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The problem of estimating the influence of an infinite series of equidistant circular holes of equal radius on the distribution of stress in an infinite plate under uniform twisting is treated according to the Poisson‐Kirchhoff theory of thin plates. The parametric coefficients included in the solution of this problem are determined by using the method of perturbation. For some special cases, numerical results are given.

Theoretical analyses are presented for the dynamic stability of a cylindrical shell partially filled with liquid, under periodic shearing forces. In the analyses, the dynamic version of the Donnell equations and the velocity potential theory are used for the motions of the shell and the contained liquid, respectively. The problem was solved by using the Galerkin method and the equations of motions coupling the shell and the liquid were derived from a type of coupled Mathieu’s equation. The instability boundaries where parametric resonance occurs were determined by using Hsu’s method. Numerical calculations were carried out for cylinders with various dimensions, i.e., radius-thickness and length-radius ratios. The effects of the liquid-filling ratio and the static shearing forces on the instability boundaries were clarified. It is found that the instability regions enlarge with increasing liquid and that the principal instability regions appear under the simultaneous action of the static shearing force.

The problem of finding stress resultants in an infinite plate under bending which contains infinite rows of circular holes of equal radius with their centers placed periodically along the horizontal and vertical lines is discussed on the basis of the Poisson‐Kirchhoff theory of thin plates. The parametric coefficients involved in the solution are determined by using the method of perturbation. For some special cases, numerical results are given.