Some Notes on Singular Solutions and the Green’s Functions in the Theory of Plates and Shells

1964 ◽  
Vol 31 (3) ◽  
pp. 441-446 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Hot Spots ◽  
Green's Functions ◽  
Green’S Functions ◽  
Cylindrical Shells ◽  
Thin Plates ◽  
Singular Solutions ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
Circular Cylindrical Shells

Singular solutions are constructed which generate the singularities for great many types of concentrated action on shallow spherical and cylindrical shells. Subsequently a technique is introduced to construct the Green’s functions for closed circular cylindrical shells. Also, the deformation of thin plates subjected to moving hot spots is discussed briefly.

Green’s Functions for Infinite and Semi-infinite Anisotropic Thin Plates

2003 ◽  
Vol 70 (2) ◽  
pp. 260-267 ◽  
Author(s):  
Z.-Q. Cheng ◽  
J. N. Reddy
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Infinite Plate ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Green Functions ◽  
Real Form ◽  
Concentrated Forces ◽  
Anisotropic Elastic ◽  
Kirchhoff Theory

This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneous in the thickness direction. Two systems of problems with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green’s functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate.

Thin Plates and Shallow Cylindrical Shells Subjected to Hot Spots

1964 ◽  
Vol 31 (1) ◽  
pp. 79-82 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Plane Stress ◽  
Hot Spots ◽  
Cylindrical Shells ◽  
Equation Of Motion ◽  
Thin Plates ◽  
Lagrange’S Equation ◽  
Singular Functions

Using Lagrange’s equation of motion for thin plates, the equations of plane stress, and the equations for shallow cylindrical shells, the deformations of thin plates and cylindrical shells subjected to bending and plane hot spots are studied. The interrelation between different singular functions associated with these problems has been indicated also.

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