” J.
Elast.
0374-3535,
21
, pp.
121
–126
.188.
Xu
,
Y.
, and
Wang
, M.
Z.
, 1994,
“General Solutions and Completeness on Elastodynamics With
Double Porosity
,” Acta Scientiarum Naturalium,
Universitatis Pekinensis
, 30
, pp.
339
–342
.189.
Nowacki
,
W.
,
1969, “On the
Completeness of Potentials in Micropolar Elasticity
,”
Arch. Mech. Stosow.
0004-0800, 21
, pp.
107
–122
.190.
Bors
, C.
I.
, 1981,
“Deformable Solids With Microstructure Having a Symmetric
Stress Tensor
,” An. Sti. Univ. Iasi
,
27
, pp.
177
–184
.191.
Wang
, M.
Z.
, 1988,
“Generalized Theory of Elasticity
,”
Sci. China, Ser. A
, 31
, pp.
1213
–1221
.192.
193.
Pao
, Y.
H.
, and Yeh
, C.
S.
, 1973,
“A Linear Theory for Soft Ferromagnetic Elastic
Solids
,” Int. J. Eng. Sci.
0020-7225, 11
, pp.
415
–436
.194.
Huang
, K.
F.
, and Wang
, M.
Z.
, 1995,
“Complete Solution of the Linear Magnetoelasticity and the
Magnetic Fields in a Magnetized Elastic Half Space
,”
J. Appl. Mech.
0021-8936,
62
, pp.
930
–934
.195.
Wang
, Z.
K.
, and Zheng
, B.
L.
, 1995,
“The General Solution of Three-Dimensional Problems in
Piezoelectric Media
,” Int. J. Solids
Struct.
0020-7683, 32
, pp.
105
–115
.196.
Ding
, H.
J.
, Chen
,
B.
, and
Liang
,
J.
,
1996, “General Solutions
for Coupled Equations for Piezoelectric Media
,” Int.
J. Solids Struct.
0020-7683, 33
, pp.
2283
–2298
.197.
Gao
, C.
F.
, Kessler
,
H.
, and
Balke
,
H.
,
2003, “Crack Problems in
Magnetoelectroelastic Solids. Part II: General Solution of Collinear
Cracks
,” Int. J. Eng. Sci.
0020-7225, 41
, pp.
983
–994
.198.
Ding
, H.
J.
, Guo
, F.
L.
, Hou
, P.
F.
, and Chi
, Y.
W.
, 1999,
“A General Solution for Static Piezothermoelectric Problems
of Crystal Class 6mm Solids
,” Acta Mech. Solida
Sin.
, 12
, pp.
189
–197
.199.
Ding
, H.
J.
, Guo
, F.
L.
, and Hou
, P.
F.
, 2000,
“A General Solution for Piezothermoelasticity of Transversely
Isotropic Piezoelectric Materials and Its Applications
,”
Int. J. Eng. Sci.
0020-7225, 38
, pp.
1415
–1440
.200.
Ding
, H.
J.
, Wang
, H.
M.
, and Chen
, W.
Q.
, 2001,
“The General Solution of Spherically Isotropic Piezoelectric
Media and Its Applications
,” Mech. Res.
Commun.
0093-6413, 28
, pp.
389
–396
.201.
Ru
, C.
Q.
, 2000,
“Electrode-Ceramic Interfacial Cracks in Piezoelectric
Multilayer Materials
,” J. Appl. Mech.
0021-8936,
67
, pp.
255
–261
.202.
Shechtman
,
D.
,
Blech
,
I.
,
Gratias
,
D.
, and
Cahn
, J.
W.
, 1984,
“Metallic Phase With Long-Range Orientational and No
Translational Symmetry
,” Phys. Rev. Lett.
0031-9007, 53
, pp.
1951
–1953
.203.
Li
, X.
F.
, and Fan
, T.
Y.
, 1998,
“New Method for Solving Elasticity Problems of Some Planar
Quasicrystals and Solutions
,” Chin. Phys.
Lett.
0256-307X, 15
, pp.
278
–280
.204.
Fan
, T.
Y.
, 1999,
Mathematical Theory of Elasticity of Quasi-Crystals and Its
Application
, Beijing Institute of
Technology
, Beijing
, in
Chinese.205.
Fan
, T.
Y.
, and Mai
, Y.
W.
, 2004,
“Elasticity Theory, Fracture Mechanics, and Some Relevant
Thermal Properties of Quasicrystalline Materials
,”
Appl. Mech. Rev.
0003-6900,
57
, pp.
325
–343
.206.
Gao
,
Y.
, and
Zhao
, B.
S.
, 2006,
“A General Treatment of Three-Dimensional Elasticity of
Quasicrystals by an Operator Method
,” Phys. Status
Solidi B
0370-1972,
243
(15
), pp.
4007
–4019
.207.
Renton
, J.
D.
, 1979,
“Note on Generalized Displacement Functions in the Presence
of Initial Stress
,” J. Struct. Mech.
0360-1218, 7
, pp.
365
–373
.208.
Westergaard
, H.
M.
, 1935,
“General Solution of the Problem of Elastostatics of an
n-Dimensional Homogeneous Isotropic Solid in an n-Dimensional
Space
,” Bull. Am. Math. Soc.
0002-9904, 41
, pp.
695
–699
.209.
Wang
, Z.
M.
, 1981,
“A Study of Elastic Stability Problems Based on Mathematical
Theory of Elasticity
,” Appl. Math. Mech.
0253-4827, 2
, pp.
49
–74
.210.
Lu
,
E.
,
1980, “On the Solution
of Reissner Model of Thick Plate
,” Compos.
Math.
0010-437X, 2
, pp.
383
–387
.211.
Hu
, H.
C.
, 1981,
The Variational Principles of Elasticity and Its
Application
, Science
,
Beijing, China
, in Chinese.212.
Wang
, L.
S.
, 1985,
“On General Solution of Problem of Elastic Shallow Thin
Shells
,” Acta Mech. Sin.
0459-1879, 17
, pp.
64
–71
.213.
Wang
,
W.
,
1996, “Completeness and
Nonuniqueness of General Solutions of Elastic Shallow Thin Shells With a
Constant Curvature
,” Acta Mech. Sin.
0459-1879, 28
, pp.
532
–541
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
