Cracking pattern of indented ice sheet bending failures

Ice sheet bending failures have been investigated extensively for ice loads on conical offshore structures and icebreakers in arctic regions. Most previous theoretical studies focus on bending failures of semi-infinite level ice, ice wedges, or finite-sized rectangular ice floes. For indented ice sheet bending failures, Nevel (1992) and Lau (2004) developed analytical ice load models by assuming a radial-before-circumferential cracking pattern. Recently, real-time simulations of ice-structure interactions are gaining increasing traction due to their great application potential. The analytical or semi-analytical models implemented into the real-time simulator significantly influence the accuracy of real-time simulations. Against this backdrop, the cracking pattern assumption needs to be more critically examined, and the criterion for cracking pattern determinations is in demand for utilizing different models for different cracking patterns in real-time simulations. Motivated by this need, the current paper establishes the cracking pattern determination criterion for indented ice sheet bending failures, based on the theory of plates on elastic foundations and normalized formulae. It is found that large indentation lengths and radii of structure waterline curvature induce a circumferential-before-radial cracking pattern. Conversely, small indentation lengths and radii of structure waterline curvature result in a radial-before-circumferential cracking pattern.

Natural vibrations of nanostrips with cracks

Employing the main equations of the theory of plates accounting for the rotational inertia the transverse vibrations of nanobeams and nanostrips are investigated. The nano strips under consideration have piecewise constant dimensions of cross sections. The nanosheets are weakened by cracks at re-entrant corners of steps. While the material behavior corresponds to the Eringen’s nonlocal theory of elasticity it is assumed that the cracks produce additional local compliance, which can be evaluated with the aid of the stress intensity factor at the cracktip. A numerical algorithm for determination of natural frequencies of nanosheets is developed.

TRANSVERSE BENDING AND FREE VIBRATIONS OF ELASTIC ISOTROPIC PLATES IN THE FORM OF ISOSCELES TRIANGLES

This paper considers elastic isotropic plates in the form of isosceles triangles with combined boundary conditions (a combination of hinged support and rigid restraint conditions along the sides of the contour). Calculations were performed using FEM to determine the integral physical characteristics in the considered problems F (the maximum deflection of uniformly loaded plates w0 and the fundamental frequency of oscillations in the unloaded state ω). On the basis of the obtained numerical results, approximating functions have been constructed: "maximum deflection - form factor of plates", "basic frequency of oscillations - form factor of plates", the structure of which corresponds to the structure of similar formulas obtained when presenting known exact solutions in the corresponding problems of technical theory of plates in isoperimetric form. Based on the properties of the form factor of plates, these approximating functions limit the whole set of considered integral physical quantities and therefore can be used as reference solutions for the calculation of triangular plates of arbitrary form applying the method of interpolation by form factor (MIFF). We consider an example of calculation of a plate in the form of a rectangular triangle with hinged support of the sides.

A theoretical solution of the axial stiffness of a cylindrical shell with a circular plate

A structure of a cylindrical shell with a circular plate end cap is usually used in connect different shaft system and it is necessary to estimate the axial stiffness in order to analyze the vibration of the rotor system. This paper builds the model of this structure. The theoretical solution of the bending deflection of the circular plate and the cylindrical shell are deduced by using the classic theory of plates and shells, and the continuity boundary conditions at the junction of the circular plate and the cylindrical shell. Furthermore, the axial stiffness of the structure is solved through considering the relationship between the external force-bending deformation. Two different boundary conditions for the left side of the cylindrical shell is considered and their axial stiffness varying with the length of the cylindrical shell is calculated. For verification, a finite element model of the structure is built and analyzed. The theoretical results fairly coincide with the finite element ones.