General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects

Journal of Sound and Vibration

Volumn 237, Issue 4, 2000, Pages 561-615

  Toorani, M H ^a   Lakis, A A ^b  

^a NATIONAL RESEARCH COUNCIL CANADA   (Canada)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; MATHEMATICAL MODELS; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; SHEAR STRESS;

INITIAL CURVATURE EFFECTS; ROTARY INERTIA;

SHELLS (STRUCTURES);

EID: 0034319803     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2000.3073     Document Type: Article

References (168)

1. SAADA A. S. Elasticity Theory and Applications. 1993;Pergamon Press, Oxford.
2. FLÜGGE W. Stresses in Shells. 1960;Julius Springer, Berlin.
3. KRAUS H. Thin Elastic Shells. 1967;John Wiley, New York.
4. NIORDSON F. I. Introduction to Shell Theory. 1980;Technical University of Denmark.
5. BERT C. W. Analysis of shells. Chamis C. C. Composite Materials - Structural Design and Analysis. 7:1975;207-258 Academic Press, New York.
6. REISSNER E. Stress-strain relations in the theory of thin elastic shells. Journal of Mathematical Physical. 31:1952;109-119.
7. NAGHDI P. M. A survey of recent progress in the theory of elastic shells. Applied Mechanics Reviews. 9:1956;365-388.
8. A. W. LEISSA, 1973, NASA SP- 288, Vibration of shells.
9. S. A. AMBARTSUMYAN, 1964, NASA-TT-F-118, Theory of anisotropic shells.
10. L. SANDERS, 1959, NASA, TR R-24, 1, 23, An improved first approximation theory for thin shells.
11. KOITER W. T. A consistent first approximation in the general theory of thin elastic shells. Proceedings of the Symposium on Theory of Thin Elastic Shells, Amsterdam, North Holland. 1960;12-32.
12. NOVOZHILOV V. V. The Theory of Thin Shells. 1959;P. Noordhoff Ltd. Leiden.
13. SOEDEL W. Vibrations of Shells and Plates. 1993;Marcel Dekker Inc. New York.
14. DONG S. B., PISTER K. S., TAYLOR R. L. On the theory of laminated anisotropic shells and plates. Journal of Aero Science. 29:1962;969-975.
15. BOGNER F. K., FOX R. L., SCHMIT L. A. A cylindrical shell discrete element. AIAA Journal. 5:1967;745-750.
16. MORLEY L. S. D. An improvement on Donnell's approximation for thin-walled circular cylinders. Quarterly Journal of Mechanical and Applied Mathematics. 12:1959;89-99.
17. REISSNER E. On axisymmetric vibrations of shallow spherical shells. Quarterly Applied Mathematics. 13:1955;279-290.
18. CHENG S. On an accurate theory for circular cylindrical shells. Journal of Applied Mechanics. 40:1973;582-588.
19. CHENG S., HE F. B. Theory of orthotropic and composite cylindrical shells, accurate and simple fourth order governing equations. Journal of Applied Mechanics. 51:1984;736-744.
20. MARKOV P. Cheng's theory for shells of general curvature. Journal of Applied Mechanical Review. 35:1982;1088-1089.
21. PADOVAN J., LESTINGI J. F. Complex numerical integration procedure for static loading of anisotropic shells of revolution. Computers and Structures. 4:1974;1159-1172.
22. BASAR Y., DING Y. Finite rotation elements for the non-linear analysis of thin shell structures. International Journal of Solids and Structures. 26:1990;83-97.
23. VOYIADJIS G. Z., SHI G. A refined two-dimensional theory for thick cylindrical shells. International Journal of Solids and Structures. 27:1991;261-282.
24. REDDY J. N. Energy and Variational Methods in Applied Mechanics. 1984;John Wiley, New York.
25. F. B. HILDEBRAND, E. REISSNER, G. B. THOMAS, 1949, NACA-TN-1833, Notes on the foundations of the theory of small displacements of orthotropic shells.
