No abstract

The rings torsion theory that is based on the assumption about flat rigid cross-section was suggested by the authors in the previous papers. The analytical expressions of torsional stiffness have been derived for different kind of loads: pure moment, shear force and surface pressure. In the present paper the analytical model of flange with attached cylindrical shell deforming under internal pressure is suggested. The mechanical system is split into two parts (flange and shell) with the help of imaginary section method. An unknown shear force and bending moments are applied to both parts according to this method. Therefore flange is loaded under internal pressure, shear force and bending moments. As mentioned above, for all these loads the angle of flange cross-section rotation can be presented in analytical form based on the rings torsion theory. Full rotation angle is presented as a sum of these angles. The radial displacement of imaginary section was determined on the basis of the assumption about flat rigid cross-section. On another hand, the rotation angle and radial displacement of imaginary section are determined on the base of the cylindrical shell bending theory too. Two linear equations in the unknown shear force and bending moment were derived by equating corresponding expressions. In such а way the analytical model of flange with attached shell deforming was built. The comparison calculations by finite element methods confirmed the adequacy of proposed model.

The problem of axial stretching of a plate with a double-periodic system of round holes arranged in a checkerboard pattern is considered. The specified problem is reduced to elasticity second problem for one period of plate, which was solved by the finite element method. As a result, the reduced elastic characteristics of the equivalent homogeneous orthotropic plate are found. The analysis of their behavior depending on dimensionless geometrical parameters is carried out. The area of variation of the geometric parameters was divided into two subareas. The behavior of the equivalent elastic characteristics in these areas is significantly different. It turned out that the double-periodic perforated plate shows significantly anisotropic behavior. The limit values of the Poisson's ratios can reach unity and, on the other hand, may be less than the original value. Dependences of the stress concentration coefficient on dimensionless geometrical parameters are obtained too. Performed comparative analysis of the obtained results with the results known from the literature, confirmed their adequacy.