The results of studies on natural vibrations of circular laminated cylindrical shells completely filled with a stationary compressible fluid and resting on an elastic foundation, which is described by the two-parameter Pasternak model, are presented. The behavior of the elastic structure and the fluid medium is described within the framework of classical shell theory and Euler’s equations. The equations of motion of the shell, together with the corresponding geometric and physical relationships, are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed into a system of differential equations using the generalized differential quadrature method. The solution to the formulated boundary value problem is carried out using Godunov’s orthogonal sweep method. To calculate the natural vibration frequencies, a combination of a step-by-step procedure followed by refinement using the bisection method is employed. The reliability of the obtained results is confirmed by comparison with known numerical and numerical-analytical solutions. For simply supported, clamped, and cantilever two-layer and three-layer cylindrical shells, the dependences of the lowest vibration frequencies on the stiffness of the elastic foundation are analyzed in detail. It is demonstrated that the nature of the influence of the elastic foundation on the fundamental frequencies and corresponding vibration modes of shells with different boundary conditions depends to a greater extent on the layup scheme and reinforcement angle of the composite material.

The work is devoted to the numerical analysis of the process of increasing the inner radius of a cylindrical sleeve made of a shape memory alloy using 3D and axisymmetric types of finite elements. Numerical modeling was performed in the Simulia Abaqus software package using user material technology. A parameter related to the third invariant of the stress deviator is used as a parameter of the stress state type. Within the framework of the work, a linear dependence of the material constants on the stress state type parameter is assumed. The problem is considered within the framework of a nonlinear deformation model of SMA during phase and structural transformations. The obtained solution takes into account the influence of the stress state type on the material behavior. Within the framework of the work, the stress-strain state of a thick-walled cylindrical sleeve was calculated in two formulations: 1. Under monotonic active loading in the low-temperature martensitic phase state (martensitic inelasticity mode). 2. During the direct thermoelastic transformation under the action of constant internal pressure upon cooling through the temperature interval of the direct martensitic transformation. The work compares the use of 3D and axisymmetric types of finite elements in the numerical analysis of the process of increasing the inner radius of a thick-walled cylindrical sleeve. In addition, the influence of the number of finite elements across the sleeve section on the resulting dependences for stresses, displacements, and the stress state type parameter was determined. It was established that the use of axisymmetric elements is preferable for solving problems of this class. The results obtained during the work can be successfully used in the design of thermomechanical connecting sleeves made of SMA.

Fused deposition modeling (FDM) is one of the most common additive manufacturing technologies in the world and is widely used in various industries both for prototyping parts and for obtaining functional polymer materials with specified properties. It is known that materials obtained by FDM have low stability of strength properties and highly pronounced anisotropic characteristics. Currently, one of the pressing problems of synthesized materials is the low strength of the interlayer bond. To solve this problem, most 3D printing methods are being improved towards optimizing technological parameters in order to obtain materials with higher and more stable mechanical properties. Based on the results of a previously conducted study on polylactide (PLA) samples, it was shown that the two-layer weave implemented between the polymer threads of the material affects the strength characteristics. Due to the relevance of using various high-temperature structural polymer materials for 3D printing of functional parts, this work investigated the effect of two-layer weave on the strength under uniaxial static tension of samples made of polyetheretherketone (PEEK). The article systematizes the most frequently encountered works in the literature on the influence of various FDM 3D printing parameters on the mechanical properties of PEEK samples. A comparison of the strength characteristics of samples with and without weave obtained under static tension is presented, and the nature of their fracture is compared. The strength characteristics obtained under static tension across the polymer threads indicate the fundamental possibility of using two-layer weave to increase the strength of polymer materials manufactured using additive technology.

This research presents the results of an experimental and analytical program to study the effect of thermal loading on the mechanical properties of the most commonly used composite materials at present temps in the market, as well as the effect of the stacking sequence and fiber orientations on the hardness of these materials under different temperatures (room temperature (~20оC) and their elevation to extreme temperatures 40, 60, 80, 100оC). In this sense, this study was conducted in two phases: the first is an experimental study that includes practical tests on the tensile strength of several types of composites at different temperatures, in addition to tests on different fibers orientations under different thermal loads. As for the second study, it is an analytical study using the ABAQUS program, related to the analysis of the thermal effect on stress intensity factor (SIF), stress concentration factor (SCF), and the stresses distribution for different stacking sequences. The conclusion drawn from both studies is that the general mechanical properties of composite materials decrease with increasing temperature, as these materials are negatively affected by increasing temperature.

The solution to the nonlinear coupled problem describing soil deformation during fluid outflow has practical applications, for example, in modeling roadbed deformation or calculating uneven settlement of engineering structures. Compaction of water-saturated dispersed soils under load is generally nonlinear and accompanied by large deformations; therefore, the development of a geometrically and physically nonlinear coupled consolidation model that accounts for the elastic-plastic behavior of the material, accompanied by changes in porosity and permeability, is highly relevant. Creating proprietary software code is advisable as it contributes to raising the level of scientific modeling and programming in our country. It is relevant to study the stability of the solution to the saddle-point consolidation problem theoretically in linear and nonlinear formulations. In this study, a fairly general formulation of the problem of coupled deformation of a porous solid medium with fluid flowing through the pores is formulated, mathematically investigated, substantiated based on models and experimental capabilities of continuum mechanics, and numerically implemented within the framework of physical and geometric nonlinearity. The problem formulation is derived in terms of velocities of the solid phase displacement and changes in water pressure in differential and variational forms. The filtration and porosity change equations are reformulated in Lagrangian coordinates of the solid skeleton according to the ALE (Arbitrary Lagrangian-Eulerian) approach using the relative fluid velocity. The applicability of the Uzawa method as the main part of the method for solving nonlinear consolidation problems is demonstrated. The convergence of the iterative process is studied theoretically. Computational experiments were conducted to solve the linear problem to confirm the theoretical convergence rate of the iterative process. Computational experiments not only confirmed the theory but also added various aspects regarding the nature of convergence not captured by theoretical consideration.

The dynamics of spatial motion of a spacecraft with an extensible, absolutely flexible cable with mass (payload) at the end in a central gravitational field is considered. In the computational model, the cable is divided into sections (finite elements), and the distributed mass of the cable is replaced by a system of lumped masses at the element nodes. The distributed gravitational load is also reduced to the nodes of the finite element model. The spacecraft is considered an absolutely rigid body, with which a moving coordinate system is associated, moving relative to some inertial coordinate system. Sections of the deployed part of the cable are considered rectilinear. The tension force and longitudinal deformation of the cable are assumed constant within a finite element. The unknown variables of the problem are the coordinates of the finite element model nodes and the rotation angles of the spacecraft relative to the inertial coordinate system. The differential equations of motion of the spacecraft with the deployed cable are derived based on the principle of virtual work in generalized coordinates, taking into account nonlinearities in elastic and inertial forces. The resulting closed system of nonlinear differential equations allows determining the time dependences of the desired quantities. Examples include solutions to two conservative problems: the fall of a cable fixed at an initial point in a plane with a mass at the free end; and the towing of a mass using a massive cable. In the towing problem, a nonlinear static problem was first solved to determine the initial configuration of the cable. The solutions were obtained by numerically integrating the nonlinear equations of motion using the Runge-Kutta-Fehlberg method of 4-5 orders with automatic step selection. The stability of the computations was monitored by checking the fulfillment of the total energy conservation law of the system.

This article describes a methodology for determining the effective mechanical properties of composite lattice shells made of carbon-carbon composite materials, intended for creating lightweight, strong, and rigid structures. This methodology is based on the asymptotic homogenization of differential equations with rapidly oscillating coefficients and allows the original lattice structure to be replaced by an equivalent structure in the form of a solid shell. In the structure of a lattice structure, as a rule, a periodically repeating fragment is observed, which, in relation to the scale of the entire structure, has a significantly smaller size and can therefore be considered as a periodicity cell for the Bakvalov asymptotic homogenization method. This method involves separating processes occurring at different scale levels based on the analysis of the original equations, which in this case are equations with rapidly oscillating coefficients. At the scale level of one periodically repeating element, a cell problem arises, and at the scale level of the entire structure, a problem for a homogeneous shell with reduced effective characteristics arises. Accordingly, the entire problem, according to the asymptotic homogenization method, is divided into two problems: the macroscale for the entire structure and the microscale for the periodically repeating fragment. This article examines the microscale problem, the methodology for its solution, and the dependence of the effective characteristics on the geometric parameters of the lattice structure. In this case, the development of the lattice shell with a periodically repeating fragment on a plane is considered, i.e., the curvature of the shell is neglected, and its mechanical behavior is described by a system of elasticity theory equations with matrix rapidly oscillating coefficients. As a result, we obtain a methodology that allows predicting the optimal geometric characteristics of lattice structures taking into account their stiffness characteristics. This article presents numerical examples of determining the effective physical and mechanical characteristics of a transition section in the form of a cylindrical lattice shell. A numerical study of the dependence of these characteristics on the angle of inclination of the spirals in the lattice structure is carried out. As a result, this methodology allows selecting the optimal angle of inclination of the spirals in the structure of the lattice transition section.

Structural elements made of elastomeric composites are often used in vibration dampers across various industries. A distinctive feature of elastomeric composites is their high reversible deformation under low loads, which makes this class of materials susceptible to vibrations of various frequencies and intensities. In this work, accelerated tests were conducted to study the effect of UV radiation on the complex of elastic-strength and elastic-hysteresis properties of elastomeric composites based on butyl rubber and EPDM, filled with carbon black P-324 with the addition of microshungite particles. Unfilled compositions were also investigated. The samples were kept under a UV lamp for one month. The elastic-strength properties of the elastomeric composite samples were studied before and after irradiation. To assess the change in the elastic-hysteresis properties of the sample surface, the nanoindentation method was used. The change in the surface structure of the elastomeric composite samples before and after UV irradiation was monitored using an optical microscope. During the experiment, a significant influence of carbon black and microshungite additives on the physical and mechanical characteristics of the samples was established. Under UV radiation exposure, significant changes in elastic-strength properties are observed in unfilled compositions. The elastic-strength properties of filled compositions did not undergo significant changes. For filled compositions based on butyl rubber, the highest strength was found compared to other compositions. The maximum value of relative hysteresis during indentation was obtained for samples based on EPDM filled with carbon black and microshungite. When analyzing the data obtained by the nanoindentation method, it was revealed that the addition of microshungite slows down the aging process of samples under UV radiation. It was found that for samples of elastomeric composites based on EPDM and butyl rubber, the degradation of the polymer matrix proceeds by different mechanisms.

The deformation process of a three-layer strip with outer layers made of shape memory alloy and an inner viscoelastic layer upon heating one of the outer layers through the temperature interval of the reverse thermoelastic phase transformation is considered. The thickness of the inner layer is 8 times greater than the thickness of the outer layers, the instantaneous modulus of the inner layer material is less than one-tenth of the martensitic Young’s modulus of the SMA, but more than 6 times greater than the long-term modulus of the inner layer material. Before creating the package, the material of the outer layers is in a completely martensitic phase state with the same specified phase-structural deformation. Unlike the known analogue, this work takes into account the nonlinearity of the phase transformation diagram and the change in the elastic moduli of the SMA during the phase transition. The problem is solved by a semi-inverse method assuming a linear distribution of longitudinal strains across the thickness of the inner layer. Mathematically, the problem is reduced to a resolving system of two ordinary linear first-order differential equations with variable coefficients with respect to the dimensionless parameters of the distribution of longitudinal stresses in the viscoelastic layer. The dependence of stresses in the outer and inner layers, the curvature of the strip, and its average longitudinal strain on the heating rate of the active layer, calculated from the reduced time equal to the ratio of physical time to the relaxation time of the viscoelastic layer material, is investigated. It was found that with increasing heating rate, the influence of the variability of the Young’s modulus of the outer layers during the phase transition on the desired quantities increases. An effect of non-monotonic stress change in all layers during monotonic heating, associated with the nonlinearity of the phase transition diagram, was discovered.