Stability of composite structural members (three-dimensional formulation)

International Applied Mechanics

Volumn 38, Issue 9, 2002, Pages 1048-1075

  Babich, I Yu ^a   Guz, A N ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; BOUNDARY CONDITIONS; BUCKLING; COMPOSITE MATERIALS; COMPRESSIVE STRENGTH; ELASTIC MODULI; FRACTURE TOUGHNESS; LINEAR EQUATIONS; LOAD LIMITS; SHEAR STRENGTH; STIFFNESS; STRESS ANALYSIS;

CRITICAL LOADS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0036936952     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021707413663     Document Type: Article

References (93)

1. S. A. Ambartsumyan, The Theory of Anisotropic Plates, Nauka, Moscow (1967).
2. S. A. Ambartsumyan, The General Theory of Anisotropic Shells, Nauka, Moscow (1974).
3. I. Yu. Babich, "On the stability of the equilibrium of an orthotropic cylindrical shell," in: Proc. 7th All-Union Conf. on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1970), pp. 76-79.
4. I. Yu. Babich, "Equilibrium stability problems for three-dimensional orthotropic bodies under small strains," Prikl. Mekh., 6, No. 2, 16-24 (1972).
5. I. Yu. Babich, "On the stability of rectangular and circular plates under small strains," Dop. AN URSR, Ser. A, No. 2, 138-142 (1974).
6. I. Yu. Babich, "Analysis of three-dimensional and applied formulations in the theory of stability of composite rods," Prikl. Mekh., 25, No. 2, 7-12 (1989).
7. I. Yu. Babich, "Analysis of design models in the theory of stability of composite rods, plates, and shells," Prikl. Mekh., 29, No. 10, 94-100 (1993).
8. I. Yu. Babich and A. N. Guz, "On the influence of the properties of a plate on the critical force," Mekh. Polim., No. 2, 355-357 (1969).
9. I. Yu. Babich and A. N. Guz, "On the influence of the properties of a circular rod on the critical force," Stroit. Mekh. Rasch. Sooruzh., No. 4, 55-57 (1969).
10. I. Yu. Babich and A. N. Guz, "Stability of a transversely isotropic cylindrical shell under axial compression," Mekh. Polim., No. 6, 1064-1068 (1969).
11. I. Yu. Babich and A. N. Guz, "Stability of composite rods, plates, and shells (three-dimensional formulation)," Prikl. Mekh., 19, No. 10, 3-19 (1983).
12. I. Yu. Babich, A. N. Guz, and L. V. Deriglazov, "Stability analysis of three-layer spherical shells," Prikl. Mekh., 19, No. 17, 19-23 (1983).
13. I. Yu. Babich, A. N. Guz, and L. V. Deriglazov, "Stability of three-layer anisotropic cylindrical shells," Prikl. Mekh., 19, No. 9, 13-20 (1983).
14. I. Yu. Babich, A. N. Guz, I. I. Chernushenko, and N. A. Shul'ga, "Estimation of the accuracy of stability theories for cylindrical shells under external pressure," Prikl. Mekh., 10, No. 10, 16-21 (1974).
15. I. Yu. Babich and L. V. Deriglazov, "On the stability of three-layer anisotropic cylindrical shells," Dokl. AN USSR, Ser. A, No. 2, 26-29 (1982).
16. I. Yu. Babich and L. V. Deriglazov, "Stability of a three-layer spherical shell," Dokl. AN USSR, Ser. A, No. 8, 31-33 (1982).
17. I. Yu. Babich, L. V. Deriglazov, and I. I. Chernushenko, "On the influence of the properties of a spherical shell on the critical load," Mekh. Komp. Mater., No. 2, 281-285 (1980).
18. I. Yu. Babich and V. I. Kilin, "On the stability of a three-layer orthotropic cylindrical shell under axial compression," Prikl. Mekh., 21, No. 6, 44-49 (1985).
19. I. Yu. Babich and V. I. Kilin, "Study into the effect of the asymmetric arrangement of the layers on the stability of three-layer cylindrical shells under axial compression," 19, 103-106, Khar'kov-Donetsk (1988).
