Two-layer Plate Research Articles

Determination of the Residual Life of Two-Layer Plates with Systems of Cracks Under Long-Term Static Loading at High Temperatures

We develop computational models aimed at the determination of the residual service life of two-layer plates with systems of cracks under long-term static loads at high temperatures. The models are based on the first law of thermodynamics of energy balance for the components and rates of their changes in a metallic two-layer body containing macrocracks and subjected to the action of long-term tension and high-temperature fields. We consider periodic and doubly periodic systems of cracks.

The study of the stiffness coefficient of the seam depending on the quantity of symmetrically located shift connection-sin an oval two-layer plate

The paper considers a two-layer isotropic plate on pliable connections, for which the theory of calculation of composite plates by A.R.Rzhanitsin was adopted. With the help of bending moments Mx(My), the numerical stiffness coefficient of the seam is calculated. The numerical basic studies were carried out on an oval two-layered plate in the case of a rigid and hinged support of the plate along the contour. It proved that the stiffness coefficient of the seam ξ depends on the main coefficient after the hard oscillation frequency ω. The authors constructed the graph of the change of the natural oscillation frequency (ω) and the graph of the change of the stiffness coefficient of the seam (ξ) on the number of shift connections (nss./ne).

Numeral determination of the tensely-deformed state of coated thin plate at shock influence punch

A numerical simulation of the impact process on a thin two-layer plate with a double-sided coating of a steel punch having a flat working part with its partial penetration into the plate was carried out applying the finite element method. To determine the structure’s stress-strain state, a non-stationary contact boundary thermo-elastoplastic problem was solved, in such way as to put in variation of the materials’ mechanical properties and their nonlinear dependence on temperature and strain rate. Analysis of the deformations and stresses fields showed that when the punch is not fully penetrated, the lower layer of the coating peels off and the brittle fracture of the upper layer occurs, i.e. redistribution of the stress field does not lead to a complete destruction of the plate or its breakdown. With the use of layered structures and durable coatings of plate elements materials in protective structures made of light metals and alloys, the resistance of the structure to an impact failure increases.

3-D exact solution of two-layer plate bonded by a viscoelastic interlayer with memory effect

An exact solution for simply supported two-layer plate sandwiching a thin viscoelastic interlayer under transverse load is proposed. The deformation of each plate layer is described by the exact three-dimensional linear elasticity equations. The viscoelastic characteristic of interlayer is simulated by the standard linear solid model, considering the memory effect of the material. The shear and transverse normal strains in the interlayer are simultaneously considered in the analysis. The analytical approach is presented to obtain the solution of stresses and displacements in the plate. The present solution can be used as a benchmark to access other simplified solutions for the problem aforementioned. The comparison analysis shows that the finite element solution has a close agreement with the present solution. However, the solution based on Kirchhoff-Love hypothesis is greatly different from the present solution for thick plates. It is indicated that the effect of the transverse normal strain in the interlayer increases with the increase of the interlayer thickness, especially for thick plates. Finally, the influences of geometric and material parameters on the plate deflections are investigated in detail.

Modeling and Determination of the Nonsteady Thermoelastic State of a Two-Layer Thermosensitive Plate

On the basis of a model of thermosensitive bodies, we determine the distribution of the unsteady temperature field and the thermoelastic state caused by this field in a two-layer plate. A solution of the nonlinear nonstationary problem of heat conduction is constructed with the use of the Kirchhoff transformation, the method of linearizing parameter, and the integral Laplace transformation with respect to time. The influence of the temperature dependence of the thermophysical and mechanical characteristics of the materials of layers on the values and nature of the distributions of temperature and thermal stresses caused by this dependence in the plate are numerically analyzed.

Finite-Layer Method: Bending and Twisting of Laminated Plates with Delaminations

Based on the finite-layer method, considering the multilayered package as a set of jointly deforming layers, a method to analyze laminated plates with delaminations, which enables one to determine all the functions describing the stress-strain state of the plate, including interlayer stresses, is proposed. A refined deformation model of an anisotropic plate-layer taking into account the transverse linear and shear deformations and ensuring the exact fulfillment of boundary conditions on surfaces of the plate with consideration of all derivatives of existing surface loads is presented. Calculation of the multilayer plate is reduced to the solution of a boundaryvalue problem for a system of ordinary differential equations including the interlaminar shear stress. The order of the system depends on the number of layers in the package. The system is stiff, and the boundary value problem is solved by the stable Godunov–Grigorenko numerical method. As examples, the calculations of bending and twisting of two-layered plates with a partial delamination are presented.

