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 the Buckling of Sandwich Columns

2001 ◽  
Author(s):  
George A. Kardomateas
Keyword(s):  
Transverse Shear ◽  
Sandwich Structure ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Dimensional Theory ◽  
Column Buckling ◽  
The Core ◽  
Timoshenko Column ◽  
Three Dimensional Elasticity

Abstract A study of the buckling of a sandwich column, based on the three dimensional theory of elasticity, and a comparison with the simple Euler or transverse shear correction Engesser / Haringx / Timoshenko column buckling formulas, is presented. All three phases of the sandwich structure (two face sheets and the core) are assumed to be orthotropic and the column is in the form of a hollow circular cylinder. The Euler or Engesser / Haringx / Timoshenko loads are based on the equivalent axial modulus. Representative results show the significance of the effect of transverse shear in these sandwich structures.

Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams

2004 ◽  
Vol 71 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Wenbin Yu ◽  
Dewey H. Hodges
Keyword(s):  
Classical Model ◽  
Computational Cost ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Cross Sectional ◽  
Variational Asymptotic ◽  
Dimensional Finite Element ◽  
Elasticity Solutions ◽  
Sectional Analysis ◽  
Three Dimensional Elasticity

The original three-dimensional elasticity problem of isotropic prismatic beams has been solved analytically by the variational asymptotic method (VAM). The resulting classical model (Euler-Bernoulli-like) is the same as the superposition of elasticity solutions of extension, Saint-Venant torsion, and pure bending in two orthogonal directions. The resulting refined model (Timoshenko-like) is the same as the superposition of elasticity solutions of extension, Saint-Venant torsion, and both bending and transverse shear in two orthogonal directions. The fact that the VAM can reproduce results from the theory of elasticity proves that two-dimensional finite-element-based cross-sectional analyses using the VAM, such as the variational asymptotic beam sectional analysis (VABS), have a solid mathematical foundation. One is thus able to reproduce numerically with VABS the same results for this problem as one obtains from three-dimensional elasticity, but with orders of magnitude less computational cost relative to three-dimensional finite elements.

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.

Sign in / Sign up

Export Citation Format

Share Document