An Unusual Closed-Form Solution for a Variable-Thickness Plate on an Elastic Foundation

1980 ◽  
Vol 47 (1) ◽  
pp. 204-204 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Closed Form ◽  
Elastic Foundation ◽  
Variable Thickness ◽  
Closed Form Solution ◽  
Form Solution

CLOSED-FORM TRIGONOMETRIC SOLUTIONS FOR INHOMOGENEOUS BEAM-COLUMNS ON ELASTIC FOUNDATION

2004 ◽  
Vol 04 (01) ◽  
pp. 139-146 ◽  
Author(s):  
IVO CALIÒ ◽  
ISAAC ELISHAKOFF
Keyword(s):  
Closed Form ◽  
Elastic Foundation ◽  
Load Distribution ◽  
Flexural Rigidity ◽  
Closed Form Solution ◽  
Form Solution ◽  
Material Density ◽  
Buckling Modes ◽  
Beam Columns ◽  
Closed Form Solutions

In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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