Boundary-Value Problems of the Thin-Walled Circular Cylinder

1954 ◽  
Vol 21 (4) ◽  
pp. 343-350
Author(s):  
N. J. Hoff
Keyword(s):  
Circular Cylinder ◽  
Differential Equations ◽  
Closed Form ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Cylindrical Shells ◽  
Shear Forces ◽  
Thin Walled

Abstract The homogeneous differential equations of Donnell’s theory of thin cylindrical shells are integrated. Expressions are obtained in closed form for the displacements, membrane stresses, moments, and shear forces.

Simplified Formulas for Boundary-Value Problems of the Thin-Walled Circular Cylinder

1955 ◽  
Vol 22 (3) ◽  
pp. 389-390
Author(s):  
Frederick V. Pohle ◽  
S. V. Nardo
Keyword(s):  
Circular Cylinder ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Circular Cylinders ◽  
Thin Walled ◽  
Simplified Form

Abstract N. J. Hoff has presented formulas which can be used in the solution of boundary-value problems of circular cylinders. The purpose of this note is to express these results in exact simplified form; a more detailed investigation appears elsewhere. The notation will be that of Hoff, unless otherwise stated.

scholarly journals Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations)

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dimitrios E. Panayotounakos ◽  
Theodoros I. Zarmpoutis
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Boundary Value Problems ◽  
Bessel Functions ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Mathematical Technique ◽  
Nonlinear Odes ◽  
Closed Form Solutions ◽  
Degenerate Equations

We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel's nonlinear differential equations (ODEs) of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind (Neumann functions), as well as of the free member of the considered ODE; the parameter being introduced furnishes the order of the above Bessel functions and defines also the desired solutions of the considered ODE as one-parameter family of surfaces. The nonlinear initial or boundary value problems are also investigated. Finally, introducing a relative mathematical methodology, we construct the exact parametric or closed form solutions for several degenerate Abel's equation of the first kind.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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