Generalized Warping Analysis of Composite Beams of an Arbitrary Cross Section by BEM. II: Numerical Applications

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

“…It is worth here noting that the shear stresses generated by the above displacement considerations exhibit an inconsistency concerning the non-vanishing of tractions xn τ on the lateral surface of the beam [22,49,50]. As shown in previous studies, this inconsistency may be responsible for non-negligible errors in estimated normal stress values.…”

“…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.…”

“…As shown in previous studies, this inconsistency may be responsible for non-negligible errors in estimated normal stress values. In the present study this inconsistency is removed by performing a suitable shear stress correction, which is discussed in detail in a previous work of the same authors [49,50]. Within the context of the above considerations, the displacement components of an arbitrary point of the beam at an arbitrary time instant are given as ( )…”

“…are the independent warping parameters introduced to describe the nonuniform distribution of primary warping due to shear [49,50]. …”

“…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.…”