A problem of non – linear deformation of five–layer conical shells with allowance for discrete ribs

A problem of non – linear deformation of multiplayer conical shells with allowance for discrete ribs under non – stationary loading is considered. The system of non – linear differential equations is based on the Timoshenko type theory of rods and shells. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance distcrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers. As a numerical example, the problem of dynamic deformation of a five-layer conical shell with rigidly clamped ends under the action of an internal distributed load was considered.

Pseudospheric shells in the construction

The architects working with the shell use well-established geometry forms, which make up about 5-10 % of the number of known surfaces, in their projects. However, there is such a well-known surface of rotation, which from the 19th century to the present is very popular among mathematicians-geometers, but it is practically unknown to architects and designers, there are no examples of its use in the construction industry. This is a pseudosphere surface. For a pseudospherical surface with a pseudosphere rib radius, the Gaussian curvature at all points equals the constant negative number. The pseudosphere, or the surface of the Beltram, is generated by the rotation of the tracersis, evolvent of the chain line. The article provides an overview of known methods of calculation of pseudospherical shells and explores the strain-stress state of thin shells of revolution with close geometry parameters to identify optimal forms. As noted earlier, no examples of the use of the surface of the pseudosphere in the construction industry have been found in the scientific and technical literature. Only Kenneth Becher presented examples of pseudospheres implemented in nature: a gypsum model of the pseudosphere made by V. Martin Schilling at the end of the 19th century.

Large Elastic Strain of The Elastomeric Torus Shell (Rubber Coupling) under the Combined Action of Torques and Centrifugal Forces

The article considers solving the problem of large axisymmetric deformations of elastomeric torus shells of revolution, loaded with jointly acting torques, axial and centrifugal forces. The task is posed due to the calculation of rubber elements of couplings. The calculations are performed according to the momentless shell theory by solving a nonlinear one-dimensional boundary value problem using the shooting method, as well as in a three-dimensional formulation using the finite element method. The calculation results are presented both for convex and concave torus shells. The load characteristics are compared for free and constrained torsion. The dependence of axial reactions in supports on torque and centrifugal forces has been investigated.

Free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure

In this paper, the free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure is investigated by the precise transfer matrix method. Under hydrostatic pressure, deformation and stress is generated in the rubber matrix composite shell. Based on the deformation characteristics of the rope structure, the deformation of the shell under hydrostatic pressure is analyzed. The stress of shell under hydrostatic pressure is included in the shell differential equation of motion in the form of pre-stress. Then considering the fluid-solid coupling boundary condition, the field transfer matrix of fluid-filled spherical shell is obtained. By the continuous condition of the state vector of the shell and the transformation relationship of the coordinate system, the transfer matrices at the position of the ring-stiffener and the connection position of the cylindrical shell and spherical shell are derived, and then the whole free vibration equation of the fluid-filled combined shells of revolution is assembled, and the natural frequencies are obtained by the boundary conditions. Eventually, the accuracy and reliability of the proposed method are verified by the results of literature and simulation results. Effects of the structural parameters of the spherical shell, the distribution of the ring-stiffeners, and the hydrostatic pressure on the natural frequencies of the fluid-filled combined shells of revolution are also discussed. Results of this paper can provide reference data for future studies in related field.