26. NAGHDI P. M. On the theory of thin elastic shells. Quarterly Applied Mathematics. 14:1957;369-380.
27. REISSNER E. On a variational theorem in elasticity. Journal of Mathematics and Physics. 29:1950;90-95.
28. DONG S. B., TSO F. K. W. On a laminated orthotropic shell theory including transverse shear deformation. Journal of Applied Mechanics. 39:1972;1091-1096.
29. REISSNER E. The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics. 12:1945;37-45.
30. E. REISSNER, 1950, NACA Report No. 975, Small bending and stretching of sandwich-type shells.
31. MINDLIN R. D. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics. 18:1951;31-38.
32. WHITNEY J. M. Shear correction factors for orthotropic laminates under static load. Journal of Applied Mechanics. 40:1973;302-304.
33. BERT C. W. Simplified analysis of static shear factors for beams of nonhomogeneous cross section. Journal of Composite Materials. 7:1973;525-529.
34. LEVINSON M. An accurate simple theory of the static and dynamic of elastic plates. Mechanics Research Communications. 7:1980;343-350.
35. REDDY J. N. A simple higher order theory for laminated composite plates. Journal of Applied Mechanics. 51:1984;745-752.
36. BHIMARADDI A. A higher order theory for free vibration analysis of circular cylindrical shells. International Journal of Solids and Structures. 20:1984;623-630.
37. GULATI S. T., ESSENBURG F. Effects of anisotropy in axisymmetric cylindrical shells. Journal of Applied Mechanics. 34:1967;659-666.
38. ZUKAS J. A., VINSON J. R. Laminated transversely isotropic cylindrical shells. Journal of Applied Mechanics. 38:1971;400-407.
39. HSU T. M., WANG J. T. S. A theory of laminated cylindrical shells consisting of layers of orthotropic lamina. AIAA Journal. 8:1970;2141-2146.
40. CHAUDHURI R. A., ABU-ARJA K. R. Closed-form solutions for arbitrary-laminated anisotropic cylindrical shells (tubes) including shear deformation. AIAA Journal. 27:1989;1597-1605.
41. KHDEIR A. A., LIBRESCU L., FREDERICK D. A shear deformable theory of laminated composite shallow shell-type panels and their response analysis I: static response. Acta Mechanica. 77:1989;1-12.
42. WHITNEY J. M., SUN C. T. A higher order theory for extensional motion of laminated anisotropic shells and plates. Journal of Sound and Vibration. 30:1973;85-97.
43. WHITNEY J. M., SUN C. T. A refined theory for laminated anisotropic cylindrical shells. Journal of Applied Mechanics. 41:1974;47-53.
44. REDDY J. N. Exact solutions of moderately thick laminated shells. Journal of Engineering Mechanics ASCE. 110:1984;794-809.
45. SANDERS J. L. Nonlinear theories for thin shells. Quarterly Applied Mathematics. XXI:1962;21-36.
46. TOURATIER M. A generalization of shear deformation theories for axisymmetric multilayered shells. International Journal of Solids Structures. 29:1992;1379-1399.
47. HE JI-FAN. Static analysis of laminated shells using a refined shear deformation theory. Journal of Reinforced Plastics and Composites. 14:1995;652-674.
48. SCIUVA D. M. An improved shear deformation theory for moderately thick multilayered anisotropic shells and plates. ASME Journal of Applied mechanics. 54:1987;589-596.
49. REISSNER E. On a certain mixed variational theorem and on laminated elastic shell. Theory in Refined Dynamic Theory of Beams, Plates and Shells. 1987;Springer-Verlag, Berlin. p. 17-27.
50. JING H. S., TZENG K. G. Refined shear deformation theory of laminated shells. AIAA Journal. 31:1993b;765-773.
51. JING H. S., LIAO M. L. Partial hybrid stress element for the analysis of thick-laminated composite plates. International Journal of Numerical Methods in Engineering. 28:1989;2813-2827.
