A Numerical Procedure for the Dynamic Plastic Response of Beams with Rotatory Inertia and Transverse Shear Effects

1979 ◽  
Vol 7 (2) ◽  
pp. 193-230 ◽  
Author(s):  
J. Gomes de Oliveira ◽  
Norman Jones
Keyword(s):  
Transverse Shear ◽  
Numerical Procedure ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Shear Effects ◽  
Transverse Shear Effects

Dynamic Plastic Response of Circular Plates With Transverse Shear and Rotatory Inertia

1980 ◽  
Vol 47 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Plastic Material ◽  
Yield Criterion ◽  
Circular Plates ◽  
Plastic Response ◽  
Governing Equations ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Shear Effects ◽  
Transverse Shear Effects

The response of a simply supported circular plate made from a rigid perfectly plastic material and subjected to a uniformly distributed impulsive velocity is developed herein. Plastic yielding of the material is controlled by a yield criterion which retains the transverse shear force as well as bending moments and the influence of rotatory inertia is included in the governing equations. Various equations and numerical results are presented which may be used to assess the importance of transverse shear effects and rotatory inertia for this particular problem.

Exact Solution of the Elastica with Transverse Shear Effects

2014 ◽  
Vol 14 (08) ◽  
pp. 1440019
Author(s):  
Adrian Marcel Zalmanovici ◽  
Reyolando Manoel Lopes Rebello da Fonseca Brasil ◽  
José Manoel Balthazar
Keyword(s):  
Exact Solution ◽  
Transverse Shear ◽  
Closed Form Solution ◽  
Numerical Procedure ◽  
Form Solution ◽  
Total Potential ◽  
Euler’S Elastica ◽  
Shear Effects ◽  
Set Up ◽  
Transverse Shear Effects

A new derivation of Euler's Elastica with transverse shear effects included is presented. The elastic potential energy of bending and transverse shear is set up. The work of the axial compression force is determined. The equation of equilibrium is derived using the variation of the total potential. Using substitution of variables an exact solution is derived. The equation is transcendental and does not have a closed form solution. It is evaluated in a dimensionless form by using a numerical procedure. Finally, numerical examples of laminates made of composite material (fiber reinforced) and sandwich panels are provided.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

1979 ◽  
Vol 46 (2) ◽  
pp. 303-310 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Shear Force ◽  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Theoretical Procedure

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

Free-Vibration of Rotating Composite Beams Incorporating Higher-Order Transverse Shear Effects

2001 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. I. Librescu ◽  
C. D. Shete
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Present Model ◽  
Structural Model ◽  
Laminated Composite ◽  
Higher Order ◽  
Rotating Blade ◽  
Box Beam ◽  
Shear Effects ◽  
Transverse Shear Effects

Abstract The free vibration behavior of a rotating blade modeled as a laminated composite hollow (single celled) box beam is studied. The geometrically nonlinear structural model developed herein incorporates a number of non-classical effects such as anisotropy, heterogeneity, transverse shear flexibility, and warping inhibition. The centrifugal and Coriolis force field effects are also included. The main focus here being the refinement of the existing model, the traction-free boundary conditions are satisfied here in contrast to the existing model. The resulting linearized equations and numerical results based on them are presented. Results obtained for the present higher-order shearable model are compared with those of the existing first-order shearable and the non-shearable models. Tailoring studies using the present model reveal an enhancement of eigenfrequency characteristics.

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