scholarly journals Contact problem for foundations with multilayer nonuniform coatings of variable thickness

2020 ◽  
Vol 162 ◽  
pp. 02004
Author(s):  
Kirill E. Kazakov ◽  
Svetlana P Kurdina
Keyword(s):  
Mathematical Model ◽  
Integral Equation ◽  
Analytical Solution ◽  
Contact Problem ◽  
Variable Thickness ◽  
Complex Shape ◽  
Integral Conditions ◽  
High Quality ◽  
Main Structure ◽  
Coating Layers

The article is devoted to study of the contact problem for a punch with a complex shape and a base with a coating consisting of nonuniform layers of variable thickness. Such a foundations are often found in practice. Coating layers in them can play a role, for example, heat or electric insulators. Such layers can be used as protection against mechanical stress on the main structure. Mathematical model of the problem is constructed. It is a mixed integral equation containing functions that describe the properties and thicknesses of the layers, as well as the shapes of the contacting bodies, and additional integral conditions. Analytical solution of the problem is presented for one of the formulation options. In the resulting solution, the functions associated with the properties and forms of bodies are distinguished by separate terms. This allows one to perform high-quality calculations and analysis of the behavior of the punch on the layer, even if these functions are rapidly changing.

On the Influence of Interlayer Nonuniformity on Contact Characteristics during the Interaction of a Pipe and a Rigid Cylindrical Insert

2021 ◽  
Vol 887 ◽  
pp. 706-710
Author(s):  
Kirill E. Kazakov
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Contact Problem ◽  
Analytical Methods ◽  
Integral Operators ◽  
Contact Stresses ◽  
Coating Properties ◽  
Discontinuous Functions ◽  
Different Types ◽  
Separate Factor

Contact problem for viscoelastic aging pipe with a longitudinally nonuniform thin elastic internal coating and a rigid cylindrical insert is considered in the paper. The basic integral equation with integral operators of different types (mixed integral equation) is given. It's analytical solution for contact stresses in insert area is presented. The solution is constructed in such a way that the function describing the inner coating nonuniformity is distinguished by a separate factor. This fact allows one to perform accurate calculations even in cases where the coating properties are described by rapidly changing and even discontinuous functions. Other known analytical methods do not allow one achieving such a results.

scholarly journals MATHEMATICAL MODELING OF EXPERIMENT ON BERKOVICH NANOINDENTATION OF ZRN COATING ON STEEL SUBSTRATE

2020 ◽  
Vol 27 ◽  
pp. 18-21
Author(s):  
Evgeniy Sadyrin ◽  
Andrey Vasiliev ◽  
Sergei Volkov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Steel Substrate ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Good Agreement

In the present paper the experiment on Berkovich nanoindentation of ZrN coating on steel substrate is modelled using the proposed effective mathematical model. The model is intended for describing the experiments on indentation of samples with coatings (layered or functionally graded). The model is based on approximated analytical solution of the contact problem on indentation of an elastic half-space with a coating by a punch. It is shown that the results of the model and the experiment are in good agreement.

scholarly journals Wear problem for tube with thin nonuniform inner coating and rigid insert with complex profile

2021 ◽  
Vol 243 ◽  
pp. 02008
Author(s):  
Kirill E. Kazakov ◽  
Svetlana P. Kurdina
Keyword(s):  
Mathematical Model ◽  
Integral Equation ◽  
Analytical Solution ◽  
Variable Properties ◽  
Complex Profile ◽  
Standard Methods ◽  
Properties Of Materials ◽  
Rigid Insert ◽  
Special Approach

The article describes the formulation of the problem of wear of an elastic pipe with a nonuniform internal coating by a rigid insert, the diameter of which is variable. For this problem, a mathematical model is built, which is a mixed integral equation. The resulting integral equation contains functions related to the variable properties of the coating and the shape of the insert. When constructing an analytical solution, a special approach was used, since standard methods do not allow taking into account the presence of rapidly changing functions in the equation, which can describe the shapes and properties of materials. In the resulting solution, the functions describing the variable properties of the coating and the profile of the insertion are separated by separate terms. This allows you to always get accurate results.