20. I. Yu. Babich, I. I. Chernushenko, and N. A. Shul'ga, "On the stability of an axially compressed orthotropic cylindrical shell under nonaxisymmetric strains," Prikl. Mekh., 10, No. 8, 102-107 (1974).
21. I. Yu. Babich, I. I. Chernushenko, and N. A. Shul'ga, "Comparative analysis of applied stability theories for composites plates and cylindrical shells," Soprot. Mater. Teor. Sooruzh., No. 25, 22-26, Budivel'nyk, Kiev (1975).
22. V. V. Bolotin, Nonconservative Problems in the Theory of Elastic Stability [in Russian], Fizmatgiz, Moscow (1961).
23. V. V. Bolotin, "Reducing three-dimensional problems of the theory of elastic stability to one- or two-dimensional problems," in: Stability Problems in Structural Mechanics [in Russian], Stroiizdat, Moscow (1965), pp. 166-179.
24. V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayered Structures [in Russian], Mashinostroenie, Moscow (1980).
25. G. A. Vanin, N. P. Semenyuk, and R. F. Emel'yanov, Stability of Reinforced Shells [in Russian], Naukova Dumka, Kiev (1978).
26. V. V. Vlasov, "Stability analysis of orthotropic cylindrical shells with a filler," Prikl Mekh., 11, No. 11, 45-49 (1975).
27. V. V. Vlasov, "Stability of orthotropic shells with a filler under external pressure," Dokl. AN USSR, Ser. A, No. 10, 899-902 (1976).
28. V. V. Vlasov and A. N. Guz, "Stability analysis of thin-walled cylindrical shells with a filler under axial compression," Izv. AN SSSR, MTT, No. 5, 93-95 (1970).
29. K. F. Voitsekhovskaya, "Rod equilibrium stability from the viewpoint of the mathematical theory of elasticity," Dokl. AN SSSR, 119, No. 5, 903-906 (1958).
30. A. S. Vol'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).
31. K. Z. Galimov, "The nonlinear Timoshenko-type theory of thin shells," in: Studies in the Theory of Plates and Shells [in Russian], Izd. Kazanskogo Univ., Kazan' (1975), pp. 92-126.
32. S. K. Godunov, "On the numerical solution of boundary-value problems for systems of ordinary differential equations," Usp. Mat. Nauk, 16, No. 3, 171-174 (1961).
33. É. I. Grigolyuk and P. P. Chulkov, Stability and Vibrations of Three-Layer Shells [in Russian], Mashinostroenie, Moscow (1973).
34. A. N. Guz, "The general solutions to the three-dimensional linearized equations of the theory of elastic stability," Dop. AN URSR, Ser. A, No. 1, 56-60 (1967).
35. A. N. Guz, "Stability analysis of elastic systems by the three-dimensional linearized elastic equations," Prikl. Mekh., 3, No. 2, 20-29 (1967).
36. A. N. Guz, "Stability of orthotropic bodies," Prikl. Mekh., 3, No. 5, 40-51 (1967).
37. A. N. Guz, "On the accuracy of the Kirchhoff-Love hypothesis in determining the critical forces under the theory of stability," Dokl. AN SSSR, 179, No. 3, 552-554 (1968).
38. A. N. Guz, "On the stability of three-dimensional elastic bodies," Prikl. Mat. Mekh., No. 5, 930-935 (1968).
39. A. N. Guz, "On the stability of a strip," Izv. AN SSSR, MTT, No. 6, 111-113 (1969).
40. A. N. Guz, "On linearized problems in the theory of elasticity," Prikl. Mat. Mekh., 6, No. 6, 3-11 (1970).
41. A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kiev (1971).
42. A. N. Guz, "A note on linearized problems in the theory of elasticity," Prikl. Mekh., 8, No. 1, 10-16 (1972).
43. A. N. Guz, Stability of Elastic Bodies under Finite Strains [in Russian], Naukova Dumka, Kiev (1973).
44. A. N. Guz, Fundamentals of Stability Theory for Mine Openings [in Russian], Naukova Dumka, Kiev (1977).
45. A. N. Guz, Stability of Elastic Bodies under Triaxial Compression [in Russian], Naukova Dumka, Kiev (1979).
46. A. N. Guz, "Analysis of design models in the theory of stability of structural members made of composite materials," Dokl. AN USSR, Ser. A, No. 7, 616-624 (1976).
47. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kiev (1986).
48. A. N. Guz, Fracture Mechanics of Composites under Compression [in Russian], Naukova Dumka, Kiev (1990).
49. A. N. Guz and I. Yu. Babich, The Three-Dimensional Theory of Elastic Stability of Rods, Plates, and Shells [in Russian], Vyshcha Shkola, Kiev (1980).
50. A. N. Guz and I. Yu. Babich, The Three-Dimensional Theory of Stability of Deformable Bodies, Vol. 4 of the six-volume series Spatial Problems in the Theory of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1985).
51. A. N. Guz, I. Yu. Babich, B. L. Pelekh, and G. A. Teters, "On the applicability of applied two-dimensional theories to stability problems for cylindrical shells with low shear stiffness under axial compression," Mekh. Polim., No. 1, 141-143 (1970).
52. A. N. Guz, V. S. Zelenskii, and Yu. V. Kokhanenko, "On the solution of spatial problems in the three-dimensional theory of elastic stability of plates and rods with inhomogeneous subcritical states," Mekh. Komp. Mater., No. 1, 49-52 (1980).
53. A. N. Guz and Yu. V. Kokhanenko, "Solution of plane problems in the three-dimensional theory of elastic stability when subcritical strains are inhomogeneous," Prikl. Mekh., 13, No. 12, 63-72 (1977).
54. A. N. Guz and D. A. Musaev, "On the stability of a transversely isotropic noncircular rod," Prikl. Mekh., 16, No. 7, 82-88 (1980).
55. A. N. Guz, B. L. Pelekh, I. Yu. Babich, and G. A. Teters, "On the applicability limits of applied theories to stability problems for rods and plates with low shear stiffness under uniaxial compression," Mekh. Polim., No. 6, 1124-1126 (1969).
56. M. A. Il'gamov, V. A. Ivanov, and B. V. Gulin, Strength, Stability, and Dynamics of Shells with an Elastic Filler [in Russian], Nauka, Moscow (1977).
57. A. Yu. Ishlinskii, "Stability of the equilibrium of elastic bodies from the viewpoint of the mathematical theory of elasticity," Ukr. Mat. Zh., 4, No. 2, 140-146 (1954).
58. Yu. V. Kokhanenko, "Solution of a three-dimensional stability problem for a plate in an inhomogeneous subcritical state," Prikl. Mekh., 12, No. 2, 117-119 (1976).
59. L. G. Leibenzon, "On the application of harmonic functions in the stability analysis of spherical and cylindrical shells," in: Collected Works [in Russian], Vol. 1, Izd. AN SSSR, Moscow (1951), pp. 50-83.
60. S. G. Lekhnitskii, The Theory of Elasticity of Anisotropic Body [in Russian], Nauka, Moscow (1977).
61. A. I. Malmeister, V. P. Tamuzh, and G. A. Teters, Resistance of Polymeric and Composite Materials [in Russian], Zinatne, Riga (1980).
62. A. N. Guz, L. P. Khoroshun, G. A. Vanin et al., Mechanics of Materials, Vol. 1 of the three-volume series A. N. Guz (general editor), Mechanics of Composites and Structural Members [in Russian], Naukova Dumka, Kiev (1982).
63. A. N. Guz, Ya. M. Grigorenko, I. Yu. Babich et al., Mechanics of Structural Members, Vol. 2 of the three-volume series A. N. Guz (general editor), Mechanics of Composites and Structural Members [in Russian], Naukova Dumka, Kiev (1983).
64. A. N. Guz, I. Yu. Babich, D. V. Babich et al., Stability of Structural Members, Vol. 10 of the twelve-volume series A. N. Guz (general editor), Mechanics of Composites [in Russian], A.S.K., Kiev (2001).
65. D. A. Musaev, "Stability of a transversely isotropic rod of rectangular cross section," Izv. AN AzSSR, Ser. Fiz.-Mat. Nauk, 16, No. 3, 37-42 (1980).
66. D. A. Musaev, "Stability of a transversely isotropic rod of elliptic cross section," Izv. AN AzSSR, Ser. Fiz.-Mat. Nauk, 16, No. 5, 110-115 (1990).
