Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

H.A.F.A. Santos (1) , P.M. Pimenta (2) , J.P. Moitinho de Almeida (1)

1 Civil Engineering Department
2 Polytechnical School of the University of Sao Paulo

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints.

Mots clés: Three-dimensional beams; Geometrically exact analysis; Complementary energy; Hybrid and multi-field variational principles

H.A.F.A. Santos, P.M. Pimenta, J.P. Moitinho de Almeida. Hybrid and multi-field variational principles for geometrically exact three-dimensional beams. International Journal of Non-Linear Mechanics, 2010, 45 (8), pp.809. ⟨10.1016/j.ijnonlinmec.2010.06.003⟩. ⟨hal-00663407⟩