A new boundary-type mesh-free method for solving the multi-domain heat conduction problem

ABSTRACTIn this article, a new high-precision boundary-type mesh-free method, called the virtual boundary mesh-free Galerkin method (VBMGM), is given for analyzing the heat conduction problem consisting of multiple media. A control equation of the proposed method is established by the the Galerkin method of the weighted residual methods. The virtual source function is approached through the radial basis function interpolation in the mesh-free method. Thus, the main feature of the proposed technique has the advantages of the mesh-free method, the boundary-element method, and the Galerkin method, a symmetrical coefficient matrix. The numerical meanings of the weighted values in the VBMGM equation, such as the partial derivatives the temperature, the heat flux, the temperature connection condition, and the heat flux connection condition, are clear. Numerical examples of a thick-walled cylinder consisting of two media and a two-layered rectangular plate are provided. The feasibility and the accuracy of the proposed technique are proved.

Buckling of a two-layered circular plate with a prestressed layer

Within the framework of nonlinear elasticity we analyze instability of a uniformly compressed circular two-layered plate with an initially compressed or stretched layer. For a constitutive relation of the material we use the incompressible neo-Hookean model. We assume that the lower layer is subjected to radial tension or compression. As a result in this layer there are initial strains and stresses. The two-layered plate is subjected to a uniform lateral compression. We study the stability of the plate with the use of the static Euler method. Within the method we determine loading parameters for which the linearized boundary-value problem has non-trivial solutions. We derive the three-dimensional linearized equilibrium equations for each layer. The solutions of the latter equations are obtained with the help of the Fourier method. The equation for critical strains is derived. We present an analysis of dependence of critical stress resultants on the initial strains and stiffness parameters.

Nonlinear Boundary-Value Problem of Heat Conduction for a Layered Plate with Inclusion

We consider a nonlinear boundary-value problem of heat conduction for an isotropic infinite heat-sensitive layered plate with heat-insulated faces containing a foreign through thermally active inclusion. By using the proposed transformation, we perform partial linearization of the initial heat-conduction equation. As a result of a piecewise-linear approximation of temperatures on the boundary surfaces of the foreign layers and the inclusion, the equation is completely linearized. We find an analytic-numerical solution of this equation with boundary conditions of the second kind in order to determine the introduced function with the use of the Fourier integral transformation. The computational formulas for the unknown values of temperature are presented in the case of a linear temperature dependence of the heat-conduction coefficients of structural materials for the two-layer plates. The numerical analysis is performed for a single-layer plate containing a through thermally active inclusion (the material of the plate is VK94-I ceramic and the material of the inclusion is silver).

Contribution of Mature Hepatocytes to Biliary Regeneration in Rats with Acute and Chronic Biliary Injury.

