Geometric and material nonlinear analyses of elastically restrained arches

Effects of approximations on non-linear in-plane elastic buckling and postbuckling analyses of shallow parabolic arches

“…In addition to the snap-through (limit point) buckling, parabolic arches can buckle also in an anti-symmetric bifurcation fashion [17,19]. It has been shown [17,19] that when this bifurcation buckling occurs, the force parameter b needs to satisfy b ¼ p; and b ¼ 1:4303p ð20Þ for pin-ended and fixed arches respectively, which can be substituted into the non-linear equilibrium equation given by Eq.…”

“…(9) and (12) has limit points [17,19]. Because limit points are local maximum or minimum points, differentiating the non-linear equilibrium equation given by Eq.…”

“…The merit of these assumptions is that they lead to the same differential equations of equilibrium and the same analytical solutions for shallow parabolic arches as those for shallow circular arches. Because analytical solutions for the non-linear in-plane elastic buckling and postbuckling of shallow circular arches with different boundary conditions under different loads are available in the open literature [3,4,[19][20][21][22][23][24][25][26][27][28][29][30], these approximation assumptions make analytical investigations of the non-linear buckling and postbuckling of shallow parabolic arches quite straightforward. Although the assumptions given by Eqs.…”

Effective treatment of complex statical and dynamical load combinations within shakedown analysis of 3D frames

“…Note how the MSE evaluation of the yield function could also be conveniently exploited in different contexts of analysis where both material and geometrical nonlinearities occur. This could be particularly convenient in path following analysis especially when using corotational approaches (see for example [33,28,34]). …”

Geometrical Nonlinearity Analysis of the Steel Network Arch Bridges / Plieninų Tinklinių Arkinių Tiltų Geometrinio Netiesiškumo Vertinimas

“…Didelis indėlis į pavienių lanksčiai ir standžiai įtvirtintų plieninių arkų elgsenos ypatumus yra įdėtas Australijos mokslininkų, tokių kaip Pi, Trahair ir Bradford, kurie vertino ne tik pavienių arkų darbo stadiją, elemento ir sistemos geometrinius rodiklius (lenkiamasis standis, arkos pakylos aukštis ir tarpatramio ilgis), bet ir pradinius įtempius, geometrinius nuokrypius ir konstrukcijos geometrinį netiesiškumą (Pi, Trahair 1999;Pi, Bradford 2004;Pi et al 2008;Zhao et al 2013). Todėl plieninių pavienių arkų ir arkų, sujungtų su styga pakabomis, geometrinio netiesiškumo vertinimas dažniausiai siejamas su arkos pastovumo užtikrinimu arba stabilumo praradimu (Pi et al 2007). Netiesinė konstrukcijos elgsena yra ypač aktuali statiš-kai neišsprendžiamoms sistemoms, tokioms kaip tinkliniai arkiniai tiltai.…”