Study on applying finite pole element method to analysis of piles under complex loads with different boundary restraints

Assumed that horizontal displacement of piles was a longitudinally cubic power function,improved pole element equation with consideration of P-△ effect was derived from the traditional finite element method incorporating the moment/ horizontal-displacement relationship and shear/horizontal-displacement relationship inferred from differential equation of piles under inclined and eccentric loads.And then the improved pole element method was presented to calculate displacement and stress of piles under inclined and eccentric loads,moments,weight of piles,horizontal and vertical distributed loads,scattering vertical forces and soil-pile friction considering the effect generated by slight inclination of piles.Case study was done for displacement and stress calculation of piles under different boundary restraints with the Matlab process edited with the improved finite pole element method.Finally conclusions were drawn as follows:(i) the improved finite pole element method was proved to be an effective method for pile analysis under complex loads with different boundary restraints;(ii) there would be great difference between the calculated results of displacement and stress of piles with different pile head restraints,while there would be little difference between the calculated results of displacement and stress of piles with different pile tip restraints.