52. KANT T., RAMESH C. K. Analysis of thick orthotropic shells. Proceedings of the IASS World Congress on Space Enclosures, Montreal Canada. 1976;401-409.
53. GRIGOLYUK E. I., KULIKOV G. M. General direction of development of the theory of multi-layered shells. Mechanics of Composite Materials. 24:1988;231-241.
54. JONES R. J. Mechanics of Composite Materials. 1975;McGraw-Hill, New York.
55. WHITNEY J. M., PAGANO N. J. Shear deformation in heterogeneous plates. Journal of Applied Mechanics. 37:1970;1031-1036.
56. BERT C. W. Structural theory or laminated anisotropic elastic shells. Journal of Composite Materials. 1:1967;414-423.
57. PAGANO N. J. Exact solutions for composite laminates in cylindrical bending. Journal of Composite Materials. 3:1969;398-411.
58. PAGANO N. J. Influence of shear coupling in cylindrical bending of anisotropic laminates. Journal of Composite Materials. 4:1970;330-343.
59. PAGANO N. J. Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials. 4:1970;20-34.
60. PAGANO N. J., WANG A. S. D. Further study of composite laminates under cylindrical bending. Journal of Composite Materials. 5:1971;521-528.
61. SRINIVAS S., RAO A. K. Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. International Journal of Solids Structures. 6:1970;1463-1481.
62. REN J. G. Exact solutions for laminated cylindrical shells in cylindrical bending. Composites Science Technology. 29:1987;81-90.
63. HIRANO Y. Buckling of angle ply laminated circular cylindrical shells. Journal of Applied Mechanics. 46:1979;233-234.
64. REDDY J. N., CHAO W. C. A comparison of closed form and finite element solutions of thick, laminated, anisotropic rectangular plates. Nuclear Engineering and Design. 64:1981;153-167.
65. REDDY J. N., PHAN N. D. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory. Journal of Sound and Vibration. 98:1985;157-170.
66. SOLDATOS K. P., TZIVANIDIS G. J. Buckling and vibration of cross-ply laminated circular cylindrical panels. Journal of Applied Mathematics and Physics. 33:1982;230-240.
67. SOLDATOS K. P., TZIVANIDIS G. J. Buckling and vibration of cross-ply laminated non circular cylindrical panels. Journal of Sound and Vibration. 82:1982;425-434.
68. CHENG S., HO B. P. Stability of heterogeneous aeolotropic cylindrical shells under combined loading. AIAA Journal. 1:1963;892-898.
69. WIDERA G. E. O., CHUNG S. W. A theory for non-homogeneous anisotropic cylindrical shells. Journal of Applied Mathematics and Physics. 21:1970;378-399.
70. WIDERA G. E. O., LOGAN D. L. Refined theories for non-homogeneous anisotropic cylindrical shells: Part I - derivation. Journal of Engineering Mechanics Division ASCE. 106:1980;1053-1074.
71. NOOR A. K., PETERS J. M. Vibration analysis of laminated anisotropic shells of revolution. Computer Methods in Applied Mechanics and Engineering. 61:1987;277-301.
72. ZIENKIEWICZ O. C. The Finite Element Method. 1989;McGraw-Hill, New York.
73. LIBRESCU L., SCHMIDT R. Refined theories of elastic anisotropic shells accounting for small strains and moderate rotations. International Journal of Non-Linear Mechanics. 23:1988;217-229.
74. KANT T., KOMMINENI. Geometrically non-linear analysis of doubly curved laminated and sandwich fibre reinforced composite shells with a higher order theory and Co finite elements. Journal of Reinforced Plastic and Composites. 11:1992;1049-1076.
75. FIGÜEIRAS J. A., OWEN D. R. J. Analysis of elasto-plastic and geometrically non-linear anisotropic plates and shells. Hinton E., Owen D. R. J. Finite Element Software for Plates and Shells. 1984;Swansea Pineridge Press.