A Simple Spline Integral Equation Method for Circular Plates with Variable Thickness

2007 ◽  
Vol 353-358 ◽  
pp. 2687-2690
Author(s):  
Xin Zhu Zhou ◽  
Jian Jun Zheng
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Analytical Solution ◽  
Variable Thickness ◽  
Order Differential Equation ◽  
Spline Interpolation ◽  
Bending Moment ◽  
Integral Equation Method ◽  
Equation Method ◽  
Circular Plates

A simple spline integral equation method is presented in this paper for the axisymmetrical bending of circular plates with variable thickness. Firstly, the fundamental solution of a second-order differential equation is derived. With the slope of the deflection surface taken as an unknown function, an integral equation is then established for circular plates with variable thickness. The integral equation is solved numerically by cubic spline interpolation and the deflection and bending moment at any point within the circular plate are obtained. Finally, the validity of the proposed method is verified with the analytical solution obtained from the literature.

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

2017 ◽  
Vol 24 (2) ◽  
pp. 448-464 ◽  
Author(s):  
Jie Yan ◽  
Changwen Mi ◽  
Zhixin Liu
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Singular Integral ◽  
Material Properties ◽  
Elastic Layer ◽  
Coated Substrate ◽  
Receding Contact ◽  
Contact Size

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

Prediction of Surface Roughness in Compressed Air Jet Assisted High Speed End Milling of Silicon Using Diamond Coated Tools

2012 ◽  
Vol 576 ◽  
pp. 41-45
Author(s):  
A.K.M. Nurul Amin ◽  
M.A. Mahmud ◽  
M.D. Arif
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Surface Finish ◽  
High Speed ◽  
End Milling ◽  
Silicon Wafers ◽  
Compressed Air ◽  
Machining Parameters ◽  
High Quality ◽  
Ductile Mode

The majority of semiconductor devices are made up of silicon wafers. Manufacturing of high-quality silicon wafers includes numerous machining processes, including end milling. In order to end mill silicon to a nano-meteric surface finish, it is crucial to determine the effect of machining parameters, which influence the machining transition from brittle to ductile mode. Thus, this paper presents a novel experimental technique to study the effects of machining parameters in high speed end milling of silicon. The application of compressed air, in order to blow away the chips formed, is also investigated. The machining parameters’ ranges which facilitate the transition from brittle to ductile mode cutting as well as enable the attainment of high quality surface finish and integrity are identified. Mathematical model of the response parameter, the average surface roughness (Ra) is subsequently developed using RSM in terms of the machining parameters. The model was determined, by Analysis of Variance (ANOVA), to have a confidence level of 95%. The experimental results show that the developed mathematical model can effectively describe the performance indicators within the controlled limits of the factors that are being considered.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

Human capital assessment model based on a single digital platformof scientific and educational resources

2021 ◽  
pp. 107-120
Author(s):  
Viktor Medennikov
Keyword(s):  
Mathematical Model ◽  
Human Capital ◽  
Quality Education ◽  
Educational Resources ◽  
Assessment Model ◽  
Educational Institutions ◽  
High Quality ◽  
High Quality Education ◽  
The Impact

The article substantiates the need to re-evaluate the role of human capital in the development of society in the digital age. Since high-quality education is the main direction of the formation of human capital in any country, the importance of creating an information space for scientific and educational institutions is demonstrated. A methodology for assessing the level of human capital on the basis of information scientific and educational resources is proposed. The author presents results of calculations obtained by this method on the example of agricultural educational institutions and a mathematical model for assessing the impact of human capital on the socio-economic situation of the regions.

Analytical Buckling Loads of Columns Weakened Simultaneously with Transverse Cracks and Partial Delamination

2019 ◽  
Vol 19 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Igor Planinc ◽  
Simon Schnabl
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Parametric Study ◽  
Transverse Crack ◽  
Transverse Cracks ◽  
Buckling Loads ◽  
Crack Location ◽  
Benchmark Solution ◽  
First Time

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution.

Sign in / Sign up

Export Citation Format

Share Document