scholarly journals Closure to “Discussion of ‘Dynamic Buckling and Post-buckling of Imperfect Cylindrical Shells Under Mechanical and Thermal Loads, Based on the Three-Dimensional Theory of Elasticity’” (1999, ASME J. Appl. Mech., 66, 1046)

1999 ◽  
Vol 66 (4) ◽  
pp. 1047-1048
Author(s):  
M. Shairyat ◽  
M. R. Eslami
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Dynamic Buckling ◽  
Thermal Loads ◽  
Dimensional Theory ◽  
Post Buckling

Dynamic Buckling and Post-buckling of Imperfect Orthotropic Cylindrical Shells Under Mechanical and Thermal Loads, Based on the Three-Dimensional Theory of Elasticity

1999 ◽  
Vol 66 (2) ◽  
pp. 476-484 ◽  
Author(s):  
M. Shariyat ◽  
M. R. Eslami
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Dynamic Buckling ◽  
Curvilinear Coordinates ◽  
Thermal Loads ◽  
Dimensional Theory ◽  
Highly Nonlinear

The three-dimensional theory of elasticity in curvilinear coordinates is employed to investigate the dynamic buckling of an imperfect orthotropic circular cylindrical shell under mechanical and thermal loads. Accurate form of the strain expressions of imperfect cylindrical shells is established through employing the general Green's strain tensor for large deformations and the equations of motion are derived in terms of the second Piola-Kirchhoff stress tensor. Then, the governing equations are properly formulated and solved by means of an efficient and relatively accurate solution procedure proposed to solve the highly nonlinear equations resulting from the above analysis. The proposed formulation is very general as it can include the influence of the initial imperfections, temperature distribution, and temperature dependency of the mechanical properties of materials, effect of various end conditions, possibility of large-deformation occurrence and application of any combination of mechanical and thermal loadings. No simplifications are done when solving the resulting equations. Furthermore, in contrast to the displacement-based layer-wise theories and the three-dimensional approaches proposed so far, the stress, force and moment boundary conditions as well as the displacement type ones, can be incorporated accurately in these formulations. Finally, a few examples of mechanical and thermal buckling of some orthotropic cylindrical shells are considered and results of the present three-dimensional elasticity approach are compared with the buckling loads predicated by the Donnell's equations, some single-layer theories, some available results of the layer-wise theory and the recently published three-dimensional approaches and the accuracy of the later methods are discussed based on the exact method presented in this paper.

Axially Symmetric Motions of Thick Cylindrical Shells

1958 ◽  
Vol 25 (1) ◽  
pp. 97-102
Author(s):  
I. Mirsky ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Present Theory ◽  
Theory Of Elasticity ◽  
Approximate Theory ◽  
Axially Symmetric ◽  
Dimensional Theory ◽  
Rotatory Inertia ◽  
Transverse Normal Stress ◽  
Wide Range

Abstract An approximate theory of axially symmetric motions of thick, elastic, cylindrical shells, in which the effect of transverse normal stress is retained, is deduced from the three-dimensional theory of elasticity. The present theory contains, in addition to the usual membrane and bending terms, also the influence of rotatory inertia and transverse shear deformation. Thus it may be specialized to a variety of shell, plate, and solid-cylinder equations. The propagation of free harmonic waves in an infinite shell is studied on the basis of the present theory and the three-dimensional theory of elasticity. Excellent agreement is obtained for the phase velocity of the lowest mode of motion for a wide range of the parameters involved.

Three-Dimensional Elasticity Solution of a Composite Beam

1967 ◽  
Vol 1 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Staley F. Adams ◽  
M. Maiti ◽  
Richard E. Mark
Keyword(s):  
Three Dimensional ◽  
Solid Wood ◽  
Theory Of Elasticity ◽  
Orthotropic Materials ◽  
Stress And Strain ◽  
Cantilever Beams ◽  
Dimensional Theory ◽  
Reinforced Plastics ◽  
Three Dimensional Elasticity ◽  
Moduli Of Elasticity

This investigation was undertaken to develop a rigorous mathe matical solution of stress and strain for a composite pole con sisting of a reinforced plastics jacket laminated on a solid wood core. The wood and plastics are treated as orthotropic materials. The problem of bending of such poles as cantilever beams has been determined by the application of the principles of three- dimensional theory of elasticity. Values of all components of the stress tensor in cylindrical coordinates are given for the core and jacket. Exact values for the stresses have been obtained from computer results, using the basic elastic constants—Poisson's ratios, moduli of elasticity and moduli of rigidity—for each ma terial. A comparison of the numerical results of the exact solu tion with strength of materials solutions has been completed.

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