76. KUI L. X., LIU G. Q., ZIENKIEWICZ O. C. A generalized displacement method for the finite element analysis of thin shells. International Journal of Numerical Methods in Engineering. 21:1985;2145-2155.
77. PRYOR C. W., BARKER R. M. A finite element analysis including transverse shear effects for applications to laminated plates. AIAA Journal. 9:1971;912-917.
78. HINRICHSEN R. L., PALAZOTTO A. N. Non-linear finite element analysis of thick composite plates using a cubic spline function. AIAA Journal. 24:1986;1836-1842.
79. SCHMIT L. A., MONFORTON G. R. Finite deflection discrete element analysis of sandwich plates and cylindrical shells with laminated faces. AIAA Journal. 8:1970;1454-1461.
80. MEROUEH K. A. On a formulation of a non-linear theory of plates and shells with applications. Computers and Structures. 24:1986;691-705.
81. SURANA K. S. Geometrically non-linear formulation for curved shell elements. International Journal of Numerical Methods in Engineering. 19:1983;581-615.
82. SURANA K. S. A generalized geometrically non-linear formulation with large rotations for finite elements with rotational degree of freedom. Computers and Structures. 24:1986;47-55.
83. DONG S. B. Free vibration of laminated orthotropic cylindrical shells. Journal of Acoustical Society of America. 44:1968;1628-1635.
84. FLÜGGE W., KELKAR V. S. The problem of an elastic circular cylinder. International Journal of Solids and Structures. 4:1968;397-420.
85. YAO J. C. Long cylindrical tube subjected to two diametrically opposite loads. The Aeronautical Quarterly. 20:1969;365-381.
86. VARADAN T. K., BHASKAR K. Bending of laminated orthotropic cylindrical shells - an elasticity approach. Composite Structures. 17:1991;141-156.
87. PAGANO N. J. The stress field in a cylindrically anisotropic body under two-dimensional surface traction. Journal of Applied Mechanics. 39:1972;791-796.
88. REN J. G. Analysis of simply supported laminated circular cylindrical shell roofs. Composite Science and Technology. 11:1989;277-292.
89. LEISSA A. W., LEE J. K., WANG A. J. Vibrations of cantilevered shallow cylindrical shells of rectangular planform. Journal of Sound and Vibration. 78:1981;311-328.
90. BERT C. W., FRANCIS P. H. Composite material mechanics: structural mechanics. AIAA Journal. 12:1974;1173-1186.
91. BERT C. W., KUMAR M. Vibration of cylindrical shells of bimodulus composite materials. Journal of Sound and Vibration. 81:1982;107-121.
92. HSU Y. S., REDDY J. N., BERT C. W. Thermoelasticity of circular cylindrical shells laminated of bimodulus composite materials. Journal of Thermal Stresses. 4:1981;155-177.
93. WHITNEY J. M., LEISSA A. W. Analysis of heterogeneous anisotropic plates. Journal of Applied Mechanics. 36:1969;261-266.
94. BERT C. W., CHEN T. L. C. Effect of shear deformation on vibration of anti-symmetric angle-ply laminated rectangular plates. International Journal of Solids and Structures. 14:1978;465-473.
95. JING S. H., TZENG. Analysis of thick laminated anisotropic cylindrical shells using a refine shell theory. International Journal of Solids and Structures. 32:1995;1459-1476.
96. SUZUKI K., LEISSA A. W. Free vibrations of non-circular cylindrical shells having circumferentially varying thickness. Journal of Applied Mechanics. 52:1985;149-154.
97. SUZUKI K., LEISSA A. W. Exact solutions for the free vibrations of open cylindrical shells with circumferentially varying curvature and thickness. Journal of Sound and Vibration. 107:1986;1-15.
98. JING H. S., TZENG K. G. Approximate elasticity solution for laminated anisotropic finite cylinders. AIAA Journal. 31:1993;2121-2129.
99. REDDY J. N. A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures. 20:1984;881-896.
100. JING H. S., TZENG K. G. On two mixed variational principles for thick laminated composite plates. Composite Structures. 23:1993a;319-337.
