直交異方性合板偏平シェルの力学特性

抄録

It is very difficult to solve precisely the fundamental equations of simply supported orthotropic plywood shallow shells (Eqs. (2)and(3)) when the axes of elastic symmetry do not coincide with those of co-ordinates (γ₁₆≠0, γ₂₆≠0, δ₁₆≠0 or δ₂₆≠0). The authors attempted to solve them by means of the computer FACOM 230-60 (Kyoto Univ.) and by application of the finite difference method, and succeeded in solving them with good approximate accuracy (see Fig. 1). The computed results, especially that on the influence of curvature, are shown in Figs. 2∼4.
As shown in Fig. 2, the elliptic paraboloidal shells and cylindrical shells are more rigid than the hyperbolic paraboloidal shells when the four edges are simply supported by means of rollers. The distribution of bending moments and membrane stresses become more complicated as shown in Figs. 3 and 4 when the fiber directions incline to the edges. Examination of these figures will make clear the mechanical characteristics of shells with orthotropic layers. Their experimental analysis was also made using the simply supported shallow cylindrical plywood shells made of beech veneer under uniformly distributed 7×7 points-load (see Fig. 5). The experimental results of the cross laminated shells whose face grains are parallel to the direction of the curvature (Ortho. 0°) and those inclined at 45° (Ortho. 45°) are shown and compared with the computed results in Figs. 6∼10. The comparison shows that good agreement between them has been obtained. But it also shows that there is a little difference between the experimental support condition and the theoretical one (see Figs. 6∼12). This difference is mainly due to the edges of the shells having slipped perpendiculer to the edges on the supports (see Figs. 8, 9 and 11). The transverse shear deflection which is neglected in the theoretical analysis is also considered to be one of the causes of the difference in Fig. 6. The deflection of the parallel laminated shell is about twice as large as that of the cross laminated shells and the strain caused by the membrane stress is about 7 times large (see Fig. 11).
And the parallel laminated shell was destroyed along the center line when the total load reached only 126kg (see Fig. 7). The strain distributions of the plywood shells under a concentrated load at the center were also observed and the experimental results are shown with the computed ones in Fig. 12.