Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature
Source abstract
Abstract
Abstract Laminated composite and sandwich structures are lightweight structures that can be found in many diverse applications especially civil, mechanical and aerospace engineering. The rapid increase in the industrial use of these structures has necessitated the development of new theories that suitable for the bending, buckling and vibration analysis of composite structures. Many review articles are reported in the literature on laminated composite plates and shells in the last few decades. But, in the whole variety of literature very few review articles are available exclusively on laminated composite and sandwich beams. In this article, a critical review of literature on bending, buckling and free vibration analysis of shear deformable isotropic, laminated composite and sandwich beams based on equivalent single layer theories, layerwise theories, zig-zag theories and exact elasticity solution is presented. In addition to this, literature on finite element modeling of laminated and sandwich beams based on classical and refined theories is also reviewed. Finally, displacement fields of various equivalent single layer and layerwise theories are summarized in the present study for the reference of researchers in this area. This article cites 515 references and highlights, the possible scope for the future research on laminated composite and sandwich beams.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Aeroelasticity and Vibration Control
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results10.1016/j.compstruct.2015.04.007 ↗
2. Recent advanced in analysis of laminated beams and plates. Part I. Shear effects and buckling10.2514/3.10202 ↗
3. Recent advances in analysis of laminated beams and plates: Part II. Vibrations and wave propagation
4. A review of refined shear deformation theories for isotropic and anisotropic laminated beams10.1177/073168401772678283 ↗
5. Advances in nonlinear vibration analysis of structures. Part-I. Beams10.1007/BF02703386 ↗
6. On the use of zigzag functions in equivalent single layer theories for laminated composite and sandwich beams: a comparative study and some observations on external weak layers10.1115/1.4023690 ↗
7. Vibrations of straight and curved composite beams: a review10.1016/j.compstruct.2013.01.001 ↗
8. Reddy · 1997
9. Wang CM, Reddy JN, Lee KH. Shear deformable beams and plates: relationships with classical solutions. The Boulevard, Langford Lane Kidlington, Oxford; UK: Elsevier Science Ltd.; 2000.
10. Carrera · 2011
11. Bernoulli J. Curvatura laminae elasticae. Acta Eruditorum Lipsiae 1694;262–276. (Also in Jacobi Bernoulli Basileensis Opera (2 vols.) 1744;1(LVIII):576.
12. Bernoulli J. Explicationes, annotations et additions. Acta Eruditorum Lipsiae 1695. (Also in Jacobi Bernoulli Basileensis Opera (2 vols.) 1744;1(LXVI):639.
13. Bernoulli J. Vritable hypothese de la resistance des solides, avec la demonstration de la corbure des corps qui font reeort. Histoire de l’ Academie des Sciences Paris 1705. (Also in Jacobi Bernoulli Basileensis Opera (2 vols.) 1744;2(CII):976–989.
14. Euler L. Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. Lausanne and Geneva; 1744.10.5479/sil.318525.39088000877480 ↗
15. Memoire sur la flexion des prismes
16. Memoire sur la torsion des prismes
17. Love · 1944
18. Timoshenko · 1953
19. Todhunter I, Pearson K. A history of the theory of elasticity and of the strength of materials from Galileo Galilei (1564–1642) to Lord Kelvin (1824–1907). Vols. I, II and III. New York: Dover publications, Inc; 1960.
20. Rayleigh · 1877
21. On the accuracy of the Bernoulli-Euler theory for beams of variable section10.1115/1.3636564 ↗
22. On the correction for shear of the differential equation for transverse vibration of prismatic bars10.1080/14786442108636264 ↗
23. Kruszewski ET. Effect of transverse shear and rotatory inertia on the natural frequency of a uniform beam. NACA Technical Note 1909; 1949.
24. Dengler MA, Goland M. Transverse impact of long beams including inertia and shear effects. In: ASME Proceedings of 1st U.S. national congress of applied mechanics, New York; 1951. p. 179–86.
