Nonlinear Finite Element Analysis of Clamped Arches

Geometric and material nonlinear analyses of elastically restrained arches

“…8, respectively. It is noted that the virtual work due to reactions p and P k of distributed and concentrated elastic restraints are generally not included in previous formulations [1][2][3][4][5][6][7][8].…”

“…In the nonlinear range, particularly after buckling, the deformations of the arch increase rapidly and become very large, so that predicting the large deformation nonlinear behaviour correctly requires consideration of the effects of large deformations on the deformed curvature and on the axial deformations as pointed out by Pi and Trahair [1]. However, in conventional formulations for curvedbeam elements [2][3][4][5][6], the nonlinear strains under in-plane loading consist only of nonlinear membrane strains and linear bending strains. The higher-order bending strain components have been ignored in the conventional finite-element (FE) formulations of curved-beam elements [2][3][4][5][6].…”

“…However, in conventional formulations for curvedbeam elements [2][3][4][5][6], the nonlinear strains under in-plane loading consist only of nonlinear membrane strains and linear bending strains. The higher-order bending strain components have been ignored in the conventional finite-element (FE) formulations of curved-beam elements [2][3][4][5][6]. Pi and Trahair [1] developed a curved-beam element for the in-plane nonlinear elastic analysis of arches by considering the effects of the higher-order curvature components due to bending and the axial deformations of the bending deformation.…”

A combined implicit–explicit algorithm in time for non‐linear finite element analysis

“…Geometry of the ÿxed-at-edges arch. [13] or [14] simulated it in the pre-buckling behaviour. A further development was performed by Pin and Trahair [15] carrying out simulations after buckling point.…”

In-plane elastic buckling of pin-ended shallow parabolic arches

“…They assumed that the arches were geometrically linear where the effect of pre-buckling deformation on the buckling was ignored. Several researchers conducted numerical analyses of the buckling of arches (Noor and Peters [5]; Calhoun and DaDeppr [6]; Elias and Chen [7]; Wen and Suhendro [8]). Recently, Pi and Trahair [9], and Moon et al [10] reported that nonlinear pre-buckling deformation is significant to the buckling of shallow arches.…”