Collapse analysis of Al 6061 alloy conical shells with circular cutouts under axial loading: experiment and simulation

The current research is conducted to investigate the experimental and numerical study of crushing behavior and buckling modes of thin-walled truncated conical shells with or without cutouts and discontinuities under axial loading. In this regard, Instron 8802 servohydraulic machine is used to perform the experiments. Additionally, the buckling modes, derived from the axial collapse phenomenon, are simulated with Finite Element (FE) software. The force-displacement diagrams extracted numerically are compared with experimental results. Various factors, including maximum force, energy absorption, specific energy, and failure modes of each case, are also discussed. The results indicate that the increasing cutout cause a decrease in the maximum force and energy absorption. Moreover, with cutouts reduction, the failure modes of the samples changed from the diamond asymmetric mode and single-lobe mode to multi-lobes, and with removing cutouts, the failure mode is observed to be completely symmetric.

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.

Existence of Solutions to a Class of Nonlinear Arbitrary Order Differential Equations Subject to Integral Boundary Conditions

We investigate the existence of positive solutions for a class of fractional differential equations of arbitrary order δ>2, subject to boundary conditions that include an integral operator of the fractional type. The consideration of this type of boundary conditions allows us to consider heterogeneity on the dependence specified by the restriction added to the equation as a relevant issue for applications. An existence result is obtained for the sublinear and superlinear case by using the Guo–Krasnosel’skii fixed point theorem through the definition of adequate conical shells that allow us to localize the solution. As additional tools in our procedure, we obtain the explicit expression of Green’s function associated to an auxiliary linear fractional boundary value problem, and we study some of its properties, such as the sign and some useful upper and lower estimates. Finally, an example is given to illustrate the results.

Natural Frequency Analysis of Multilayer Truncated Conical Shells Containing Quiescent Fluid on Elastic Foundation with Different Boundary Conditions

In this paper, natural frequency of a multilayer truncated conical composite shell conveying quiescent fluid on elastic foundation with different boundary conditions is investigated and analyzed. The governing equations are presented based on the first-order shear deformation theory. Bernoulli’s equation and velocity potential have been used in the shell-fluid interface to obtain the fluid pressure. The fluid used in this study is considered non-compressible and non-viscous. The beam functions and the Galerkin weight functions method are used to describe and solve the coupled system of differential equations. Three types of boundary conditions are considered to investigate the natural frequency of the conical shells. The results show that the presence of the fluid in the conical shell reduces the fundamental natural frequency values. Also, by changing the semi-vertex conical angle from [Formula: see text] to [Formula: see text] for the simply support boundary conditions, the fundamental natural frequency value for the composite conical shell without and with fluid increases, and the presence of the elastic foundation increases the frequencies of the empty and full-fluid composite conical shells.