A thin shallow shell in the form of a paraboloid of revolution

1971 ◽  
Vol 7 (12) ◽  
pp. 1339-1344
Author(s):  
V. S. Zhgenti
Keyword(s):  
Shallow Shell ◽  
Paraboloid Of Revolution ◽  
Thin Shallow Shell

Torsional Vibrations of Pretwisted Cantilever Plates

1978 ◽  
Vol 100 (3) ◽  
pp. 528-534 ◽  
Author(s):  
K. Gupta ◽  
J. S. Rao
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fourth Order ◽  
Shallow Shell ◽  
Torsional Vibrations ◽  
Cantilever Plate ◽  
Order Ordinary Differential Equation ◽  
Aspect Ratios ◽  
Constant Coefficients ◽  
Thin Shallow Shell

A pretwisted cantilever plate is treated as a thin shallow shell. Its potential and kinetic energies in torsional vibration are determined by assuming an appropriate displacement field. Applying Hamilton’s principle, the problem is reduced to a fourth-order ordinary differential equation with constant coefficients, which is solved to obtain the first four torsional frequencies of vibration. Plates of aspect ratios varying from 1.0 to 8.0 are analyzed with pretwist angles varying from 0 to 90 deg. Results of the present analysis are compared with existing theoretical and experimental results.

Point Load on a Shallow Elliptic Paraboloid

1966 ◽  
Vol 33 (3) ◽  
pp. 575-585 ◽  
Author(s):  
Kevin Forsberg ◽  
Wilhelm Flu¨gge
Keyword(s):  
Power Series ◽  
Axial Symmetry ◽  
Shallow Shell ◽  
Point Load ◽  
Singular Solutions ◽  
Elliptic Paraboloid ◽  
Concentrated Loading ◽  
Shell Equations ◽  
Shell Geometry ◽  
Thin Shallow Shell

The present work is a study of a thin shallow shell having a specific type of deviation from axial symmetry, i.e., the portion of an elliptic paraboloid near its vertex. The singular solutions to the homogeneous shallow-shell equations are expressed as power series in terms of a parameter γ, which is a measure of the deviation of the shell geometry from axial symmetry. These singular solutions can be directly related to concentrated loading at the vertex of the shell. The solution converges in the range γ = 0 (sphere) to γ = 1/2 (cylinder). Detailed graphical results are presented for the stress resultants and radial deflection of a shell subjected to a point load at its vertex.

Warpage Analysis between Straight and Conformal Cooling Channels on Thin Shallow Shell

2013 ◽  
Vol 594-595 ◽  
pp. 676-685
Author(s):  
Norshah Afizi Shuaib ◽  
M. Fathullah ◽  
Z. Shayfull ◽  
S.M. Nasir ◽  
M.F.M.A. Hamzas
Keyword(s):  
Shallow Shell ◽  
Simulation Software ◽  
Design Stage ◽  
Mold Design ◽  
Conformal Cooling ◽  
Cooling Channels ◽  
Conformal Cooling Channels ◽  
Filling Time ◽  
Differential Shrinkage ◽  
Thin Shallow Shell

Warpage is a type mold defect due to non-uniform temperature variation which causes differential shrinkage rate on the moulded parts. An accurate warpage prediction is so important in helping mould designers to achieve successful mold design with minimum warpage defects. This work is performed with a purpose to determine and compare the best parameters can be selected in manufacturing of thin shallow shell using two different types of cooling channels which are straight cooling channels and conformal cooling channels. The results were obtained using Taguchi Method and Analysis of Variance (ANOVA) and run through simulation software. Both parameters are then compared with each other in recommending to the mold designers which is the best to be applied at mold design stage. It has been found from this work that two factors that significantly cause warpage on both cooling channels are packing pressure and filling time.

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