Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery
Source abstract
Abstract
This study focuses on the static analysis of functionally graded conical shells and panels and extends a previous formulation by the first three authors. A 2D Unconstrained Third order Shear Deformation Theory (UTSDT) is used for the evaluation of tangential and normal stresses in moderately thick functionally graded truncated conical shells and panels subjected to meridian, circumferential and normal uniform loadings. To investigate the behavior of the functionally graded structures at issue, a four parameter power law function is considered. The initial curvature effect is discussed and the role of the parameters in the power law function is shown. The conical shell problem described in terms of seven partial differential equations is solved by using the generalized differential quadrature (GDQ) method. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. The stress recovery is worked out to reconstruct the correct distribution of transverse stress components. Accurate stress profiles for general loading combinations applied at the extreme surfaces are obtained. The influence of the semi vertex angle is pointed out.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Load-Bearing Analysis · Structural Analysis and Optimization
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References (100+)
Show source-provided references
1. The effect of transverse shear deformation on the bending of elastic plates10.1115/1.4009435 ↗
2. Reissner E. Small bending and stretching of sandwich type shells. NACA-TN 1832; 1949.
3. Influence of rotary inertia and shear on flexural motion of isotropic elastic plates10.1115/1.4010217 ↗
4. Shear correction factors for orthotropic laminates under static loads10.1115/1.3422950 ↗
5. The effect of transverse shear deformation on the bending of laminated plates10.1177/002199836900300316 ↗
6. Shear deformation in heterogeneous anisotropic plates10.1115/1.3408654 ↗
7. A consistent treatment of transverse shear deformations in laminated anisotropic plates10.2514/3.50194 ↗
8. A refined nonlinear theory of plates with transverse shear deformation
9. A higher order theory of plate deformation – Part 1: Homogeneous plates10.1115/1.3424154 ↗
10. A high order theory of plate deformation – Part 2: Laminated plates10.1115/1.3424155 ↗
11. Murthy MVV. An improved transverse shear deformation theory for laminated anisotropic plates. NASA Technical paper; 1981. p. 1–37.
12. An accurate simple theory for the static and dynamics of elastic plates10.1016/0093-6413(80)90049-X ↗
13. A simple higher order theory for laminated composite plates10.1115/1.3167719 ↗
14. A higher order shear deformation theory of laminated elastic shells10.1016/0020-7225(85)90051-5 ↗
15. A generalization of two dimensional theories of laminated composite plates10.1002/cnm.1630030303 ↗
16. An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates10.1115/1.3173074 ↗
17. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates. An evaluation of a new displacement field10.1016/0022-460X(86)90169-0 ↗
18. A nonlinear modified couple stress-based third-order theory of functionally graded plates10.1016/j.compstruct.2011.10.006 ↗
19. A rational deduction of plate theories from the three dimensional linear elasticity10.1002/zamm.19970770509 ↗
20. A layer wise laminate theory rationally deduced from the three dimensional elasticity10.1115/1.2788926 ↗
21. On the physical significance of higher order kinematic and static variables in a three dimensional shell formulation10.1016/S0020-7683(99)00321-2 ↗
22. Refined first order shear deformation theory models for composites laminates10.1115/1.1572901 ↗
23. Developments, ideas and evaluations based upon Reissner’s mixed variational theorem in the modelling of multilayered plates and shells10.1115/1.1385512 ↗
24. A study of transverse normal stress effect on vibration of multilayered plates and shells10.1006/jsvi.1999.2271 ↗
25. Simple and effective elements based upon Timoshenko–Mindlin shell theory10.1016/S0045-7825(01)00320-6 ↗
26. Analysis of thickness locking in classical, refined and mixed theories for layered shells10.1016/j.compstruct.2007.10.009 ↗
27. Free vibration and stability of functionally graded shallow shells according to a 2D higher order deformation theory10.1016/j.compstruct.2007.07.006 ↗
28. Variable kinematic models applied to free-vibration analysis of functionally graded material shells10.1016/j.euromechsol.2010.06.001 ↗
29. Effects of thickness stretching in functionally graded plates and shells10.1016/j.compositesb.2010.10.005 ↗
30. Generalized shear deformation theory for bending analysis of functionally graded plates10.1016/j.apm.2005.03.009 ↗
31. Three dimensional analysis of a functionally graded coating/substrate system of finite thickness10.1098/rsta.2007.2194 ↗
32. A consistent first approximation in the general theory of thin elastic shells
33. A review of meshless methods for laminated and functionally graded plates and shells10.1016/j.compstruct.2011.02.018 ↗
34. Elastic solution of a two dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads10.1007/s00707-010-0380-z ↗
35. Bending analysis of moderately thick functionally graded conical panels10.1016/j.compstruct.2010.10.020 ↗
36. Vibration and damping analysis of multilayered conical shells10.1016/0263-8223(95)00117-4 ↗
37. Generalized differential quadrature method for the free vibration of truncated conical panels10.1006/jsvi.2001.3993 ↗
38. Free vibration analysis of conical shells via the element-free kp-Ritz method10.1016/j.jsv.2004.01.005 ↗
39. The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method10.1016/j.mechrescom.2009.02.003 ↗
40. The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure10.1016/j.compstruct.2008.08.010 ↗
41. 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures10.1016/j.jsv.2009.07.031 ↗
42. Free vibration analysis of functionally graded panels and shells of revolution10.1007/s11012-008-9167-x ↗
43. Free vibration analysis of functionally graded conical shell panels by a meshless method10.1016/j.compstruct.2010.08.014 ↗
44. FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations10.1016/j.ijmecsci.2011.03.007 ↗
45. Thermally induced dynamic instability of laminated composite conical shells10.1016/S0020-7683(02)00234-2 ↗
46. Axisymmetric static and dynamic buckling of laminated thick truncated conical cap10.1016/S0020-7462(02)00036-7 ↗
47. Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells10.1016/j.jsv.2005.07.039 ↗
48. Thermoelastic stability of functionally graded truncated conical shells10.1016/j.compstruct.2005.06.004 ↗
49. Thermal and mechanical instability of functionally graded truncated conical shells10.1016/j.tws.2007.07.011 ↗
50. The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure10.1016/j.compstruct.2009.08.033 ↗
51. Influence of the initial imperfection on the nonlinear buckling response of FGM truncated conical shells10.1016/j.ijmecsci.2011.06.007 ↗
52. Numerical investigations of functionally graded cylindrical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery10.1016/j.compstruct.2012.05.034 ↗
53. An Unconstrained third order plate theory10.1016/0045-7949(91)90316-E ↗
54. Differential quadrature and long term integration10.1016/0022-247X(71)90110-7 ↗
55. Differential quadrature for multi-dimensional problems10.1016/0022-247X(84)90111-2 ↗
56. Shu C. Generalized differential–integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. Ph.D. thesis, University of Glasgow; 1991.
