Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads

The nonlinear analysis with an analytical approach on dynamic torsional buckling of stiffened functionally graded thin toroidal shell segments is investigated. The shell is reinforced by inside stiffeners and surrounded by elastic foundations in a thermal environment and under a time-dependent torsional load. The governing equations are derived based on the Donnell shell theory with the yon Karman geometrical nonlinearity, the Stein and McElman assumption, the smeared stiffeners technique, and the Galerkin method. A deflection function with three terms is chosen. The thermal parameters of the uniform temperature rise and nonlinear temperature conduction law are found in an explicit form. A closed-form expression for determining the static critical torsional load is obtained. A critical dynamic torsional load is found by the fourth-order Runge-Kutta method and the Budiansky-Roth criterion. The effects of stiffeners, foundations, material, and dimensional parameters on dynamic responses of shells are considered.

A SURVEY OF WORKS ON THE THEORY OF TOROIDAL SHELLS AND CURVED TUBES

This paper gives a survey of works on the theory of toroidal shells which were done by our two universities in recent years.

A NOVEL SOLUTION OF TOROIDAL SHELLS UNDER AXISYMMETRIC LOADING

Several improvements are made for existing asymptotic expansions for the axisymmetric toroidal shells. The new expansions are numerically satisfactory and satisfy the accuracy of the theory of thin shells. All of them are expressed in terms of generalized Airy functions , instead of Bessel or Airy function for the homogeneous and Lommel function for the particular solutions, respectively, as in the existing work. In this paper, three particular solutions are given, one of which is just the solution obtaine d by Tumarkin(1959) and Clark(1963).

Analysis and experiment of a vessels shell cover in submarine structure

This paper aims to achieve analysis and experiment resuhs that relate to mechanics capability and structural parameter of a special saddle shell of revolution. Theoretically speaking, the saddle shell of revolution consists of a toroidal shell and a spherical shell. The shells simultaneous equations can be solved with harmonious terms. Where, the fundamental equations can be solved by as-ymptotic exponential perturbation method. The equations of special solution can be solved by Hovozhilovs special solution. This new idea is from a study of some existing solutions of the toroidal shell. The resuhs have been proved by compared with some experimental results. The experiments aims to study the effect caused by change of material parameter, or by change of different geometric dimensions of the saddle shell, which include the change of thickness, the change of radius of shell, and the change of ribs. Finally, the accepted product of the saddle shell were reinforced by a toroidal rib has been submitted.

Approximate Calculation of U-shaped Bellows

U shaped bellows are widely used for sealed connections that require some flexibility. Since the structure of U shaped bellows is complex,numerical methods are often used to calculate mechanical parameters such as stiffness, displacement, etc. In this paper approximate formulas are derived for calculating the stiffness and the stresses of a U shaped bellows with a slender ring shell. These formulas can be used for designing bellows and selecting corrugation parameters. Comparison between the results of the approximate caculation and a finite element calculation showed that the approximate formulas are applicable for μ<0 5.