ANALYTICAL ELEMENT FOR TIMOSHENKO BEAM ON ELASTIC FOUNDATION

Based on a double-parameter elastic foundation model and a Timoshenko deep beam model, the deflection control equation of an elastic foundation beam is deduced, its analytical general solution is obtained, and analytical displacement shape functions for the deflection, section flexural angle and shear angle of a double-parameter elastic foundation deep beam are constructed. The potential energy functions for the beam model and beam-foundation model are established, respectively. The corresponding elements for a double-parameter elastic foundation deep beam are obtained via the minimum potential energy principle, and their element formulas are also received. The calculation results show that the relative error of the element for beam model under a uniformed load is 0.221%, and that under a non-uniformed load is zero. The relative error of the element for the beam-foundation model under the uniformed load is zero, that under a concentrated force at two ends is 6.597%, and that under the concentrated force at mid-span is 102.716%. And there are no shear locking problems with this double-parameter Timoshenko beam element.