The solution asymptotics of classical and nonclassical, static and dynamic boundary-value problems for thin bodies

International Applied Mechanics

Volumn 38, Issue 7, 2002, Pages 765-782

  Agalovyan, L A ^a  

^a INSTITUTE OF ORGANIC CHEMISTRY   (Armenia)

Author keywords

[No Author keywords available]

Indexed keywords

SEISMIC EFFECTS;

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; RESONANCE; VECTORS;

ELASTICITY;

EID: 0036412743     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020877123771     Document Type: Article

References (102)

1. L. A. Agalovyan, The Asymptotic Theory of Anisotropic Plates and Shells [in Russian], Nauka, Moscow (1997).
2. L. A. Agalovyan, "On the interaction of the boundary layer with the internal stress-strain state of a strip," Izv. AN Arm. SSR, Mekh., 30, No. 5, 48-62 (1997).
3. L. A. Agalovyan, "On the boundary layer in plates," Dokl. AN Arm. SSR, 45, No. 3, 149-155 (1972).
4. L. A. Agalovyan and Sh. M. Khachatryan, "Papkovich's generalized orthogonality and existence conditions for damped solutions in a plane problem for an orthotropic half-strip," Dokl. AN Arm. SSR, 50, No. 3, 157-163 (1975).
5. L. A. Agalovyan and Sh. M. Khachatryan, "Asymptotic stress-strain analysis of an orthotropic strip," Uch. Zap. Yerevanskogo Univ., Estestv. Nauki, No. 1 (134), 22-30 (1977).
6. L. A. Agalovyan and Sh. M. Khachatryan, "On some plane problems for an orthotropic strip," Uch. Zap. Yerevanskogo Univ., Estestv. Nauki, No. 2 (135), 20-26 (1977).
7. L. A. Agalovyan, A. V. Saakyan, and A. G. Sarkisyan, "On the stress-strain state of an anisotropic strip with variable elastic characteristics," Izv. NAN Arm., Mekh., 51, No. 1, 3-15 (1998).
8. L. A. Agalovyan and A. M. Khachatryan, "Asymptotic stress-strain analysis of an anisotropic laminated beam," Izv. AN Arm. SSR, Mekh., 39, No. 2, 3-14 (1986).
9. L. A. Agalovyan and A. M. Khachatryan, "A note on the solution of the first boundary-value problem for an anisotropic strip based on the geometrically nonlinear theory of elasticity," Izv. VUZov RF Severo-Kavkaz. Region, Estestv. Nauki, Special Edition, 16-18 (2001).
10. L. A. Agalovyan, "Asymptotic integration in the development of an approximate theory of anisotropic shells," Prikl. Mat. Mekh., 30, No. 2, 388-398 (1966).
11. L. A. Agalovyan, "The bending theory for orthotropic plates revisited," Izv. AN SSSR, Mekh. Tverd. Tela, No. 6, 114-121 (1966).
12. L. A. Agalovyan, "On the reduction of three-dimensional boundary conditions to two-dimensional in the theory of anisotropic plates," Uch. Zap. Yerevanskogo Univ., Estestv. Nauki, No. 2 (138), 20-27 (1978).
13. L. A. Agalovyan, "On the bending equations for anisotropic plates," in: Proc. 7th All-Union Conf. on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1970), pp. 17-21.
14. L. A. Agalovyan, Yu. M. Bagdasaryan, and A. M. Khachatryan, "Stress-strain analysis of plates with general anisotropy," Izv. NAN Armenii, Mekh., 49, No. 3, 10-22 (1996).
15. L. A. Agalovyan and A. G. Sarkisyan, "Derivation of the two-dimensional equations for inhomogeneous plates with general anisotropy," in: Issues of Optimal Control, Stability, and Strength of Mechanical Systems [in Russian], Izd. Yerevanskogo Univ., Yerevan (1997), pp. 180-186.
16. L. A. Agalovyan, "Some relations of the classical linear theory of anisotropic shells and possibilities for their refinement,"Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 109-120 (1972).
17. L. A. Agalovyan, "On allowing for transverse shears in design of orthotropic shells," in: Proc. 8th All-Union Conf. on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1973), pp. 7-13.
18. L. A. Agalovyan, "On the reduction of the three-dimensional elastic problem to two-dimensional for orthotropic shells and the errors of some applied theories," Dokl. AN Arm. SSR, 69, No. 3, 151-156 (1979).
