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Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, March 1, 2013 - 04:00 to 05:00

Location:

GLK 104

Event Link:

Guest Speaker:

Institution:

Structural Engineering OSU

Abstract:

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.