Generalized Warping Analysis of Composite Beams of an Arbitrary Cross Section by BEM. I: Theoretical Considerations and Numerical Implementation

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

“…In the current study, which is an extension of a previous work of the same authors [49][50] at the dynamic regime, a general boundary element formulation for the dynamic nonuniform warping analysis of beams of arbitrary cross section, taking into account shear lag effects due to both flexure and torsion, is presented. The beam cross section (thin-or thick-walled) is homogeneous and can surround a finite number of inclusions.…”

“…The beam is subjected to the combined action of arbitrarily distributed or concentrated dynamic axial loading and transverse loading, as well as to bending, twisting, and warping moments. Nonuniform warping distributions are taken into account by using four independent warping parameters multiplying a shear warping function in each direction [49][50] and two torsional warping functions, which are obtained by solving corresponding boundary value problems. It is worth mentioning here that the stress field arising from the preceding kinematical considerations leads to the violation of the longitudinal local equilibrium equation and the corresponding boundary condition [22] due to inaccurate representation of shear stresses.…”

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 aim of this Chapter is to propose a new formulation by enriching the beam's kinematics both with out-of-and inplane deformation modes and, thus, take into account both cross section's warping and distortion in the final 1D analysis of curved members, towards developing GBT further for curved geometries while employing independent warping parameters, which are commonly used in Higher Order Beam Theories (HOBT). The approximating methods and schemes proposed by Dikaros and Sapountzakis [13,32] are employed and extended in this study. Adopting the concept of end-effects and their exponential decay away from the support [3], appropriate residual strains are added to those corresponding to rigid body movements.…”

“…The obtained set of modes contains axial, flexural and torsional modes in order of significance without distinction between them. To avoid the additional effort needed in order to recognize the most significant modes, the iterative local equilibrium scheme described in the work of Dikaros and Sapountzakis [32] is adopted until the error due to residual terms becomes minimal. The functions derived are evaluated employing 2D BEM [33].…”