Whether hepatocytes can convert into biliary epithelial cells (BECs) during biliary injury is much debated. To test this concept, we traced the fate of genetically labeled [dipeptidyl peptidase IV (DPPIV)-positive] hepatocytes in hepatocyte transplantation model following acute hepato-biliary injury induced by 4,4’-methylene-dianiline (DAPM) and D-galactosamine (DAPM+D-gal) and in DPPIV-chimeric liver model subjected to acute (DAPM+D-gal) or chronic biliary injury caused by DAPM and bile duct ligation (DAPM+BDL). In both models before biliary injury, BECs are uniformly DPPIV-deficient and proliferation of DPPIV-deficient hepatocytes is restricted by retrorsine. We found that mature hepatocytes underwent a stepwise conversion into BECs after biliary injury. In the hepatocyte transplantation model, DPPIV-positive hepatocytes entrapped periportally proliferated, and formed two-layered plates along portal veins. Within the two-layered plates, the hepatocytes gradually lost their hepatocytic identity, proceeded through an intermediate state, acquired a biliary phenotype, and subsequently formed bile ducts along the hilum-to-periphery axis. In DPPIV-chimeric liver model, periportal hepatocytes expressing hepatocyte nuclear factor-1β (HNF-1β) were exclusively DPPIV-positive and were in continuity to DPPIV-positives bile ducts. Inhibition of hepatocyte proliferation by additional doses of retrorsine in DPPIV-chimeric livers prevented the appearance of DPPIV-positive BECs after biliary injury. Moreover, enriched DPPIV-positive BEC/hepatic oval cell transplantation produced DPPIV-positive BECs or bile ducts in unexpectedly low frequency and in mid-lobular regions. These results together suggest that mature hepatocytes but not contaminating BECs/hepatic oval cells are the sources of periportal DPPIV-positive BECs. We conclude that mature hepatocytes contribute to biliary regeneration in the environment of acute and chronic biliary injury through a ductal plate configuration without the need of exogenously genetic or epigenetic manipulation.

Асимптотические решения несвязанных задач стационарной теплопроводности и термоупругости с неклассическими граничными условиями для двухслойных пластин.

Асимптотические решения несвязанных задач стационарной теплопроводности и термоупругости с неклассическими граничными условиями для двухслойных пластин.

Three-Dimensional Deformation of a Multilayer Plate with Elastic Links Between its Layers

We proposed a method for the determination of the stress–strain state of a multilayer plate with elastic links between the layers in the case of its three-dimensional deformation. The solution of the problem is based on the method of compliance functions with application of the two-dimensional Fourier integral transformation. We construct recursive relations for finding the compliance matrices. For a two-layer plate subjected to the action of normal concentrated loads, we analyze the influence of the coefficients of elastic links on the distribution of stresses and displacements in the layers.

Calculation of Plates of Variable Rigidity on Elastic Foundation with Variable Coefficient of Subgrade Reaction

In the present paper is given the calculation of plates on an elastic basis with variable and constant coefficient of subgrade reaction. The calculation of plates bending is carried out by the finite element method. The calculation results are compared for different models of plate and an elastic basis. For a two-layer plate on an elastic basis, which has a heterogeneity in the plan, the results of calculation taking into account the increase of the height of the upper structure.

Расчет плит переменной жесткости на упругом основании методом конечных разностей

The article describes the calculation of plates on the elastic basis, both two-layer and single-layer. The calculation is based on the solution of the differential equation of bending plate by finite difference method. The calculation results are compared with the numerical solution in the program complex. The percentage of differences of values depending on the method of division or method of solving is shown. We considered a problem when a foundation plate and a construction are plates, which are deformed together, that, in fact, corresponds to the problem of bending a two-layer plate on elastic basis. In case of a two-layer plate in order to find the solution of the problem we need to solve the equation of bending of plates that are structurally similar to the traditional, but still give different results. In solving finite difference operators derivatives are substituted into differential equation which must be in accordance with each grid point, as well as at the border. If we consider the problem in the conventional formulation, only the lower layer is bended in the plate; the analysis of the plate, which takes into account the weight of its own layers, both layers are deformed together. Also when considering a two-layer plate, the neutral layer is deposed away from the upper layer, consequently, the whole foundation plate may be in the condition of stretching. When comparing the results of analytical and numerical calculations of the values obtained in general there are little discrepancies. Thus, there is the possibility of holding combined calculation of the “structure-foundation-base system” by finite difference method using a two-layer model of a plate on elastic basis.

