scholarly journals Discussion: “Three-Dimensional Elasticity Solution and Edge Effects in a Spherical Dome” (Cheng, S., and Angsirikul, T., 1977, ASME J. Appl. Mech., 44, pp. 599–603)

1978 ◽  
Vol 45 (3) ◽  
pp. 700-701
Author(s):  
H. S. Levine ◽  
J. M. Klosner
Keyword(s):  
Edge Effects ◽  
Three Dimensional ◽  
Elasticity Solution ◽  
Spherical Dome ◽  
Three Dimensional Elasticity

Three-Dimensional Elasticity Solution and Edge Effects in a Spherical Dome

1977 ◽  
Vol 44 (4) ◽  
pp. 599-603 ◽  
Author(s):  
Shun Cheng ◽  
T. Angsirikul
Keyword(s):  
Edge Effects ◽  
Thin Shell ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Uniform Thickness ◽  
Spherical Dome ◽  
Elasticity Solutions ◽  
The Subject ◽  
Three Dimensional Elasticity

The subject of this analysis is a homogeneous, isotropic, and elastic spherical dome of uniform thickness subjected to prescribed edge stresses at the end surface. Starting from three-dimensional equations of theory of elasticity, solutions of Navier’s equations and the characteristic equation are obtained. Eigenvalues are computed for various values of the thickness and radius ratio and their special features are analyzed. Coefficients of the nonorthogonal eigenfunction expansions are then determined through the use of a least-squares technique. Many numerical results are obtained and illustrated by figures. These results show that the method presented herein yields very satisfactory solutions. These solutions are fundamental to the understanding of thin shell theories.

Three-Dimensional Elasticity Solution for Sandwich Plates With Orthotropic Phases: The Positive Discriminant Case

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
George A. Kardomateas
Keyword(s):  
Characteristic Equation ◽  
Orthotropic Material ◽  
Three Dimensional ◽  
Sandwich Plates ◽  
Elasticity Solution ◽  
Material Constants ◽  
Real Roots ◽  
Three Dimensional Elasticity ◽  
Rectangular Sandwich Plates ◽  
Positive Discriminant

A three-dimensional elasticity solution for rectangular sandwich plates exists only under restrictive assumptions on the orthotropic material constants of the constitutive phases (i.e., face sheets and core). In particular, only for negative or zero discriminant of the cubic characteristic equation, which is formed from these constants (case of three real roots). The purpose of the present paper is to present the corresponding solution for the more challenging case of positive discriminant, in which two of the roots are complex conjugates.

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