19. L. A. Agalovyan, "On the structure of the solution to one class of plane elastic problems for an anisotropic body," in: Mechanics (Interuniversity Collection) [in Russian], Issue 2, Izd. Yerevanskogo Univ. (1982), pp. 7-12.
20. L. A. Agalovyan, "An elastic boundary layer for one class of plane problems," in: Mechanics (Interuniversity Collection) [in Russian], Issue 3, Izd. Yerevanskogo Univ., Yerevan (1984), pp. 51-58.
21. L. A. Agalovyan, "A note on the stress-strain analysis a two-layer strip and the validity of the Winkler hypothesis," in: Proc. 13th All-Union Conf. on the Theory of Plates and Shells [in Russian], Part 1, Tallinn (1983), pp. 13-18.
22. L. A. Agalovyan and S. Kh. Adamyan, "The stress-strain state of a two-layer rectangular strip with variable elastic characteristics," Izv. AN Arm. SSR, Mekh., 39, No. 5, 3-15 (1986).
23. L. A. Agalovyan and S. Kh. Adamyan, "On the modulus of subgrade reaction for substructures with variable elastic characteristics," Dokl. AN Arm. SSR, 84, No. 3, 115-118 (1987).
24. L. A. Agalovyan and G. G. Khachatryan, "On the asymptotic solution of elastic boundary-value problems for nonclassical domains," Dokl. AN Arm. SSR, 88, No. 5, 198-201 (1989).
25. L. A. Agalovyan and G. G. Khachatryan, "On the asymptotic solution of the second and mixed elastic boundary-value problems for an anisotropic strip of variable width," in: Solids Mechanics [in Russian], Izd. AN Arm. SSR (1993), pp. 33-41.
26. L. A. Agalovyan, R. S. Gevorkyan, and G. G. Khachatryan, "Mixed boundary-value problems for anisotropic plates of variable thickness," Prikl. Mat. Mekh., 60, No. 2, 290-298 (1996).
27. L. A. Agalovyan, R. S. Gevorkyan, and G. G. Khachatryan, "The asymptotic solution of mixed boundary-value problems for two-layer anisotropic plates of variable thickness," Izv. NAN Armenii, Mekh., 51, No. 2, 27-36 (1998).
28. L. A. Agalovyan and R. S. Gevorkyan, "The asymptotic solution of mixed boundary-value problems for a strip with rheological properties," in: Solids Mechanics [in Russian], Izd. AN Armenii (1993), pp. 25-32.
29. L. A. Agalovyan and R. S. Gevorkyan, "On the action of a concentrated and stepwise continuous load on a two-layer strip with elastic and viscoelastic layers," in: Proc. 1st All-Union Conf. on Technological Strength Problems for Supporting Structures [in Russian], 1, Part 2, Zaporozhye (1991), pp. 265-271.
30. L. A. Agalovyan and R. S. Gevorkyan, "The asymptotic solution of mixed boundary-value problems for a two-layer strip with elastic and rheological layers," Izv. RAN, Mekh. Tverd. Tela, No. 5, 120-128 (1992).
31. L. A. Agalovyan, R. S. Gevorkyan, and A. V. Saakyan, "On the asymptotic solution of boundary-value problems for incompressible strips," Dokl. NAN Armenii, 97, No. 3, 13-18 (1997).
32. L. A. Agalovyan and R. S. Gevorkyan, "On the action of a concentrated force on a two-layer strip," in: Proc. 6th All-Union Conf. on Composite Materials [in Russian], 2, Izd. Yerevanskogo Univ., Yerevan (1987), pp. 13-14.
33. L. A. Agalovyan, M. G. Asratyan, and R. S. Gevorkyan, "A note on the asymptotic solution for a two-layer strip under a concentrated force and stepwise continuous load," Prikl. Mat. Mekh., 54, No. 5. 831-836 (1990).
34. L. A. Agalovyan, M. G. Asratyan, and R. S. Gevorkyan, "A problem on a concentrated force acting on a strip," in: Mechanics (Interuniversity Collection) [in Russian], Issue 8, Izd. Yerevanskogo Univ., Yerevan (1991), pp. 61-70.
35. L. A. Agalovyan, "On the influence of boundary conditions on the stress-strain state of thin bodies," Izv. NAN i GIU RA, Tekhn. Nauki, 48, No. 3, 136-140 (1995).
36. L. A. Agalovyan and A. B. Tovmasyan, "On a mixed boundary-value problem for an anisotropic thermoelastic strip," Dokl. AN Arm. SSR, 92, No. 2, 76-81 (1991).
