The Morley-Koiter Equations for Thin-Walled Circular Cylindrical Shells: Part 2—Solution for a Line Loaded Cylinder With Close-Spaced Circumferential Grooves

1973 ◽  
Vol 40 (4) ◽  
pp. 966-970 ◽  
Author(s):  
C. P. Mangelsdorf
Keyword(s):  
Boundary Conditions ◽  
Evaluation Procedure ◽  
Equilibrium Equations ◽  
Line Load ◽  
Various Boundary Conditions ◽  
Longitudinal Line ◽  
Symmetrical Loading ◽  
Circular Cylindrical Shells ◽  
Simple Supports ◽  
Thin Walled

In Part 1, modified Donnell equilibrium equations were solved for the case of symmetrical loading and supports using Fourier series. An evaluation procedure for various boundary conditions was suggested. In Part 2, an application of the general solution is made for a shell with small circumferential grooves (or ribs) subjected to a longitudinal line load after approximations to allow for such groves are introduced. The solution is completed for boundary conditions of classical simple supports and relaxed simple supports and the results compared with experimental data.

The Morley-Koiter Equations for Thin-Walled Circular Cylindrical Shells: Part 1—General Solution for Symmetrical Shells of Uniform Thickness

1973 ◽  
Vol 40 (4) ◽  
pp. 961-965 ◽  
Author(s):  
C. P. Mangelsdorf
Keyword(s):  
General Solution ◽  
Evaluation Procedure ◽  
Uniform Thickness ◽  
Equilibrium Equations ◽  
Line Load ◽  
Longitudinal Line ◽  
Symmetrical Loading ◽  
Circular Cylindrical Shells ◽  
Simple Supports ◽  
Thin Walled

Modified Donnell equilibrium equations are solved in Part 1 for the case of symmetrical loading and supports, using Fourier series. An evaluation procedure for simple, fixed, and relaxed simple conditions is suggested. In Part 2, an application of the general solution is made for a shell with small circumferential grooves (or ribs) subjected to a longitudinal line load after approximations to allow for such grooves are introduced. The solution is completed for the boundary conditions of classical simple supports and relaxed simple supports and the results compared with experimental data.

Free vibration analysis of porous laminated rotating circular cylindrical shells

2019 ◽  
Vol 25 (18) ◽  
pp. 2494-2508 ◽  
Author(s):  
Ahmad Reza Ghasemi ◽  
Mohammad Meskini
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Equilibrium Equations ◽  
Rotating Speed ◽  
Simply Supported ◽  
Numerical Result ◽  
Love’S Shell Theory ◽  
Circular Cylindrical Shells

In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

Elastic Local Buckling of Transversely Isotropic Thin-Walled Compression Members with Varying Thickness

2004 ◽  
Vol 261-263 ◽  
pp. 627-632
Author(s):  
S.K. Jeong ◽  
Soon Jong Yoon ◽  
Sun Kyu Cho
Keyword(s):  
Boundary Conditions ◽  
Local Buckling ◽  
Transversely Isotropic ◽  
Longitudinal Direction ◽  
Graphical Form ◽  
Width Ratio ◽  
Various Boundary Conditions ◽  
Varying Thickness ◽  
Compression Members ◽  
Thin Walled

The problem addressed in this paper is the elastic local buckling of thin-walled compression members whose plate components are tapered in thickness along the longitudinal direction. In the design of structural system in construction, shipbuilding, and aerospace industries, such structural plate components are frequently encountered. The elastic buckling analysis of transversely isotropic plates with varying thickness and various boundary conditions is performed to derive the buckling equation of thin-walled members composed of tapered plate components. In the analytical solution, the energy approach is adopted. The analytical results are presented in a graphical form in which the plate buckling coefficients are suggested with respect to the width ratio of plate elements and the degree of taper. In addition, using the buckling equations of plates with specific boundary conditions, the simplified form of equation for the local buckling coefficient of structural members such as L-section, T-section, and Box-section is suggested.

scholarly journals Strength of thin-walled elastic building structures

2021 ◽  
Vol 274 ◽  
pp. 03019
Author(s):  
Lilya Kharasova
Keyword(s):  
Boundary Conditions ◽  
Strain State ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Nonlinear Operator Equation ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Generalized Displacements ◽  
Thin Walled

The existence theorem is proved within the framework of the shear model by S.P. Timoshenko. The stress-strain state of elastic inhomogeneous isotropic shallow thin-walled shell constructions is studied. The stress-strain state of shell constructions is described by a system of the five equilibrium equations and by the five static boundary conditions with respect to generalized displacements. The aim of the work is to find generalized displacements from a system of equilibrium equations that satisfy given static boundary conditions. The research is based on integral representations for generalized displacements containing arbitrary holomorphic functions. Holomorphic functions are found so that the generalized displacements should satisfy five static boundary conditions. The integral representations constructed this way allow to obtain a nonlinear operator equation. The solvability of the nonlinear equation is established with the use of contraction mappings principle.

scholarly journals Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading

1998 ◽  
Vol 5 (5-6) ◽  
pp. 343-354 ◽  
Author(s):  
T.Y. Ng ◽  
K.Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Axial Loading ◽  
Various Boundary Conditions ◽  
Transverse Modes ◽  
First Approximation ◽  
Ritz Procedure ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Parametric Response

In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

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