Elasticity Solutions for Plates

Plates ◽  
2021 ◽  
pp. 159-180
Author(s):  
K. Bhaskar ◽  
T. K. Varadan
Keyword(s):  
Elasticity Solutions

Indentation Technique to Investigate Elastic Moduli of Thin Films on Substrates

1988 ◽  
Vol 130 ◽  
Author(s):  
D. S. Stone ◽  
T. W. Wu ◽  
P.-S. Alexopoulos ◽  
W. R. Lafontaine
Keyword(s):  
Thin Film ◽  
Experimental Data ◽  
Thin Films ◽  
Closed Form ◽  
Elastic Moduli ◽  
Depth Sensing ◽  
Indentation Technique ◽  
Average Displacement ◽  
Elasticity Solutions ◽  
Poor Adhesion

AbstractClosed-form elasticity solutions are introduced, that predict the average displacement beneath square and triangular, uniformly loaded areas at the surface of a bilayer. The solutions aid in the application of depth-sensing indentation techniques for measuring thin film elastic moduli. The elasticity solutions agree closely with experimental data of Al, Si, 1 μm Al on Si, and 2 μm Cr on Si. The case of poor adhesion between the film and substrate is briefly examined.

On the Axial Rigidity of a Perforated Strip and the Strain Energy Release Rate in a Centrally Notched Strip Subjected to Uniaxial Tension

1964 ◽  
Vol 86 (4) ◽  
pp. 693-697 ◽  
Author(s):  
R. G. Forman ◽  
A. S. Kobayashi
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Uniaxial Tension ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Theoretical Studies ◽  
Correction Factors ◽  
Elasticity Solutions

This paper presents theoretical studies on the axial rigidities in strips with circular and elliptical perforations and subjected to uniaxial tension. Greenspan’s original derivations on these axial rigidities [2] were improved by using the elasticity solutions by Howland [6] and Ishida [7] for infinite strips with circular and elliptical perforations, respectively. Finally, the correction factors for centrally notched strips subjected to uniaxial tension were rederived from the above results following the energy approach by Irwin and Kies [3].

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

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