57. Shu · 2000
58. Differential quadrature method in computational mechanics: a review10.1115/1.3101882 ↗
59. A differential quadrature method solution for shear-deformable shells of revolution10.1016/j.engstruct.2005.06.005 ↗
60. Free vibration analysis of spherical caps using a G.D.Q. numerical solution10.1115/1.2217970 ↗
61. Vibration analysis of damaged circular arches with varying cross-section
62. Vibration analysis of conical shell structures using GDQ method
63. Vibration analysis of spherical structural elements using the GDQ method10.1016/j.camwa.2006.03.039 ↗
64. Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches10.1016/j.jsv.2006.07.001 ↗
65. Nonconservative stability problems via generalized differential quadrature method10.1016/j.jsv.2008.01.056 ↗
66. 2-D solution for free vibration of parabolic shells using generalized differential quadrature method10.1016/j.euromechsol.2007.12.007 ↗
67. Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law function10.1016/j.cma.2009.04.011 ↗
68. Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution10.1016/j.euromechsol.2009.04.005 ↗
69. Free vibrations of three parameter functionally graded parabolic panels of revolution10.1016/j.mechrescom.2009.02.001 ↗
70. Critical flow speeds of pipes conveying fluid by the generalized differential quadrature method
71. 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution10.1016/j.compstruct.2011.02.006 ↗
72. Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler–Pasternak elastic foundations10.1016/j.compstruct.2011.07.002 ↗
73. General anisotropic doubly-curved shell theory: a differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian10.1016/j.jsv.2012.05.036 ↗
74. Laminated composite rectangular and annular plates: a GDQ solution for static analysis with a posteriori shear and normal stress recovery10.1016/j.compositesb.2012.01.065 ↗
75. General higher order shear deformation theories for the vibration analysis of completely double-curved laminated shells and panels10.1016/j.compstruct.2012.08.005 ↗
76. Static analysis of functionally graded doubly-curved shells and panels of revolution10.1007/s11012-012-9643-1 ↗
77. Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method10.1016/j.ijmecsci.2012.05.007 ↗
78. Free-form laminated doubly-curved shells and panels of revolution on Winkler–Pasternak elastic foundations: a 2-D GDQ solution for static and free vibration analysis10.4236/wjm.2013.31001 ↗
79. Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories10.1016/j.compstruct.2013.01.002 ↗
80. General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels10.1016/j.compstruct.2013.04.009 ↗
81. Mixed static and dynamic optimization of four-parameter functionally graded completely doubly-curved and degenerate shells and panels using GDQ method10.1155/2013/867079 ↗
82. Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape10.1016/j.compstruct.2013.07.034 ↗
83. Radial basis function method applied to doubly-curved laminated composite shells and panels with a general higher-order equivalent single layer formulation10.1016/j.compositesb.2013.07.026 ↗
84. Analysis of sandwich plates by generalized differential quadrature method10.1155/2013/964367 ↗
85. FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundation: a GDQ solution for static analysis with a posteriori stress and strain recovery
86. Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method10.1016/j.compstruct.2013.08.038 ↗
87. Winkler–Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels10.1016/j.compositesb.2013.06.020 ↗
88. Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a unified formulation10.1016/j.compositesb.2013.10.088 ↗
89. Soft core plane state structures under static loads using GDQFEM and cell method
90. On static analysis of composite plane state structures via GDQFEM and cell method
91. GDQFEM numerical simulations of continuous media with cracks and discontinuities
92. Generalized differential quadrature finite element method for vibration analysis of arbitrarily shaped membranes10.1016/j.ijmecsci.2013.12.008 ↗
93. The G.D.Q. method for the harmonic dynamic analysis of rotational shell structural elements10.12989/sem.2004.17.6.789 ↗
94. Forced vibrations of functionally graded plates in the three dimensional setting10.2514/1.13160 ↗
95. Static analysis of shear-deformable shells of revolution via G.D.Q. method10.12989/sem.2005.19.4.459 ↗
96. Analysis of composite plates by trigonometric shear deformation theory and multiquadrics10.1016/j.compstruc.2005.04.002 ↗
97. Analysis of composite plates using higher order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method10.1016/S1359-8368(03)00083-0 ↗
98. A high order collocation method for the static and vibration analysis of composite plates using a first order theory10.1016/j.compstruct.2008.09.006 ↗
99. Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations10.1016/j.compositesb.2011.01.031 ↗
100. A hybrid stress approach for laminated composite plates within the first order shear deformation theory10.1016/j.ijsolstr.2007.10.020 ↗