A kinematically exact finite element formulation of elastic–plastic curved beams

Abstract

A finite element, large displacement formulation of static elasticplastic analysis of slender arbitrarily curved planar beams is presented. Nonconservative and dynamic loads are at present not included. The Bernoulli hy

Variable order secant matrix technique applied to the elastic postbuckling of arches

“…The results of the present study are very efficient even for 10 elements. It is seen from Table I that using a 16 element discretization of the arch, the present formulation predicted exactly the same result presented by Saje et al [21]. The next problem is the bending of semi-circular cantilever arch with rectangular cross section (B × H ) as shown in Figure 4.…”

“…The vertical and horizontal deformation of the arch crown in the postbuckled state is presented in Figure 3. Table I presents the results of the present study compared with the Table I it is seen that the most accurate results for the circular arch problem is reported by Saje et al [21]. The results of the present study are very efficient even for 10 elements.…”

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

“…the works presented by (Cardona and Geradin, 1988), (Simo and Vu-Quoc, 1991), (Pimenta and Yojo, 1993), (Simo et al, 1995), Ibrahimbegovic and Mikdad, 2000;Ibrahimbegovic and Knopf-Lenoir, 2003), (Saje et al, 1998), Jelenic and Crisfield, 1999), (Planinc and Saje, 1999), Atluri, 1988, 1989;Atluri, 1996, 1998;Atluri et al, 2001), (Betsch and Steinmann, 2002), (Zupan and Saje, 2003b), (Kapania and Li, 2003b,a), (Romero, 2004), (Mata et al, 2007), (Makinen, 2007), (Lens and Cardona, 2008), (Ghosh and Roy, 2008) and (Pimenta et al, 2008).…”

Dual extremum principles for geometrically exact finite strain beams

“…Since these pioneering works, considerable progress has been made on the geometrically exact analysis of three-dimensional framed structures, from both theoretical and numerical points of view, see e.g. Cardona and Géradin (1988) [6], Ibrahimbegovic and co-workers (1995,2000,2003) [16,19,18,17], Petrov and Géradin (1998) [31], Saje et al (1998) [36], [7,22], Gruttmann et al (2000) [15], Atluri and co-workers (1988,1989,1996,1998,2001) [20,21,33,2], Betsch and Steinmann (2002) [3], Pimenta and Campello (2003) [32], Zupan and Saje (2003) [50], [24,23], Mata et al (2007) [27], Makinen (2007) [26], Santos et al (2009) [38,37] and many others.…”