モード重畳法による複層ラチスドームの非線形座屈解析に関する研究

Abstract

The primary objective of this paper is to research on characteristics of geometrically non-linear buckling behaviour of double layer latticed spherical domes by means of modal analysis.Modal analysis is applied to derivation of the system matrices of simultaneous differential equations representing the displacements by linear combination of several eigen modes which are independent and orthogonal each other and transforming variables into generalized coordinates which are coefficients multiplied to eigen modes.These eigen modes were calculated from the global system matrices.By using modal analysis method in the buckling analysis of double layer latticed domes, it will be expected to reduce the large dimension stiffness matrices of 3-dimensional displacement variables of global systems to the small things of generalized coordinates extremely.The merit of use of modal analysis, moreover, is to avoid the degeneration of system matrices in multi degrees on bifurcation points.We can decrease the possiblity of divergence in the procedure of numerical calculation.It is, therefore, very effective to determine the direction of post-buckling path on the bifurcation points.Arc length method and Newton-Raphson iteration method is used to obtain the geometrically non-linear equilibrium path.Three different non-linear stifihess matrices of the slope-deflection method for the unit members are derived for the analysis of the system of rigid nodes.