Wavelet-Analysis-Based Chaotic Synchronization of Vibrations of Multilayer Mechanical Structures

The chaotic synchronization of the vibrations of contacting multilayer beam–plate–shell structures under external loading is studied. There are gaps between their layers. Such systems are called structurally nonlinear. Their behavior is studied comprehensively, and the influence parameters that characterize the safe and critical modes are determined. A method to study the chaotic phase synchronization of various nature is developed. Vibration synchronization for the following systems is analyzed: (i) a stack of two-layer plates (each equation is linear; however, there is structural nonlinearity if the plates contact), (ii) a plate reinforced with a beam, (iii) a stack of two-layer beams (each component is both physically and geometrically nonlinear; their contact interaction causes structural nonlinearity), (iv) a stack of two-layer shells (each component is both physically and geometrically nonlinear; their contact interaction causes structural nonlinearity)

Influence of Different Combinations of Explosively Welded Plates with the Same Areal Density on Their Antipenetration Performance

In order to analyze the influence of different thickness distributions on the antipenetration performance of layered plates with a good surface-to-surface combination, five types of two-layer steel/aluminum and three-layer steel/aluminum/steel plates with the same areal density were manufactured by the method of explosive welding. Ballistic experiments and numerical simulation were performed to study the antipenetration performance of the plates impacted by a spherical steel projectile of diameter 8 mm. A 14.5-mm riffled gun was used to launch the projectile, and the numerical simulation were carried out by using the LS-DYNA 3D explicit finite-element code. Effects of the number of layers, their thickness distribution, and total thickness on the antipenetration performance of the layered plates were investigated. Results showed that the antipenetration performance of the multilayer plates was better than that of a monolithic plate with the same areal density — the ballistic limit speed of the two-layer and three-layer plates, on the average, increased by 9.6 and 19.9% compared with that of the monolithic one. In addition, the antipenetration performance of the three-layer plates was better than that of the two-layer ones if the thickness of the steel and aluminum plates was same. The influence of layer thickness distribution on the antipenetration performance was more pronounced for the two-layer plates.

Multilayered and FGM structural elements under mechanical and thermal loads. Part I: Comparison of finite elements and analytical models

Nowadays modern composites with various internal structures are used for manufacturing of structural parts of airplanes and in other branches of engineering. They have a layered structure or can be produced as functionally graded materials (FGM). For specific applications some porosity is necessary to satisfy technological process requirements.In this paper several numerical models of structural parts of airplanes made of different composites were elaborated. The finite element (FE) analysis and the mechanical response of the structural elements were compared with previously formulated simplified analytical models [1,2]. The calculations concern estimation of deformation states in:–a layered exhaust pipe covered by thermal barrier coating (TBC) subjected to an internal pressure and a temperature gradient,–a two-layered plate under thermal loading,–three-layered beams subjected to bending with non-symmetrical cross-section,–a FGM beam element subjected to bending load,–a FGM two-layered rod subjected to uniaxial tension.For each considered case a good correlation of the results using both methods – analytical and numerical ones – was obtained, which proves correctness of the theoretical derivations, [1,2]. The paper provides also own general procedure for modelling of FGM in the ABAQUS.

Modeling of Processes Taking Place during Powder Coating Treatment by an Electron Beam or a Plasma Jet

This paper considers the problem of nding the temperature eld in two-layer metallic materials heated by a moving source of radiation. It describes developed by the authors numerical method for solving the problem of heating a two-layer plate by a moving axially symmetric surface heat source with regard to the function of distribution of the power density of the beam for which the program of computation in C was implemented. The calculation results were used for selecting the optimal parameters (speed and power density of the source) of modifying radiation of protective powder coatings on steel substrates.

A piezoelectric gyroscope based on thickness-shear modes of an AlN bimorph with inclined c-axes

We propose a new structure for piezoelectric gyroscope application. It consists of a two-layered plate of AlN with inclined c-axes. Through a theoretical analysis, it is shown that when the plate is electrically driven into thickness-shear (TSh) vibration in one direction and is rotating about the plate normal, the rotation causes a TSh vibration in a perpendicular direction with an electrical output which can be used to measure the angular rate of the rotation. Since AlN can be made into thin film devices much smaller than conventional crystal acoustic wave devices, the proposed gyroscope can be made much smaller than existing piezoelectric gyroscopes. The structure can also work with other crystals of class 6mm such as ZnO and polarized ceramics.

Estimation of the Subcritical Growth Period for a Through Crack of High-Temperature Creep in a Two-Layer Plate

The procedure for energy approach-based estimation of the subcritical growth period for a high-temperature creep crack in a two-layer plate is proposed. The validity of the procedure is illustrated by the example of central crack extension in the plate.