EXACT-SOLUTIONS FOR TIMOSHENKO BEAMS ON ELASTIC FOUNDATIONS USING GREENS-FUNCTIONS

In this paper, a unified formulation is given for bending, buckling, a nd vibration problems of uniform Timoshenko and Euler-Bernoulli beams resting on various models of elastic foundations. Canonical Green's fu nctions are derived for these beams, which can be readily used to furn ish exact solutions. In addition to elucidating the behavior of the be ams, the exact solutions serve as important benchmark results for chec king the convergence and accuracy of approximate solutions obtained fr om numerical methods. For this purpose, deflection, buckling, and vibr ation results for beams on elastic foundations are presented.