37. L. A. Agalovyan and A. B. Tovmasyan, "On the asymptotic solution of a mixed boundary-value problem for a two-layer thermoelastic strip," in: Topical Problems of Inhomogeneous Mechanics [in Russian], Yerevan (1991), pp. 5-10.
38. L. A. Agalovyan, "A note on the stress-strain analysis of a two-layer anisotropic strip with imperfect contact between the layers," Dokl. NAN Armenii, 95, No. 3, 146-150 (1995).
39. L. A. Agalovyan and A. B. Tovmasyan, "On the stress-strain state of a two-layer thermoelastic strip for imperfect contact between the layers," in: Modern Problems in the Mechanics of Contact Interactions [in Russian], Yerevan (1996), pp. 19-26.
40. L. A. Agalovyan and R. S. Gevorkyan, "Nonclassical boundary-value problems for plates with general anisotropy," in: The Mechanics of Composite Structures [in Russian], Nauka, Novosibirsk (1984), pp. 105-110.
41. L. A. Agalovyan and R. S. Gevorkyan, "On the asymptotic solution of nonclassical boundary-value problems for two-layer anisotropic thermoelastic shells," Izv. AN Arm. SSR, Mekh., 42, No. 3, 28-36 (1989).
42. L. A. Agalovyan and R. S. Gevorkyan, "On the asymptotic solution of mixed three-dimensional problems for two-layer anisotropic plates," Prikl. Mat. Mekh., 50, No. 2, 271-278 (1986).
43. L. A. Agalovyan and R. S. Gevorkyan, "On nonclassical boundary-value problems for three-layer thermoelastic plates and some applications," in: Proc. 14th All-Union Conf. on the Theory of Plates and Shells [in Russian], 1, Izd. Tbilisskogo Univ., Tbilisi (1987), pp. 28-34.
44. L. A. Agalovyan and A. B. Tovmasyan, "The asymptotic solution of a mixed three-dimensional internal problem for an anisotropic thermoelastic plate," Izv. NAN RA, Mekh., 46, No. 3, 3-11 (1993).
45. L. A. Agalovyan, "On the natural frequencies of an anisotropic strip," in: Proc. Sci. Conf. (on the occasion of the 60th anniversary of GPI) [in Russian], Armenia, Gyumri (1994), pp. 23-26.
46. L. A. Agalovyan and L. G. Gulgazaryan, "On the nature of the boundary layer in an orthotropic strip under natural vibrations," Dokl. NAN Armenii, 100, No. 4, 314-321 (2000).
47. L. A. Agalovyan and L. S. Sarkisyan, "On the natural vibrations of a two-layer orthotropic strip," in: Proc. 18th Int. Conf. on the Theory of Shells and Plates [in Russian], 1, Saratov (1997), pp. 30-38.
48. L. A. Agalovyan and L. G. Gulgazaryan, "On the natural frequencies and boundary layer for an orthotropic plate in a mixed boundary-value problem," Izv. NAN RA, Mekh., 54, No. 2, 32-41 (2001).
49. L. A. Agalovyan, "A note on the solution of some model dynamic problems of seismology," in: Proc. Int. Conf. on Applied and Mathematical Aspects of Natural Sciences [in Russian], Yerevan (1999), pp. 11-16.
50. L. A. Agalovyan and L. M. Khalatyan, "The asymptotics of the forced vibrations of an orthotropic strip with mixed boundary conditions," Dokl. NAN Armenii, 99, No. 4, 315-321 (1999).
51. L. A. Agalovyan, "The asymptotics of the natural and forced vibrations of anisotropic beams and plates," Izv. NAN Armenii, Ser. Tekhn. Nauk, 52, No. 3, 283-288 (1999).
52. L. A. Agalovyan and M. L. Agalovyan, "Nonclassical boundary-value problems on the natural and forced vibrations of anisotropic plates," in: Proc. 19th Int. Conf. on the Theory of Shells and Plates [in Russian], Izd. Nizhegorodskogo Univ., Nizhnii Novgorod (1999), pp. 16-21.
53. L. A. Agalovyan, "The asymptotic solution of dynamic mixed problems for anisotropic strips and plates," Izv. VUZov RF, Severo-Kavkaz. Region, Estestv. Nauki, 3, 8-11 (2000).
54. L. A. Agalovyan, "On one class of problems on the forced vibrations of anisotropic plates," in: Problem of the Mechanics of Thin Deformable Bodies [in Russian], Izd. NAN Armenii, Yerevan (2002), pp. 9-19.
55. L. A. Agalovyan, "On some results in the asymptotic theory of beams, plates, and shells," in: Problem of Solids Mechanics [in Russian], Izd. NAN Armenii, Yerevan (1997), pp. 31-50.
