Analysis and Assessment of the Effects of Corrosive Hydrogen Media on the Stress-Strain State of a Spherical Titanium Alloy Shell

2022 ◽  
Vol 1049 ◽  
pp. 85-95
Author(s):  
Violetta Kuznetsova ◽  
Maria Barkova ◽  
Alexandr Zhukov ◽  
Igor Kartsan
Keyword(s):  
Mathematical Model ◽  
Titanium Alloy ◽  
Stress State ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Strain State ◽  
Step Method ◽  
Hollow Spherical Shell ◽  
The Finite Difference Method ◽  
Aggressive Effect

We consider the creation of a mathematical model describing the effect of corrosive hydrogen environment on the stress state of a hollow spherical shell made of titanium alloy grade VT1-0, the load is evenly distributed throughout the shell. The solution of the problem in practice was carried out by two-step method of sequential perturbation of parameters using MatLab and Maple programs. To solve the system of solving differential equations the finite difference method was applied. The solution of the diffusion equation of the aggressive hydrogen medium has been considered and the obtained solution has been compared with the results of the classical theory which does not take into account the aggressive effect of the corrosive medium.

scholarly journals Mathematical Modelling of Non-Isothermal Moisture Transfer and Rheological Behavior in Cappilary-Porous Materials with Fractal Structure During Drying

2014 ◽  
Vol 7 (4) ◽  
pp. 111 ◽  
Author(s):  
Yaroslav Sokolowskyi ◽  
Volodymyr Shymanskyi
Keyword(s):  
Mathematical Model ◽  
Finite Difference Method ◽  
Fractional Order ◽  
Rheological Behavior ◽  
Strain State ◽  
Fractal Structure ◽  
Moisture Transfer ◽  
The Finite Difference Method ◽  
Predictor Corrector ◽  
The Mathematical Model

The mathematical model of non-isothermal moisture transfer and rheological behavior of wood during drying with taking into account the fractal structure of this material is regarded in the article. The mathematical tools of integration and differentiation of fractional order for description the mathematical model of this process was used. For finding the numerical solution of this problem the finite-difference method predictor-corrector was used. Results show the practicability of using the mathematical tools of integration and differentiation of fractional order to calculate the temperature and humidity fields and the stress-strain state during drying timber.

scholarly journals Dynamic methods of spatial calculation of structures based on a plate model

2019 ◽  
Vol 97 ◽  
pp. 04072 ◽  
Author(s):  
Elyor Toshmatov ◽  
Makhamtali Usarov ◽  
Gayratjon Ayubov ◽  
Davronbek Usarov
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Strain State ◽  
Plate Model ◽  
Dynamic Calculation ◽  
Transverse Vibrations ◽  
Dynamic Methods ◽  
The Finite Difference Method ◽  
Spatial Stress

This article was devoted to the development of methods of the dynamic calculation based on the finite difference method of laminar structures in the framework of the bimoment theory, which takes into account the spatial stress-strain state. Were given the solutions of the problem of transverse vibrations of the plate model of structures.

Heat and Mass Transfer Analysis of Fabric in the Tenter Frame

1997 ◽  
Vol 67 (5) ◽  
pp. 311-316 ◽  
Author(s):  
Sang Il Park ◽  
Doo Hyun Baik
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference Method ◽  
Moisture Content ◽  
Heat And Mass Transfer ◽  
Initial Moisture Content ◽  
Transfer Coefficients ◽  
Operation Parameters ◽  
The Finite Difference Method ◽  
Experimental Values

A mathematical model is developed for heat and mass transfer analysis of fabric in the tenter frame. Using the model, the calculated transient fabric temperatures in the tenter frame agree well with the experimental values measured by Beard. Variations in temperature and moisture content distribution are solved using the finite-difference method. The effects of operation parameters, such as temperature and humidity in the tenter, initial moisture content of the fabric, and heat and mass transfer coefficients, are examined using the model.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

Heat Diffusion in Heterogeneous Bodies Using Heat-Flux-Conserving Basis Functions

