Eulerian formulation for large-displacement analysis of space frames

In this paper, a new general procedure is presented for modeling the effects of large displacements on the response of space frames subjected to conservative loading. An incremental definition of rotations is adopted based on an improved rotational transformation matrix, and a convected (Eulerian) system is employed for establishing the contribution of individual elements to the strain energy (U). The Eulerian displacements are obtained by means of element-based local vectors in which the vectors representing the principal axes of bending follow the deformed configuration of the element and are continuously updated to a position normal to the element chord. The nonlinear solution procedure is formalized in terms of transformations between the Eulerian and the global systems, and expressions for geometric stiffness and transformation matrices are explicitly derived. Verification examples utilizing an elastic quartic formulation and employing the nonlinear analysis program ADAPTIC are presented to demonstrate the accuracy and versatility of this method in the large-displacement analysis of space frames.