Dual extremum principles for geometrically exact finite strain beams

H.A.F.A. Santos (1) , J.P. Moitinho de Almeida (1)

1 Department of Civil Engineering and Architecture

Both necessary and sufficient conditions for the existence of two complementary-dual extremum principles for geometrically exact finite strain (one-dimensional) beam models are investigated by means of two different approaches. One is based on the results published by Gao and Strang, and the other relies on the approach proposed by Noble and Sewell. While the former is limited to beam models restricted to moderate large deformations, the latter is valid for arbitrarily large deformations (and strains). The numerical implementation of the complementary-dual extremum principles can lead to simple true global upper bounds of the error of the approximate solutions.

Mots clés: Geometrically exact finite strain beams; Complementary-dual extremum principles; Error estimation; Global upper bounds

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

H.A.F.A. Santos, J.P. Moitinho de Almeida. Dual extremum principles for geometrically exact finite strain beams. International Journal of Non-Linear Mechanics, 2010, 46 (1), pp.151. ⟨10.1016/j.ijnonlinmec.2010.08.003⟩. ⟨hal-00701877⟩