25. Mindlin RD, Deresiewicz H. Timoshenko’s shear coefficient for flexural vibrations of beams. In: Proc. of the second U. S. national congress of applied mechanics; 1954. p. 175.10.21236/AD0013061 ↗
26. Sokolnikoff · 1956
27. Some solutions of the Timoshenko beam equations10.1115/1.4011317 ↗
28. Second approximations of method of internal constraint and its applications10.1016/0020-7403(61)90038-8 ↗
29. The shear co-efficient in Timoshenko beam theory10.1115/1.3625046 ↗
30. On the accuracy of Timoshenko beam theory
31. Analysis of short beams10.2514/3.6067 ↗
32. Timoshenko · 1970
33. Timoshenko · 1970
34. Simplified analysis of static shear factor for beams of nonhomogeneous cross section10.1177/002199837300700410 ↗
35. Shear coefficient for orthotropic beams10.1177/002199837300700411 ↗
36. On Timoshenko’s correction for shear in vibrating beams10.1088/0022-3727/8/16/003 ↗
37. Transverse vibrations of beams, exact versus approximate solutions10.1115/1.3157757 ↗
38. On the transverse vibration of beams of rectangular cross-section10.1115/1.3171735 ↗
39. Bounds for stiffness of prismatic beams10.1061/(ASCE)0733-9445(1984)110:6(1410) ↗
40. On the shear deformation theory for dynamic analysis of beams10.1016/S0022-460X(85)80033-X ↗
41. On the shear coefficient in beam bending10.1016/0093-6413(87)90059-0 ↗
42. An engineering theory for beam bending10.1007/BF00537197 ↗
43. A new theory for bending of thick sandwich beams10.1016/0020-7403(89)90033-7 ↗
44. Generalized beam theory applied to shear stiffness10.1016/0020-7683(91)90188-L ↗
45. Refined engineering beam theory based on the asymptotic expansion approach10.2514/3.10598 ↗
46. Static shear correction factor for laminated rectangular beams10.1016/1359-8368(95)00014-3 ↗
47. Improved engineering theory for uniform beams10.1007/BF01170406 ↗
48. Shear correction factors and an energy consistent beam theory10.1016/S0020-7683(98)00050-X ↗
49. Shear stresses in prismatic beams with arbitrary cross-sections10.1002/(SICI)1097-0207(19990710)45:7<865::AID-NME609>3.0.CO;2-3 ↗
50. Shear correction factors in Timoshenko’s beam theory for arbitrary shaped cross-sections10.1007/s004660100239 ↗
51. Shear coefficients for Timoshenko beam theory10.1115/1.1349417 ↗
52. A displacement method for the analysis of flexural shear stresses in thin-walled isotropic composite beams10.1016/S0045-7949(02)00223-7 ↗
53. Hutchinson’s shear coefficient for anisotropic beams10.1016/S0022-460X(02)01532-8 ↗
54. Deformation of short composite beam using refined theories10.1016/j.jmaa.2008.05.070 ↗
55. A Timoshenko beam theory with pressure corrections for layered orthotropic beams10.1016/j.ijsolstr.2011.04.009 ↗
56. A new method to determine the shear coefficient of Timoshenko beam theory10.1016/j.jsv.2011.02.012 ↗
57. Celebrating the centenary of Timoshenko’s study on effects of shear deformation and rotary inertia10.1115/1.4031965 ↗
58. On the problem of the beam and the plate in the theory of elasticity
59. Bending of rectangular beams10.1115/1.4010417 ↗
60. On the stresses and deflections of rectangular beams10.1115/1.4011333 ↗
61. On the significance of the inclusion of the effect of transverse normal strain in problems involving beams with surface constraints10.1115/1.3423502 ↗
62. Higher order effects in thick rectangular elastic beams10.1016/0020-7683(68)90072-3 ↗
63. Beam theories: a variational approach
64. A consistent higher order beam theory
65. Toward a new engineering theory of bending: fundamentals10.2514/3.7938 ↗
