Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Friday, March 1, 2013 - 04:00 to 05:00
GLK 104

Speaker Info

Structural Engineering OSU

Force-based beam-column elements have been shown superior to standard
displacement-based elements in simulating the material nonlinear response of frame
structures. However, when extending the force-based formulation to geometric
nonlinearity, complications arise because a displacement field must be used in order to
determine second order nonlinear geometric effects. The curvature-based displacement
interpolation (CBDI) procedure is presented for geometrically nonlinear Euler-Bernoulli
beams. The CBDI procedure uses Lagrangian polynomials in order to approximate the
displacement field of a force-based element. The extension to Timoshenko beams using a
curvature-shear-based displacement interpolation (CSBDI) procedure is also presented.
Both the CBDI and CSBDI procedures create an influence matrix whose eigenvalues
correspond to the critical buckling loads of Euler-Bernoulli and Timoshenko beams,
respectively. In addition to critical linear-elastic buckling loads, the eigenvalues
of the CBDI and CSBDI influence matrices provide an accurate approach to finding the
critical buckling loads of weakened columns.