A Computationally Attractive Beam Theory Accounting for Transverse Shear and Normal Deformations
Abstract
In the simplest cases of beam bending, vibration and stability, analytic solutions can be obtained using the Bernoulli-Euler (classical) or Timoshenko beam theories, with the latter accounting for the deformation due to transverse shear. Analytic solutions can be either difficult or impossible to obtain for the many practical applications of beams as reinforcing members in plate and shell structures and whenever nonlinear deformation/material behavior is considered. In all of these cases, the finite element method enables the analyst to obtain sufficiently accurate approximate solutions. The principal benefit of the Timoshenko beam modeling is the ability to properly account for transverse shear deformation, the effect that can be significant in deep beams and those made of laminated composites which are known to exhibit relatively low transverse shear stiffness. Since the Timoshenko theory does not account for the deformation in the transverse normal direction, it precludes solutions to problems which lend themselves to the three-dimensional state of stress. An example is the composite beam subject to impact loading or high-frequency vibrational modes (i.e., short-wavelength loading).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1991
- Accession Number
- ADA231938
Entities
People
- Alexander Tessler