Pointwise equilibrating polynomial element for nonlinear analysis of frames

A pointwise equilibrating polynomial (PEP) element is proposed for nonlinear analysis of frames in which each member can be modeled by one element in most cases. The formulation of the element is based on the imposition of compatibility conditions at end nodes as well as the satisfaction of equilibrium at midspan. The resulting expression for this new element is accurate in describing the force-versus-displacement relations at the element level, is simple, and it does not lead to a significant numerical truncating error in the computer analysis. Its implementation in a nonlinear analysis program is straightforward. The accuracy of the analysis results by the element was found to be considerably higher than its cubic counterpart in a number of well-known examples. The limitation or inconvenience of the method of stability function such as the separation of the solution for tensile, compressive, and zero load cases is eliminated.