単繊維の曲げモーメントに関する研究 : (第 1 報)曲げモーメントと曲率の理論的考察

概要

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A relation between bending moment M and curvature 1/ρ on the theoretical consideration is not easy. Therefore, in order to make clear a relation between bending moment M and curvature 1/ρ on the theory, the author and research professor P. Grosberg did a research studing in the theoretical fields. On the theoretical relation between bending moment M and curvature 1/ρ of single fibre is following. Since, as first step, length on the X and Y axis of end point of single fibre in each time of rotation is obtained from Equations (1) and (2). x=ρ・sinθ_<ƒ>=ℓ・sinθ_<ƒ>/θ_<ƒ>…(1) y=(1-cosθ_<ƒ>)・ℓ/θ_<ƒ>…(2) but, as a angle range of θ_<ƒ> is following. Namely, -π/2≦θ_<ƒ>≦+π/2…(3) Where θ_<ƒ> is obtained by theoretical equation of x and y. A calculational value P in each time of E_s and E_G is obtained by θ_B. But, θ_B is obtained as a measuring value. A bending moment M of single fibre is obtained by following equation. M=P・x…(4) Also, a curvature 1/ρ of single fibre is obtained from factors of θ_<ƒ> and ℓ. Since, 1/ρ=θ_<ƒ>/ℓ…(5) Where ℓ is constant value. Thus, bending moment M and curvature 1/ρ of single fibre is obtained from Equations (1)-(5) and these factors of x, y, θ_<ƒ>, P, . θ_B and ℓ. As a name of many factors between bending moment M and curvature 1/ρ of single fibre is following.
金城学院大学の論文
1973-12-25