67. V. L. Narusberg and R. B. Rikards, "Influence of transverse shear on the stability of an orthotropic cylindrical shell with an elastic filler under axial compression," Mekh. Polim., No. 2, 267-273 (1973).
68. V. V. Novozhilov, Fundamentals of the Nonlinear Theory of Elasticity [in Russian], Gostekhizdat, Moscow (1948).
69. V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudpromgiz, Leningrad (1962).
70. B. L. Pelekh, Theory of Shells with Finite Shear Stiffness [in Russian], Naukova Dumka, Kiev (1973).
71. A. O. Rasskazov, I. I. Sokolovskaya, and N. A. Shul'ga, Theory and Design of Laminated Orthotropic Plates and Shells [in Russian], Vyshcha Shkola, Kiev (1983).
72. R. B. Rikards and G. A. Teters, Stability of Composite Shells [in Russian], Zinatne, Riga (1974).
73. A. A. Samarskii, An Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).
74. N. P. Semenyuk, "On the equations of the geometrically nonlinear Timoshenko-type theory of shells," Prikl. Mekh., 14, No. 2, 128-132 (1978).
75. I. I. Gol'denblat (ed.), Resistance of Fiberglasses [in Russian], Mashinostroenie, Moscow (1968).
76. S. N. Sukhinin, V. P. Troshin, and L. A. Troshina, "Stability analysis of three-layer cylinders under axial compression," Prikl. Probl. Prochn. Plastichn., 13, No. 2, 133-139 (1979).
77. Yu. M. Tarnopol'skii and A. V. Roze, Features of the Design of Reinforced-Plastic Parts [in Russian], Zinatne, Riga (1969).
78. G. A. Teters, Compound Loading and Stability of Polymeric Shells [in Russian], Zinatne, Riga (1969).
79. V. T. Tomashevskii, "On the influence of the transverse shear and stress state on the stability of an anisotropic cylinder," Prikl. Mekh., 2, No. 4, 7-16 (1966).
80. L. A. Troshina, "Stability of asymmetric three-layer cylindrical shells with a weakly rigid filler under axial compression," Mekh. Komp. Mater., No. 3, 472-475 (1983).
81. M. A. Biot, "Fundamental skin effect in anisotropic solid mechanics," Int. J. Solids Struct., 2, 645-663 (1966).
82. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer Verlag, Berlin (1999).
83. A. N. Guz, "Description and study of some nonclassical problems of fracture mechanics and related mechanisms," Int. Appl. Mech., 36, No. 12, 1537-1564 (2000).
84. A. N. Guz, "Constructing the three-dimensional theory of stability of deformable bodies," Int. Appl. Mech., 37, No. 1, 1-37 (2001).
85. A. N. Guz, "Elastic waves in bodies with initial (residual) stresses," Int. Appl. Mech., 38, No. 1, 23-59 (2002).
86. A. N. Guz and I. Yu. Babich, "Three-dimensional stability problems of composite materials and composite construction," Rozpr. Inz., 27, No. 3, 613-631 (1979).
87. A. N. Guz, I. Yu. Babich, and V. N. Chekhov, "The three-dimensional theory of stability of fibrous and laminated materials," Int. Appl. Mech., 37, No. 9, 1103-1141 (2001).
88. A. N. Guz and Yu. V. Kokhanenko, "Numerical solution of three-dimensional stability problems for elastic bodies," Int. Appl. Mech., 37, No. 11, 1369-1399 (2001).
89. A. N. Guz and F. G. Makhort, "The physical fundamentals of the ultrasonic nondestructive stress analysis of solids," Int. Appl. Mech., 36, No. 9, 1119-1149 (2000).
90. Yu. V. Kokhanenko, "Numerical study of three-dimensional stability problems for laminated and ribbon-reinforced composites," Int. Appl. Mech., 37, No. 3, 317-345 (2001).
91. "Micromechanics of composite materials: Focus on Ukrainian research," Appl. Mech. Reviews, Special Issue, 45, No. 2, 13-103 (1992).
92. E. Reissner, "On the theory of bending of elastic plates," J. Math. Phys., 23, No. 1, 184-191 (1944).
93. S. P. Timoshenko, "On the correction for shear of the differential equation for transverse vibrations of prismatic bars," Phil. Mag., 41, No. 6, 50-57 (1921).