On the Explicit Representation of Transfer-Matrices of Curved Beams and Their Applications

概要

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The method of computing the stiffness constants of a curved beams by a simple finite element approach, where the beam is considered as a cascade-connection of straight elements, is used for the calculation of transfer-matrices of elasticity M^^-. Usually the calculations are carried out directly in numerical level by using an automatic computer according to the formula M^^- = M_1・M_2……M_n, where M_i is the transfer-matrix of the i-th element. By this method, however, an accumulation of errors decreases the accuracy, and few papers treated the characteristics of these matrices in general cases. In this paper, the author presents general explicit representations of matrices M^^- for two-dimensional curved beams. It is shown that the resultant matrix M^^- = M_1・M_2……M_n, where M_i = T_i(λ_iI+Φ_i), is generally representated in analytic-explicit forms, provided T_i is commutative-orthogonal and λ_iI+Φ_i are some triangular matrices. According to these results, the dilemma of increasing errors in the calculation against an increased number of partitions in order to obtain more precise results can be removed.
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