101. MINDLIN R. D., MEDICK M. A. Extensional vibrations of elastic plates. Journal of Applied Mechanics. 26:1959;561-569.
102. REN-HUAI L., LING-HUI H. A simple theory for non-linear bending of laminated composite rectangular plates including higher-order effects. International Journal of Non-Linear Mechanics. 26:1991;537-545.
103. SHAMES I. H., DYM C. L. Energy and Finite Element Methods in Structural Mechanics. 1985;McGraw-Hill, New York.
104. BRAUSH D. O., ALMROTH B. O. Buckling of Bars, Plates and Shells. 1975;McGraw-Hill, New York.
105. J. M. ROTTER, P. T. JUMISKI, 1988, Research Report No. R563, The University of Sydney, Non-linear strain-displacement relations for axisymmetric thin shells.
106. FU Y. M., CHIA C. Y. Non-linear vibration and post buckling of general laminated circular cylindrical thick shells with non-uniform boundary conditions. International Journal of Non-Linear Mechanics. 28:1993;313-327.
107. CHU H. N. Influence of large amplitude on flexural vibrations of a thin circular cylindrical shells. Journal Aeronautical Science. 28:1961;602-609.
108. NOWINSKI J. L. Non-linear transverse vibrations of orthotropic cylindrical shells. AIAA Journal. 1:1963;617-620.
109. D. A. EVENSON, 1967, NASA TN D- 4090, Non-linear flexural vibrations of thin walled circular cylinders.
110. ATLURI S. A perturbation analysis of non-linear flexural vibrations of a circular cylindrical shell. International Journal of Solids and Structures. 8:1972;549-569.
111. CHEN J. C., BABCOCK C. D. A perturbation analysis of non-linear flexural vibrations of a circular cylindrical shell. AIAA Journal. 13:1975;868-876.
112. RAMACHANDRAN J. Non-linear vibrations of cylindrical shells of varying thickness in an incompressible fluid. Journal of Sound and Vibration. 64:1979;97-106.
113. KHOT N. S. Buckling and post buckling behaviour of composite cylindrical shells under axial compression. AIAA Journal. 8:1970;229-235.
114. IU V. P., CHIA C. Y. Non-linear vibration and post-buckling of unsymmetric cross-ply circular cylindrical shells. International Journal of Solids Structure. 24:1988;195-210.
115. LIBRESCU L. Refined geometrically nonlinear theories of anisotropic laminated shells. Quarterly Applied Mathematics. 45:1987;1-22.
116. REDDY J. N., CHANDRASHEKHARA K. Nonlinear analysis of laminated shells including transverse shear strains. AIAA Journal. 23:1985;440-441.
117. ROTHERT H., DI S. Geometrically nonlinear analysis of laminated shells by hybrid formulation and higher order theory. IASS Bulletin. 35:1994;15-32.
118. NOOR A. K., PETERS J. M. Non-linear analysis of anisotropic panels. AIAA Journal. 24:1986;1545-1553.
119. STEIN M. Non-linear theory for plates and shells includes the effects of transverse shearing. AIAA Journal. 24:1986;1537-1544.
120. PALAZOTTO A. N., WITT W. P. Formulation of a non-linear compatible finite elements for analysis of laminated composites. Computers and Structures. 21:1985;1213-1234.
121. DENNIS S. T., PALAZOTTO A. N. Static response of a cylindrical composite panel with cutouts using a geometrically non-linear theory. AIAA Journal. 28:1990;1082-1088.
122. TSAI C. T., PALAZOTTO A. N. On the finite element analysis of non-linear vibration for cylindrical shells with high-order shear deformation theory. International Journal of Non-Linear Mechanics. 26:1991;379-388.
123. MARTIN R. E., DREW D. Non-Linear Analysis of Anisotropic Shells of Revolution. 1971;Texas A&M University, Inst of statistic.