66. Technical theory of beam with normal strain10.1061/(ASCE)0733-9399(1984)110:8(1233) ↗
67. Toward a consistent beam theory10.2514/3.8685 ↗
68. A new rectangular beam theory10.1016/0022-460X(81)90493-4 ↗
69. Further results of a new beam theory10.1016/S0022-460X(81)80180-0 ↗
70. On Bickford’s consistent higher order beam theory10.1016/0093-6413(85)90027-8 ↗
71. Levinson M. Consistent and inconsistent higher order beam and plate theories: some surprising comparisons. In: Proceedings of Euromech Colloquium 219 on refined dynamical theories of beams, plates and shells and their applications, Kassel, F.R. Germany; 1986. p. 122–30.10.1007/978-3-642-83040-2_11 ↗
72. An error estimate for solutions in beam theory10.1002/zamm.19870670322 ↗
73. On the accuracy of a beam theory10.1016/0093-6413(87)90024-3 ↗
74. A simple and accurate beam theory10.1007/BF01174627 ↗
75. Observations on higher-order beam theory10.1061/(ASCE)0893-1321(1993)6:4(408) ↗
76. Stiffness analysis of beams using a higher order theory10.1016/0045-7949(94)00505-W ↗
77. A higher order beam finite element for bending and vibration problems10.1016/0022-460X(88)90244-1 ↗
78. A finite element model for a higher order shear deformable beam theory10.1016/0022-460X(88)90278-7 ↗
79. An exact high order beam element10.1016/S0045-7949(02)00438-8 ↗
80. Ghugal YM. A single variable parabolic shear deformation theory for flexure and flexural vibration of thick isotropic beams. In: Proc. of 3rd international conference on structural engineering, mechanics and computation, Cape Town, South Africa; 2007.
81. Analogy between refined beam theories and the Bernoulli-Euler theory10.1016/0020-7683(91)90105-O ↗
82. Ghugal YM, Shimpi RP. A trigonometric shear deformation theory for flexure and free vibration of isotropic thick beams. Structural Engineering Convention (SEC-2000), IIT Bombay, India; 2000.
83. Flexure and vibration of thick beams using trigonometric shear deformation theory
84. Ghugal · IEI (India) J · 2011 · 92 · 3
85. A trigonometric shear deformation theory for flexure of thick beams
86. A trigonometric shear deformation theory for flexure of thick beams10.1016/j.proeng.2013.01.004 ↗
87. Flexural analysis of deep beam subjected to parabolic load using refined shear deformation theory
88. Flexure of cantilever thick beams using trigonometric shear deformation theory
89. Memoire sur la Theorie des Plaques Elastiques Planes
90. Verallgeneinerte theorie der plattenstatik10.1007/BF00538133 ↗
91. Uber die Randquerkrafte bei gestutzten platten10.1002/zamm.19550350604 ↗
92. Panc · 1975
93. Vlasov VZ, Leont’ev UN. Beams, Plates and shells on elastic foundations. Translated from Russian by Barouch, A. In: Pelz T, editor. Israel Program for Scientific Translations Ltd., Jerusalem; 1960. p. 1–8.
94. Vibration of beams and plate strips with three-dimensional flexibility10.1115/1.3176054 ↗
95. A transverse shear and normal deformable orthotropic beam theory10.1016/0022-460X(92)90717-C ↗
96. A hyperbolic shear deformation theory for flexure and vibration of thick isotropic beams10.1142/S0219876209002017 ↗
97. A refined shear deformation theory for flexure of thick beams10.1590/S1679-78252011000200005 ↗
98. Flexure of thick beams using new hyperbolic shear deformation theory
99. Mechanical behaviour of laminated composite beam by the new multi-layered laminated Composite Structure model with transverse shear stress continuity10.1016/S0020-7683(02)00647-9 ↗
100. Comparison of various refined beam theories for the bending and free vibration analysis of thick beams