An improved lower bound for deflections of laminated cantilever beams including the effect of transverse shear deformation

1974 ◽  
Vol 25 (1) ◽  
pp. 89-98 ◽  
Author(s):  
S. Nair ◽  
E. Reissner
Keyword(s):  
Lower Bound ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Transverse Shear Deformation ◽  
Cantilever Beams

Upper and Lower Bounds for Deflections of Laminated Cantilever Beams Including the Effect of Transverse Shear Deformation

1973 ◽  
Vol 40 (4) ◽  
pp. 988-991 ◽  
Author(s):  
E. Reissner
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Lower Bound ◽  
Lower Bounds ◽  
Plane Stress ◽  
Transverse Shear ◽  
Upper And Lower Bounds ◽  
Transverse Shear Deformation ◽  
Cantilever Beams ◽  
Exact Boundary

We state a method for obtaining upper and lower-bound results for the end deflection of a narrow rectangular cantilever beam, treated as a problem in plane stress. Reference is made to well-known earlier approximate results for this problem, using elementary polynomial solutions of Airy’s differential equation, and using approximate, rather than exact boundary conditions, without the establishment of bounds for the error in the approximate solution. Application of the bound method is here limited by the use of simple polynomial approximations for stresses and displacements, with the possibility remaining to obtain improved bounds by more elaborate choices of approximation functions.

Whirling of Composite-Material Driveshafts Including Bending-Twisting Coupling and Transverse Shear Deformation

1993 ◽  
Author(s):  
Charles W. Bert ◽  
Chun-Do Kim
Keyword(s):  
Composite Material ◽  
Shear Deformation ◽  
Timoshenko Beam ◽  
Transverse Shear ◽  
Critical Speed ◽  
Numerical Results ◽  
Transverse Shear Deformation ◽  
First Order ◽  
Shear Deformable

Abstract A simplified theory for predicting the first-order critical speed of a shear deformable, composite-material driveshaft is presented. The shaft is modeled as a Bresse-Timoshenko beam generalized to include bending-twisting coupling. Numerical results are compared with those for both thin and thick walled shell theories and generalized Bernoulli-Euler theory.

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