Generalized warping effect in the dynamic analysis of beams of arbitrary cross section

In this paper a general formulation for the nonuniform warping dynamic analysis of beams of arbitrary simply or multiply connected cross section, under arbitrary external loading and general boundary conditions is presented taking into account the effects of rotary and warping inertia. The nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, respectively, which are obtained by solving the corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation. A shear stress “correction” is also performed in order to improve the stress field arising from the employed kinematical considerations. Ten initial boundary value problems are formulated with respect to the displacement and rotation components as well as to the independent warping parameters and solved using the Analog Equation Method, a Boundary Element Method based technique in combination with an appropriate time integration scheme. The warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure BEM approach.