Vibration analysis of 3-D composite beam elements including warping and shear deformation effects

In this paper, the dynamic analysis of 3-D composite beam elements restrained at their edges by the most general boundary conditions and subjected in arbitrarily distributed dynamic loading is presented. For the solution of the problem at hand, a boundary element method is developed for the construction of the 14×14 stiffness matrix and the nodal load vector of a member of an arbitrarily shaped composite cross section, taking into account both torsional warping and shear deformation effects, which together with the corresponding mass and damping matrices lead to the formulation of the equation of motion. To account for shear deformations, the concept of shear deformation coefficients is used, defining these factors using a strain energy approach. Eight boundary value problems with respect to the variable along the bar angle of twist, to the primary warping function, to a fictitious function, to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure BEM approach. Both free and forced vibrations are considered, taking also into account effects of transverse, longitudinal, rotatory, torsional and warping inertia and damping resistance. Numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy.