Vol 24, No 1 (2024)

A two-dimensional formulation and method for numerical solution of problems of deformation and loss of stability of multilayer elastoplastic shells of rotation under quasi-static and dynamic axisymmetric loading with torsion have been developed. The defining system of equations is written in a Cartesian or cylindrical coordinate system. Modeling of the process of deformation of shell layers is carried out on the basis of hypotheses of solid mechanics or the theory of Timoshenko-type shells, taking into account geometric nonlinearities. Kinematic relations are written in speeds and formulated in the metric of the current state. The elastic-plastic properties of the shell are described by the generalized Hooke's law or the theory of plastic flow with nonlinear isotropic hardening. The variational equations of motion of the shell layers are derived from the three-dimensional balance equation of the virtual powers of the work of continuum mechanics, taking into account the accepted hypotheses of the theory of shells, either a plane deformed state or a generalized axisymmetric deformation with torsion. Modeling of the contact interaction of shell layers is based on the condition of rigid gluing or the condition of non-penetration along the normal and sliding along the tangential. To solve the governing system of equations, a finite-difference method and an explicit time integration scheme of the “cross” type are used. The method was tested on the problem of buckling of a three-layer cylindrical shell with elastoplastic load-bearing layers of aluminum alloy D16T and an elastic filler under quasi-static and dynamic loading by hydrostatic pressure, linearly increasing with time. The problem was solved in two versions: all three layers were modeled as a finite element of a continuous medium, or the load-bearing layers were modeled as shell elements, and the filler as elements of a continuous medium. The results of calculations using the two models are in good agreement with each other in terms of ultimate pressures and modes of buckling.

The problem of obtaining estimates of the strength and resource characteristics of critical engineering infrastructure facilities under operational multiparametric nonstationary thermomechanical impacts is considered. The basic degradation mechanisms in structural materials (metals, alloys) under these influences are identified. The methodology of resource assessment of responsible engineering facilities  based on end-to-end modeling of the entire life cycle of the object is substantiated. End-to-end modeling forms a set of computational experiments of different levels of complexity, each of which has its own characteristic features and semantics. From the perspective of the mechanics of the degraded continuum, a mathematical model of the damaged medium has been developed, in which the processes of thermoplasticity and damage accumulation are generated by thermal fatigue. The model describes the effects of cyclic thermoplastic deformation; kinetics of damage accumulation; conditions of macroscopic destruction of the material. The model postulates the representation of the yield surface and the principle of gradiency of the velocity vector of plastic deformations at the loading point. A variant of the thermoplasticity equations describes the main effects in proportional and disproportionate modes. The thermoplasticity model is constructed as a system of “nested” models and contains the forms of equations of the theory of plastic flow under small deformations: various variants of isotropic hardening (ideally plastic material with a constant flow surface, linear isotropic hardening, variant of isotropic nonlinear hardening), various cases of kinematic hardening (linear kinematic hardening, the case of purely nonlinear kinematic hardening) and the general case of translational isotropic hardening. The kinetics of fatigue damage accumulation is described by introducing a scalar damage parameter and based on the energy principles of taking into account the main effects of the damage accumulation process for arbitrary complex loading modes. The condition of reaching the critical damage value is used as a criterion for macroscopic destruction. The relationship between the components of the model is carried out by introducing effective stresses. The paper presents a numerical analysis of the thermal fatigue life of a compact sample with stress concentrators simulating the operation of parts in the nozzle box of a steam turbine of a nuclear power plant. During the analysis, the characteristic features of thermal fatigue in the details of power equipment were studied. It is shown that the end-to-end modeling technology can be effectively used to assess the resource characteristics of power equipment parts under operational loading conditions.

The axisymmetric problem for the transverse compression of a thin elastic disk is considered in slip absence.  An asymptotic solution for the interior stress-strain state is constructed. An approach to determining a plane boundary layer localized near the outer contour of the disk is outlined.

The aerospace industry often uses cylindrical shells with elliptical cross-section, which are manufactured from composite material using a filament winding method. During the fabrication process or operation of the structure, there is a probability of shape imperfection in the form of deviation from a circular cross-section. The vibration analysis of such structures containing fluid requires an in-depth study to determine the performance characteristics affecting their life cycle. In this article we develop a mathematical formulation and present the corresponding finite element algorithm for determining the natural frequencies of vibrations of layered composite elliptical cylindrical shells filled with fluid. The problem is solved in a three-dimensional formulation by the finite element method. The curvilinear surface of the shell is represented as a set of flat rectangular segments, in which the relations of the classical laminated plate theory are fulfilled. The membrane displacements are described using bilinear Lagrange shape functions. The deflection in the direction normal to the lateral surface and the rotation angles are approximated by incompatible cubic Hermite polynomials. Small vibrations of an ideal compressible fluid are described in the framework of the acoustic approximation by a wave equation for hydrodynamic pressure, which, together with the boundary conditions and the impermeability condition on the wetted surface, is transformed to a weak form. The verification of the developed numerical algorithm is carried out by comparing the obtained natural frequencies of vibration with the known data presented in the literature for layered composite circular cylindrical shells. A number of examples are considered to evaluate the influence of geometrical dimensions of the structure, boundary conditions at the shell edges and the ratio of ellipse semi-axes. New quantitative and qualitative dependencies have been established, and the possibility of the natural frequency control through the selection of parameters of composite material has been shown. 

For obtaining new metal matrix composites, one needs to develop approaches to the selection of reinforcing additives, the identification of the relationship of the properties of the resulting material with the composition, concentration and morphology of the additives introduced, the creation and search for new affordable and cheap additives. As one of the solutions to this problem, the authors propose to obtain aluminum matrix composites based on the structuring of an Al matrix with titanium carbide nanostructures ($\leq 5$ nm) by atomic layer deposition (ALD). The resulting material has an important feature — the absence of obvious interface boundaries between the Al matrix and the reinforcing carbide phase, that ensures the components binding into a single whole. Composites, for the hardening of which a reinforcing phase with surface carbide nanostructures is used, in addition to a higher tensile strength, demonstrate a more plastic fracture pattern characteristic of dispersed hardening of materials. With an increase in the amount of the composite reinforcement from 1 to $5\%$, embrittlement of the material does not occur, as is observed when carbide particles are introduced into the Al matrix by other methods. 

The effect of a constant intensity heat flux on forced oscillations of a circular three-layer plate with an asymmetric thickness is investigated. The plate is thermally insulated along the contour and the lower plane. An approximate solution of the thermal conductivity problem was used, obtained by averaging the thermophysical parameters of the materials of the layers over the thickness of the package. According to the Neumann hypothesis, free plate oscillations caused by an instantaneous drop in heat flow are summed up with forced oscillations from the power load. The deformation of the plate package corresponds to the polyline hypothesis. In relatively thin outer bearing layers, Kirchhoff's hypotheses are valid. In sufficiently thick incompressible filler, the deformed normal retains straightness and length, but rotates by an additional angle. The formulation of the corresponding initial boundary value problem includes the equations of motion obtained using the d'Alembert principle and the variational Lagrange method. The initial conditions are assumed to be homogeneous, the contour of the plate is pivotally supported. The analytical solution of an inhomogeneous system of partial differential equations is obtained using the method of expansion into a series according to a system of proper orthonormal functions. As a result, analytical expressions are written out for three desired functions – plate deflection, shear and radial displacement in the filler. An example of oscillations under the action of an instantaneously applied uniformly distributed load is considered. A numerical parametric analysis of the natural oscillation frequencies and the resulting solution depending on the intensity of the heat flux for a plate with layers of titanium alloy, fluoroplast-4, and duralumin is given.