Nonlinear Elastic Frame Analysis by Finite Element

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Abstract
Plane and space frames are considered. The member end rotations relative to the chords of the deformed member are assumed to be small. Large translations and rotations of the chord are allowed. The longitudinal and transverse displacements are respectively interpolated by linear and cubic functions. The axial strain due to the transverse displacement is averaged over the element length. The averaging is shown to reduce the strain energy and the element stiffness. Without it the element would generally be too stiff. The incremental stiffness matrices are derived in Lagrange coordinates for small rotations. Solution procedures based on a fixed coordinate system and a moving or updated coordinate system are presented. Numerical results indicated that the fixed coordinate procedure works well for small displacement problems. The updated procedure is necessary if large displacements are involved. Comparison of numerical results with those of other methods indicates that the methods presented are competitive.