MIXED FORMULATION OF NONLINEAR BEAM FINITE-ELEMENT

Recent studies show that beam finite elements that enforce equilibrium rather than compatibility along the element are better suited for the description of the nonlinear behavior of frame elements. This is part icularly true for elements that exhibit loss of strength and stiffness under monotonic and cyclic loads. Existing formulations, however, fai l to define a consistent way of implementing the force method in the c ontext of imposed kinematic, rather than static, boundary conditions, as is the case for element models in a standard finite element program . This paper derives the general formulation of a beam finite element from a mixed approach which points the way to the consistent numerical implementation of the element state determination in the context of a standard finite element program. The element state determination cent ers on a new iterative solution algorithm that is based on residual de formations rather than residual forces at the section and element leve l. Equilibrium is enforced in a strict sense along the element, while the section constitutive relation is satisfied within a specified tole rance when the algorithm converges. The proposed algorithm is general and can be used with any section constitutive relation.