124. BUDIANSKY B., RADKOWSKI P. Numerical analysis of unsymmetrical bending shells of revolution. AIAA Journal. 1:1963;1833-1842.
125. 0finite elements. Computers and Structures. 52:1994;1243-1259.
126. DOWELL E. H., VENTRES C. S. Modal equations for non-linear flexural vibrations of cylindrical shells. International Journal of Solids and Structures. 4:1968;975-991.
127. HORRIGMOE G., BERGAN P. G. Incremental variational principles and finite element models for non-linear problems. Computer Methods in Applied Mechanics and Engineering. 7:1976;201-217.
128. WUNDERLICH W. Incremental formulation for geometrically non-linear problems. Bathe K. J., Oden J. T., Wunderlich W. Formulations and Computational Algorithms in Finite Element Analysis. 1977;193-239 MIT Press, Cambridge.
129. STRICKLIN J. A., HAISLER W. E., VON REISEMAN W. A. Evaluation of solution procedures for materials and/or geometrical non-linear structural analysis. AIAA Journal. 11:1973;292-299.
130. NOOR A. K., HARTLEY S. J. On linear shell analysis via mixed isoparametric elements. Computers and Structures. 7:1977;615-626.
131. CHAO W. C., REDDY J. N. Geometrically non-linear analysis of layered composite shell. Dvorak G. J. Mechanics of Composite Materials. 58:1983;19-31 AMD, New York.
132. WU R. W. H., WITMER E. A. The dynamic responses of cylindrical shells including Geometric and material non linearities. International Journal of Solids and Structures. 10:1974;243-260.
133. DATT G., TOUZOT G. Une présentation de la méthode des éléments finis. 1984;Moloine SA Editeur, Paris.
134. BATHE K. J. Finite Element Procedure in Engineering Analysis. 1982;Prentice-Hall, Englewood Cliffs.
135. REDDY J. N. An Introduction to the Finite Element Method. 1984;McGraw-Hill, New York.
136. GALLAGHER R. H. Introduction aux éléments finis. 1986;Prentice-Hall, Englewood Cliffs.
137. LAKIS A. A., PAÏDOUSSIS M. P. Free vibration of cylindrical shells partially filled with liquid. Journal of Sound and Vibration. 19:1971;1-15.
138. LAKIS A. A., PAÏDOUSSIS M. P. Prediction of the response of a cylindrical shell to arbitrary of boundary layer-induced random pressure field. Journal of Sound and Vibration. 25:1972;1-27.
139. LAKIS A. A., PAÏDOUSSIS M. P. Dynamic analysis of axially non-uniform thin cylindrical shells. Journal of Mechanical Engineering Science. 14:1972;49-71.
140. LAKIS A. A. Effects of fluid pressures on the vibration characteristics of cylindrical vessels. Proceedings of the International Conference on Pressure Surges, London, UK. 1976;11-15.
141. LAKIS A. A., DORÉ R. General Method for Analysing Contact Stresses on Cylindrical Vessels. International Journal Solids and Structures. 14:1978;499-516.
142. LAKIS A. A., LAVEAU A. Non-linear dynamic of anisotropic cylindrical shells containing a flowing fluid. International Journal of Solids and Structures. 28:1991;1079-1094.
143. LAKIS A. A., SINNO M. Free vibration of axisymmetric and beam-like cylindrical shells partially filled with liquid. International Journal for Numerical Methods in Engineering. 33:1992;235-268.
144. SELMANE A., LAKIS A. A. Vibration analysis of anisotropic open cylindrical shells containing flowing fluid. Journal of Fluids and Structures. 11:1997;111-134.
145. SELMANE A., LAKIS A. A. Influence of geometric non-linearities on the vibration of orthotropic open cylindrical shells. International Journal for Numerical Methods in Engineering. 40:1997;1115-1137.
146. SELMANE A., LAKIS A. A. Non-linear dynamic analysis of orthotropic open cylindrical shells subjected to a flowing fluid. Journal of Sound and Vibration. 202:1997;67-93.
