2次元地動が励起する剛床要素系の複素化変位・変形応答における平面分布上の幾何特性

概要

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For dynamic systems subjected to horizontally 2-D earthquake motions, the condition of in-plane rigidity for floors is shown to lead to findings of marked mathematical regularities characterizing necessarily and sufficiently their planar distribution field of 2-D and complex-valued displacement/deformation response. Corresponding tensorial formulations provide four variates at a single point located on/between rigid-floor elements. They consist of three intensity-related variates (major and minor intensities, and directivity of principal axes) in the real part plus one correlation-related variate in the imaginary part. The contour lines for major and minor intensities form a family of orthogonal trajectories which is an assemblage of confocal ellipses and hyperbolas, respectively, with a common set of orthogonal symmetry axes, and coincide totally with the flow lines for directivity of principal axes. On the other hand, the contour lines for correlation factor between principal directions are composed of an evolutionary transition from ellipses to hyperbolas including a single point. Parabola or line as boundary situations. Even though distorted obliquely on the distribution plane, the latter is featured by one-directional symmetry indicating positive upper and negative lower bounds for the correlation factor.
一般社団法人日本建築学会の論文
1996-03-20