1988 ◽  
Vol 110 (2) ◽  
pp. 276-282 ◽  
Author(s):  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Solution Method ◽  
Basis Functions ◽  
Heat Diffusion ◽  
Simple Geometry ◽  
The Finite Difference Method

The generalized analytical derivation presented here enables one to obtain solutions to the diffusion equation in complex heterogeneous geometries. A new method of constructing basis functions is introduced that preserves the continuity of temperature and heat flux throughout the domain, specifically at the boundary of each inclusion. A set of basis functions produced in this manner can be used in conjunction with the Green’s function derived through the Galerkin procedure to produce a useful solution method. A simple geometry is selected for comparison with the finite difference method. Numerical results obtained by this method are in excellent agreement with finite-difference data.

scholarly journals Strength resistance of reinforced concrete elements of high-rise buildings under dynamic loads

2018 ◽  
Vol 33 ◽  
pp. 02049 ◽  
Author(s):  
Mikhail Berlinov
Keyword(s):  
Reinforced Concrete ◽  
Strain State ◽  
Load Capacity ◽  
Phenomenological Theory ◽  
Dynamic Loads ◽  
Successive Approximations ◽  
Step Method ◽  
High Rise ◽  
The Finite Difference Method ◽  
Concrete Elements

A new method for calculating reinforced concrete constructions of high-rise buildings under dynamic loads from wind, seismic, transport and equipment based on the initial assumptions of the modern phenomenological theory of a nonlinearly deformable elastic-creeping body is proposed. In the article examined the influence of reinforcement on the work of concrete in the conditions of triaxial stress-strain state, based on the compatibility of the deformation of concrete and reinforcement. Mathematical phenomenological equations have been obtained that make it possible to calculate the reinforced concrete elements working without and with cracks. A method for linearizing of these equations based on integral estimates is proposed, which provides the fixation of the vibro-creep processes in the considered period of time. Application of such a technique using the finite-difference method, step method and successive approximations will allow to find a numerical solution of the problem. Such an approach in the design of reinforced concrete constructions will allow not only more fully to take into account the real conditions of their work, revealing additional reserves of load capacity, but also to open additional opportunities for analysis and forecasting their functioning at various stages of operation.

A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

2014 ◽  
Vol 6 (5) ◽  
pp. 693-698 ◽  
Author(s):  
Kosuke Abe ◽  
Nobuyuki Higashimori ◽  
Masayoshi Kubo ◽  
Hiroshi Fujiwara ◽  
Yuusuke Iso
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
View Point ◽  
Rounding Errors ◽  
The Finite Difference Method

AbstractThe Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.

scholarly journals A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Reem Edwan ◽  
Shrideh Al-Omari ◽  
Mohammed Al-Smadi ◽  
Shaher Momani ◽  
Andreea Fulga
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Finite Volume ◽  
Difference Method ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Finite Difference Method ◽  
Volume Method

AbstractConvection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this context, we present an alternative way for estimating the space fractional derivative by utilizing the fractional Grünwald formula. The proposed methods are conditionally stable with second-order accuracy in space and first-order accuracy in time. Many comparisons are performed to display reliability and capability of the proposed methods. Furthermore, several results and conclusions are provided to indicate appropriateness of the finite volume method in solving the space fractional convection–diffusion equation compared with the finite difference method.

scholarly journals Mathematical Model of the Processoof Pearlite Austenitization

2014 ◽  
Vol 59 (3) ◽  
pp. 981-986 ◽  
Author(s):  
I. Olejarczyk-Wożeńska ◽  
H. Adrian ◽  
B. Mrzygłód
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Diffusion Mechanism ◽  
System Of Differential Equations ◽  
Ttt Diagram ◽  
Austenite Transformation ◽  
The Finite Difference Method

Abstract The paper presents a mathematical model of the pearlite - austenite transformation. The description of this process uses the diffusion mechanism which takes place between the plates of ferrite and cementite (pearlite) as well as austenite. The process of austenite growth was described by means of a system of differential equations solved with the use of the finite difference method. The developed model was implemented in the environment of Delphi 4. The proprietary program allows for the calculation of the rate and time of the transformation at an assumed temperature as well as to determine the TTT diagram for the assigned temperature range.

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