Formulation of geometrically non-linear problems in the spatial reference frame

This paper presents a new formulation for geometrically non-linear problems and their numerical treatment by the p-version of the finite element method. The formulation is characterized by a weak form based on the spatial representation of the equilibrium equations, a deformed geometry mapped by the displacement field, a natural description for non-conservative loads that keeps the symmetry of the equations, and a direct (non-incremental) iterative algorithm to solve the equations. The paper is concerned only with problems for which the solution is unique, i.e. the load-displacement curves are single-valued, and the strains are small. Examples are presented. (C) 1997 by John Wiley & Sons, Ltd.