一般多重有向連続体理論 : 基礎式と比較考察について

概要

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By extending a macro polyad to n single-directors, this paper aims at releasing the homogeneous deformation of a macro director polyad space which includes n micro director polyads in the previous paper. A general multi-directed continum is an assemblage of material points which have n single-directors and n' micro director polyads. Mechanics of it is derived from the previous paper (§2) and some special cases are considered (§3). Then several theories associated with the generalized continua are compared with the theory presented here, and they are unifyingly interpreted by expressing the n single-directors field microscopic analytically (§4). Although the basic equations seem ones by Ericksen & Truesdell or Toupin who formulated the theory of n dimensional directed continua, they will contribute to a viewpoint of giving some explicte structures to the director space and of indicating the variety of ideas corresponding to micro structures. Accordingly the present theory will be able to have more extensive applications to actual media. Regularly reticulated framestructres and prismatic shells must be successful models of general multi-directed continua. The most important subject of the remainder is a reasonable reduction of unknown variables against increasing them by the multiplication of the directors.
社団法人日本建築学会の論文
1975-01-30