56. L. A. Agalovyan, "On the asymptotic method in the theory of plates and shells," in: The Mechanics of Shells and Plates in the 21st Century [in Russian], Izd. Saratovskogo Gos. Tekhn. Univ., Saratov (1999), pp. 129-151.
57. M. L. Agalovyan, "On one eigenvalue problem in seismology," Dokl. NAN Armenii, 96, No. 2, 23-28 (1996).
58. M. L. Agalovyan, "On eigenvalues and eigenfunctions of one differential operator," Uch. Zap. Yerevanskogo Univ., 2(187), 8-14 (1997).
59. M. L. Agalovyan, "On the boundary-layer solution for a strip under natural vibrations," in: Current Issues of Optimal Control and Stability of Systems [in Russian], Izd. Yerevanskogo Univ., Yerevan (1997), pp. 132-135.
60. M. L. Agalovyan, "On the determination of the natural frequencies and eigenfunctions in a three-dimensional mixed boundary-value problem for plates," in: Current Issues of Optimal Control and Stability of Systems [in Russian], Izd. Yerevanskogo Univ, Yerevan (1997), pp. 128-131.
61. S. A. Ambartsumyan, The Theory of Anisotropic Plates [in Russian], Nauka, Moscow (1967).
62. S. A. Ambartsumyan, The General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).
63. Yu. M. Bagdasaryan and A. M. Khachatryan, "Stress-strain study of a curvilinear rod by the method of asymptotic integration," Izv. AN Armenii, Mekh., 44, No. 1, 3-12 (1991).
64. V. M. Barsegyan and A. M. Khachatryan, "On the asymptotic solution of a mixed problem for a three-layer strip with various contact conditions," Izv. NAN Armenii, Mekh., 54, No. 1, 17-25 (2001).
65. V. Vazov, Asymptotic Expansions of the Solutions of Ordinary Differential Equations [Russian translation], Mir, Moscow (1968).
66. A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of the Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).
67. I. I. Vorovich, "Some mathematical issues of the theory of plates and shells," in: Proc. 2nd All-Union Congr. on Theoretical and Applied Mechanics [in Russian], Issue 3, Nauka, Moscow (1966), pp. 116-136.
68. R. S. Gevorkyan, "On the asymptotic solution of mixed boundary-value problems for laminated plates with alternating elastic and Theological layers," Izv. NAN Armenii, Mekh., 44, No. 2, 67-78 (1991).
69. R. S. Gevorkyan, "An asymptotic boundary-value solution for a three-layer strip whose medium layer is incompressible," in: Issues of Optimal Control, Stability, and Strength of Mechanical Systems [in Russian], Izd. Yerevanskogo Univ., Yerevan (1997), pp. 212-215.
70. R. S. Gevorkyan, "On the action of a discrete load on a laminated plate," in: Proc. All-Union Seminar on Topical Problems of Inhomogeneous Mechanics [in Russian], Izv. Yerevanskogo Univ., Yerevan (1991), pp. 93-99.
71. R. S. Gevorkyan, "Boundary-layer asymptotics for one class of boundary-value problems for anisotropic plates," Izv. AN Arm. SSR, Mekh., 37, No. 6, 3-15 (1984).
72. A. L. Gol'denveizer, "Construction of an approximate bending theory for a plate by the asymptotic integration of the elastic equations," Prikl. Mat. Mekh., 26, No. 4, 668-686 (1962).
73. A. L. Gol'denveizer, The Theory of Elastic Thin Shells [in Russian], Nauka, Moscow (1976).
74. A. L. Gol'denveizer, "On approximate methods for design of thin elastic shells and plates," Izv. RAN, Mekh. Tverd. Tela, No. 3, 134-149 (1997).
75. A. N. Guz and Yu. N. Nemish, Perturbation Methods in Three-Dimensional Elastic Problems [in Russian], Vyshcha Shkola, Kiev (1982).
76. L. G. Gulgazaryan, "On the natural vibrations of a two-layer orthotropic strip with imperfect contact between the layers," in: Proc. Rep. Conf. of Young Scientists [in Russian], Yerevan (1999), pp. 39-44.
77. A.M. Il'in, Method of Matched Asymptotic Expansions of Boundary-Value Solutions [in Russian], Nauka, Moscow (1989).
78. S. A. Lomov, An Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).
79. A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).