147. SELMANE A., LAKIS A. A. Dynamic analysis of anisotropic open cylindrical shells. Journal of Computers and Structures. 62:1997;1-12.
148. LAKIS A. A., TUY N. Q., SELMANE A. Analysis of axially non-uniform thin spherical shells. Proceedings of the International Symposium on Structural Analysis and Optimization, Paris, France. 1989;80-85.
149. LAKIS A. A., VAN DYKE P., OURICHE H. Dynamic analysis of anisotropic fluid-filled conical shells. Journal of Fluids and Structures. 6:1992;135-162.
150. LAKIS A. A., SELMANE A. Analysis of non-uniform circular and annular plates. Proceedings of Third International Conference on Numerical Methods in Engineering, Swansea. 1990;239-248.
151. LAKIS A. A., SELMANE A. Hybrid finite element analysis of non-uniform circular and annular plates. Proceedings of the International Conference on Advances in Structural Testing, Analysis and Design, Bangalore, India. 1990;499-505.
152. LAKIS A. A., SELMANE A. Classical solution shape functions in the finite element analysis of circular and annular plates. International Journal for Numerical Methods in Engineering. 40:1997;969-990.
153. PAÏDOUSSIS M. P., DENIS J. P. Flutter of thin cylindrical shells conveying fluid. Journal of Sound and Vibration. 20:1972;9-26.
154. WEAVER D. S., UNNY T. E. On the dynamic stability of fluid conveying pipes. Journal of Applied Mechanics ASME. 40:1973;48-52.
155. CHENG L. Fluid-structural coupling of a plate ended cylindrical shell: vibration and internal sound field. Journal of Sound and Vibration. 174:1994;641-654.
156. JAIN R. K. Vibration of fluid-filled, orthotropic cylindrical shells. Journal of Sound and Vibration. 37:1974;379-388.
157. PAÏDOUSSIS M. P., LI G. X. Pipes conveying fluid: a model dynamical problem. Journal of Fluids and Structure. 7:1993;137-204.
158. AU-YANG M. K. Dynamics of coupled fluid-shells. ASME Journal of Vibration, Acoustics and Reliability in Design. 108:1986;339-347.
159. BROWN S. J. A survey of studies in to the hydrodynamic response of fluid-coupled circular cylinders. ASME Journal of Pressure Vessels Technology. 104:1982;2-19.
160. BRENNEMAN B., AU-YANG M. K. Fluid-structure dynamics with modal hybrid method. Journal of Pressure Vessel Technology. 114:1992;133-138.
161. CROUZET-PASCAL, GARNET H. Response of a ring-reinforced cylindrical shell, immersed in a fluid medium, to an axisymmetric step pulse. Journal of Applied Mechanics. 39:1972;521-526.
162. MACNEAL R. H., CITERLEY R., CHRGIAN M. A new method for analysing fluid-structure interaction using MSC/NASTRAN. Transactions of the Fifth International Conference on Structural Mechanics in Reactor Technology, PaperB4/9 , Berlin, Germany. 1979.
163. GONÇALVES P. B., BATISTA R. C. Frequency response of cylindrical shells partially submerged or field with liquid. Journal of Sound and Vibration. 113:1987;59-70.
164. HAN R. P. S., LIU J. P. Free vibration analysis of a fluid-loaded variable thickness cylindrical tanks. Journal of Sound and Vibration. 176:1994;235-253.
165. LIBRESCU L. Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures. 1975;Noordhoff International Publishing, Leyden.
166. LIBRESCU L. On the theory of multilayered anisotropic shells. Part I (Translation Plenum Press, U.S.A.). Mechanika Polimerov. 1975;1038-1050.
167. LIBRESCU L. On the theory of multilayered anisotropic shells. Part II (Translation Plenum Press, U.S.A.). Mechanika Polimerov. 1976;100-109.
168. BRULL M., LIBRESCU L. Strain measures and compatibility equations in the linear high-order shell theories. Quarterly Journal of Applied Mathematics. 40:1982;15-25.