Justification scheme for milling waffle background

In the manufacture of dry and fuel compartments of missiles ensuring weight tolerance is a priority. In practice, this is ensured by the introduction of lightweight materials together with the optimal design of the supporting set of ribs (waffle background) of orthotropic shells and waffle shells. The manufacturing technology of which is difficult and costly in view of the difficulty of ensuring the accuracy and perfection of the shape of the waffle background cell. In modern conditions, when manufacturing a waffle shell for a fuel tank, reinforcement processing is carried out by milling on a monolithic blank using specialized machine systems. At the same time, the choice of the waffle background processing scheme remains an urgent issue: on a flat panel or on a bent shell. The problem of selection arises due to the requirements for the accuracy of the waffle background. It is important to maintain the part mass tolerance and geometric perfection of the cell shape. All this generally affects the perception of design loads and the carrying capacity of the rocket. At the same time, the methods and processes of processing the waffle background should be productive and economically feasible. The proposed justification will make it possible at the start of the design of new promising products to more accurately determine the technological and production costs necessary for the production of parts with a waffle background with given parameters and accuracy.

Aeroelastic stability of a cylindrical shell of linearly varying thickness

For the first time, the aeroelastic stability equations of a composite cylindrical shell of linearly varying thickness are obtained on the basis of the bending theory of orthotropic shells for a shell subjected to axial forces and supersonic gas flow. The solution of the equations is assumed of the form of a trigonometric series in the axial coordinate. The problem is reduced to an infinite system of algebraic equations by the Bubnov-Galerkin method. The obtained characteristic equation is approximated by the Lagrange polynomial, whose stability is investigated with the use of the Routh-Hurwitz criterion. As a numerical example, the effect of the thickness gradient, structural damping and axial force on the critical velocity for a composite shell of linearly varying thickness in supersonic gas flow is shown. The refinement in the value of the critical velocity resulting from the use of the suggested model is about 35% as compared to the results for a shell of averaged constant thickness. This indicates the relevance of this model for aircraft weight optimization. The suggested approach expands the range of problems to be solved and allows for the analysis of the aeroelastic stability for orthotropic cylindrical shells of linearly varying thickness in supersonic gas flow.

Bistable polar-orthotropic shallow shells

We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in order to enhance morphing structures. The material law causes stress singularities when the circumferential stiffness is smaller than the radial stiffness ( β < 1), requiring a careful choice of the trial functions in our Ritz approach, which employs a higher-order geometrically nonlinear analytical model. Bistability is found to strongly depend on the orthotropic ratio, β , and the in-plane support conditions. An investigation of their interaction offers a new perspective on the effect of the hoop stiffness on bistability: while usually perceived as promoting, it is shown to be only stabilizing insofar as it prevents radial expansions; however, if in-plane supports are present, it becomes a redundant feature. Closed-form approximations of the bistable threshold are then provided by single-curvature-term approaches. For significantly stiffer values of the radial stiffness, a strong coupling of the orthotropic ratio and the support conditions is revealed: while roller-supported shells are monostable, fixed-pinned ones are most disposed to stable inversions; insight is given by comparing to a simplified beam model. Eventually, we show that cutting a central hole is a suitable method to deal with stress singularities: while fixed-pinned shells are barely affected by a hole, the presence of a hole strongly favours bistable inversions in roller-supported shells.

Nonlinear Deformation of Flexible Orthotropic Shells of Variable Thickness in an Unsteady Magnetic Field

The analysis of the stress state of a flexible orthotropic shell under the influence of a time-varying mechanical force and a time-varying external electric current is performed, taking into account the mechanical and electromagnetic orthotropy. The effect of thickness on the stress-strain state of the orthotropic shell is investigated. The results obtained indicate the influence of thickness on the deformation of the shell and the need to take this factor into account in the design schemes.