80. A. G. Sarkisyan, "On the nature of the stress-strain state of an anisotropic two-layer strip," in: Issues of Optimal Control, Stability, and Strength of Mechanical Systems [in Russian], Yerevan (1997), pp. 234-238.
81. A. G. Sarkisyan, "On the stress-strain state of an anisotropic three-layer strip," Dokl. NAN Armenii, 97, No.3, 40-48 (1997).
82. L. S. Sarkisyan, "On the natural frequencies of a two-layer orthotropic strip," Dokl. NAN Armenii, 97, No. 3, 19-25 (1997).
83. S. O. Sarkisyan, "Construction of an asymptotic two-dimensional magnetoelastic theory for conductive thin shells in a transient inhomogeneous magnetic field," Izv. AN Arm. SSR, Mekh., 42, No. 5, 25-34 (1989).
84. S. O. Sarkisyan, The General Two-Dimensional Theory of Magnetoelasticity for Thin Shells [in Russian], Izd. AN Armenii, Yerevan (1992).
85. S. O. Sarkisyan, "Asymptotic theory and the variational equation of the plane problem for an elastic thin plate based on the moment theory of elasticity," Dokl. NAN Armenii, 99, No. 2, 138-147 (1999).
86. S. O. Sarkisyan, "Asymptotic theory and the variational equation of the bending problem for an elastic thin plate based on the moment theory of elasticity," Dokl NAN Armenii, 99, No. 3, 216-225 (1999).
87. S. O. Sarkisyan, "The asymptotic theory of thin shells based on the asymmetric theory of elasticity," in: Proc. 19th Int. Conf. on the Theory of Shells and Plates [in Russian], Izd. Nizhegorodskogo Univ., Nizhnii Novgorod (1999), pp. 186-189.
88. S. P. Timoshenko, Theory of Elasticity [in Russian], ONTI, Moscow (1937).
89. A. M. Khachatryan, "On the boundary layer of laminated beams," Izv. AN Arm. SSR, Mekh., 40, No. 2, 19-25 (1987).
90. A. M. Khachatryan, "Stress-strain study of an anisotropic two-layer curvilinear strip with perfect and imperfect contacts between layers," Izv. NAN Armenii, Mekh., 53, No. 1, 18-27 (2000).
91. A. M. Khachatryan, "On the equations of a two-layer anisotropic cylindrical shell with imperfect contact between layers," Vestn. Nizhegorodskogo Univ., Ser. Mekh., 2, 123-129 (2000).
92. Sh. M. Khachatryan, "On the stress-strain analysis of an anisotropic strip," Izv. AN Arm. SSR, Mekh., 29, No. 6, 19-32 (1976).
93. Sh. M. Khachatryan, "On stress states and the equations determining them for cylindrical shells with general anisotropy," Izv. AN Arm. SSR, Mekh., 32, No. 3, 26-41 (1979).
94. L. A. Aghalovyan and R. S. Gevorgyan, "The asymptotic solution of some model problems of seismostability construction and seismology," in: Earthquake Hazard and Seismic Risk Reduction, Kluwer Acad. Publ. (2000), pp. 433-446.
95. L. A. Aghalovyan, R. S. Gevorgyan, and A. M. Khachatryan, "Linear and nonlinear models of seismoisolating foundations," J. Struct. Control, No. 2, 237-247 (2001).
96. L. A. Aghalovyan, "On one approach of studying the free and forced vibrations of bases and fundaments of structures," in: Earthquake Hazard and Seismic Risk Reduction, Kluwer Acad. Publ. (2000), pp. 395-402.
97. L. A. Aghalovyan, R. S. Gevorgyan, A. V. Sahakyan, and M. L. Aghalovyan, "Asymptotics of forced vibrations of bases, foundations and seismoisolators," J. Struct. Control, 8, No. 2, 249-263 (2001).
98. K. O. Friedrichs, "Kirchhoff's boundary conditions and the edge effect for elastic plates," in: Proc. Symp. on Applied Mathematics, 3, Amer. Math. Soc., New York (1950).
99. K. O. Friedrichs, "Asymptotic phenomena in mathematical physics," Bull. Amer. Math. Soc., 61, 485 (1955).
100. K. O. Friedrichs and R. F. Dressler, "A boundary-layer theory for elastic plates," Comm. Pure Appl. Math., 14, No.1 (1961).
101. A. E. Green, "Boundary layer equations in the linear theory of thin elastic shells," Proc. Roy. Soc., Ser. A, 268, No. 1339 (1962).
102. A. E. Green, "On the linear theory of thin elastic shells," Proc. Roy. Soc., Ser. A, 266, No. 1325 (1962).