Development of Numerical Method with High Accuracy using Incremental Perturbation Method for Predicting Critical Behaviors of Spatial Frames

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In structural design, it is indispensable to predict the final state of the structure as accurately as possible. The most definite final state is a mechanical critical state of structure under various external disturbances. The aim in this research is to develope the high-precise numerical analysis method that is able to simulate various critical behaviors of spatial steel frames. In the derivation of the analysis method, 3-dimensional finite rotation is very carefully dealt and the incremental perturbation method is adopted to ensure the accuracy of simulation of the critical behaviors. The results in this research are summarized as follows :(1) A critical behavior of timber single-layr lattice dome with steel joint-members is simulated sufficiently by the beam-column FEM method refined in this research. The rotational buckling of joints observed in a full-scale experiment is almost perfectly by this method. The second bifurcation of rotational buckling of joints is shown at first in this numerical experiment.(2) A numerical method is proposed which is able to predict with good accuracy the critical behavior of elastic spatial frames with flexural torsion. The warping function is used for estimating the flexural torsion in elements. The lateral buckling behaviors of elastic beams are analyzed by the proposed method.(3) An effective strategy for truncation error control is proposed in order to compute an appropriate value of the time length in a numerical dynamic analysis of structure. The strategy estimates relative truncation errors both in odd power terms and in even power terms of perturbation expansion series, and is demonstrated to be efficient and accurate in a free vibration response of a linear single-degree-of-freedom system.