A higher order beam finite element with warping eigenmodes

Generalized warping analysis of curved beams by BEM

“…7a [29], (E ¼ 4 Â 10 7 kN=m 2 , G ¼ 2 Â 10 7 kN=m 2 , L ¼ 10 m, R ¼ 6:366 m) under a concentrated load either P z ¼ 1000 kN or P y ¼ 1000 kN eccentrically applied at its free end, is examined. In Table A4 of Appendix A the geometric constants of the cross section are presented.…”

Isogeometric Methods in Dynamic Analysis of Curved Beams Including Warping and Distortional Effects

“…(3a), (3b) and (3c) for the warping and two distortional functions, respectively. As mentioned earlier, the iterative equilibrium scheme described by Ferradi, Cespedes and Arquier [1] as well as Dikaros and Sapountzakis [32] is employed here until a sufficient number of modes is obtained to represent accurately the non-uniform warping effects and the corresponding distortional ones. In order to initialize the above stated boundary value problem, the rigid body movements of the cross section are employed.…”

“…The analysis of such members employing the so-called "Higher-Order Beam Theories" [1][2][3] is of increased interest due to their important advantages over more elaborate approaches based on shell or solid finite elements [4], which are mainly incorporated in commercial software.…”

Generalized Warping Effect in the Dynamic Analysis of Beams of Arbitrary Cross Section

“…As a consequence, discrepancies in stress components near fixed supports or concentrated loads may arise [12,13,21,49,50]. In the present study, a correction of stress components is performed without increasing the number of global kinematical unknowns, following the analysis presented in [49,50].…”