多重有向連続体理論序説 : 一般化された連続体力学理論における director frame の多重化について

Abstract

This paper tries to construct the theory of multi-directed continuum mechanics, by multiplying the director frame based on the thought of generalized continua. The multi-directed continuum corresponds to the medium which has many degrees of freedom for the deformation of every material particle. Mathematically it is considered as an assemblage of material points which have a macro director polyad (i.e. frame) and n micro director polyads. And actually, one of such continua will be the continuous model of discrete or heterogeneous media (e.g. reticulated framestructures, prismatic shells, layered media, and composit materials). Independently of dimension the basic equations are formulated by Hamilton's principle (§4), after defining the geometrical relations (§2) and the strain measures (§3). In section 5 some different expressions of them are concidered for comparison. Therefore by varying values of indices, they can form the theories of one, two and three dimension respectively, and fundamentally imply the concepts in many published works of the generalized continuum mechanics. Section 6 is a review of the concept of directors and gives the outline of an ideal multi-directed continuum model for actual media by analogy. Then it is noted that the deformation of a macro polyad space which includes micro polyads, is constrained homogeneously.