NON-LINEAR STATIC AND DYNAMIC ANALYSIS OF FRAMED STRUCTURES

The present study is concerned with methods of nonlinear static and dynamic analysis of structures, particularly for application to geometrically nonlinear space frames. The displacement formulation of the finite element method is adopted. Large displacements are accounted for by using a material (Lagrangian) description of motion from a fixed reference frame, assuming small strains and moderately large rotations. Curved beam elements are considered by introduction of initial deflections in the element stiffness relations. Higher order axial interpolation polynomials are included in order to obtain an appropriate coupling between axial forces and bending for the frame members. Efficient methods for instability and postbuckling problems have been a main point for the study of nonlinear static behaviour. This also includes evaluation of nonlinear numerical solution methods, some of which being applicable also in dynamic analysis. The efficiency of these methods are discussed in connection with the nonlinear dynamic response analyses presented. For the integration of the incremental equations of motion, a method based on transformation to generalized coordinates on modal basis is proposed and studied as an alternative to direct integration. Numerical examples are presented for both static and dynamic analyses, and it has been considered important to show the applicability of the nonlinear analysis methods to practical structural problems. The advantages of post-processing and extensive use of computer graphics in presenting results for nonlinear space structure analyses are demonstrated. © 1979.