Nonlinear mathematical model of stress-deformed state of spatially loaded rods with account for temperature

2021 ◽  
Author(s):  
Shahzoda Anarova ◽  
Shokhimardon Ismoilov
Keyword(s):  
Mathematical Model ◽  
Nonlinear Mathematical Model ◽  
Deformed State

scholarly journals RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

2020 ◽  
Vol 42 (2) ◽  
pp. 68-75
Author(s):  
V.G. Demchenko ◽  
А.S. Тrubachev ◽  
A.V. Konyk
Keyword(s):  
Mathematical Model ◽  
Heat Storage ◽  
Quantitative Estimation ◽  
The Real ◽  
State Of The Union ◽  
Real Geometry ◽  
Deformed State ◽  
The Mathematical Model ◽  
Minimization Of Functional

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

scholarly journals Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

2020 ◽  
Vol 16 (32) ◽  
pp. 195-223
Author(s):  
Edgardo Pérez
Keyword(s):  
Mathematical Modeling ◽  
College Students ◽  
Mathematical Model ◽  
Drinking Behavior ◽  
Preventive Measure ◽  
Nonlinear Mathematical Model ◽  
Consumption Behavior ◽  
Existence And Stability ◽  
Drugs And Crime ◽  
The Impact

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

A Nonlinear Mathematical Model for Ship Turning Circle Simulation in Waves

2005 ◽  
Vol 49 (02) ◽  
pp. 69-79 ◽  
Author(s):  
Ming-Chung Fang ◽  
Jhih-Hong Luo ◽  
Ming-Ling Lee
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Regular Waves ◽  
Nonlinear Mathematical Model ◽  
Ship Maneuvering ◽  
Sea Trial ◽  
Six Degrees Of Freedom ◽  
Strip Theory ◽  
Calm Water ◽  
Maneuvering Motion

In the paper, a simplified six degrees of freedom mathematical model encompassing calm water maneuvering and traditional seakeeping theories is developed to simulate the ship turning circle test in regular waves. A coordinate system called the horizontal body axes system is used to present equations of maneuvering motion in waves. All corresponding hydrodynamic forces and coefficients for seakeeping are time varying and calculated by strip theory. For simplification, the added mass and damping coefficients are calculated using the constant draft but vary with encounter frequency. The nonlinear mathematical model developed here is successful in simulating the turning circle of a containership in sea trial conditions and can be extended to make the further simulation for the ship maneuvering under control in waves. Manuscript received at SNAME headquarters February 19, 2003; revised manuscript received January 27, 2004.

Determination Coefficient of Stress Concentration Using a Conformed Display on a Circle of a Single Radius

2021 ◽  
Vol 316 ◽  
pp. 928-935
Author(s):  
Alexander Shapoval ◽  
Iurii Savchenko ◽  
Oleg Markov
Keyword(s):  
Mathematical Model ◽  
Stress Concentration ◽  
Elastic Body ◽  
Defect Formation ◽  
Point Of View ◽  
Determination Coefficient ◽  
Arbitrary Loading ◽  
Deformed State ◽  
Single Radius

Developed a mathematical model, which makes it possible to optimize, from the point of view of defect formation, the parameters of stress concentration in a deformable elastic body of the materials being processed, destruction is considered as a method for creating defects at a submicroscopic level in various media. Getting expressions of conformal reflection of single circle on an arbitrary area, using a conformal reflection and transformation of Laplace, it is possible to design behavior of a tensely deformed state of solid at the arbitrary loading.

Information dualism of the problem of optimum terminal control of dynamic object

2021 ◽  
pp. 85-90
Author(s):  
V.P. Ivanov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Law ◽  
Computational Algorithms ◽  
Terminal Control ◽  
Dynamic Object ◽  
Nonlinear Mathematical Model ◽  
Dynamical Object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

Optimizing Series Repairable Systems with Imperfect Repair

2013 ◽  
pp. 83-93
Author(s):  
Mohammed Hajeeh
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Optimal Solution ◽  
Closed Form Expression ◽  
Repairable Systems ◽  
Nonlinear Mathematical Model ◽  
Repair Rate ◽  
Imperfect Repair ◽  
Repair Models ◽  
Minimum Costs

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

A mathematical model to achieve sustainable forest management

2015 ◽  
Vol 06 (04) ◽  
pp. 1550040 ◽  
Author(s):  
A. K. Misra ◽  
Kusum Lata
Keyword(s):  
Mathematical Model ◽  
Sustainable Forest Management ◽  
Forest Products ◽  
Model System ◽  
Forest Resources ◽  
Genetically Engineered ◽  
Population Pressure ◽  
Nonlinear Mathematical Model ◽  
Modeling Process ◽  
Genetically Engineered Plants

Forest resources are important natural resources for all living beings but they are continuously depleting due to overgrowth of human population and their development activities. Therefore, conservation of forest resources is an important problem for sustainable development. In view of this, in this paper, we have proposed and analyzed a nonlinear mathematical model to study the effects of economic and technological efforts on the conservation of forest resources. In the modeling process, it is assumed that due to increase in population size, the demand of population (population pressure) for forest products, lands, etc., increases and to reduce this population pressure, economic efforts are employed proportional to the population pressure. Further, it is assumed that technological efforts in the form of genetically engineered plants are applied proportional to the depleted level of forest resources to conserve them. Model analysis reveals that increase in economic and technological efforts increases the density of forest resources but further increase in these efforts destabilizes the system. Numerical simulation is carried out to verify analytical findings and explore the effect of different parameters on the dynamics of model system.

Longitudinal Instability in Braked Landing Gear

1981 ◽  
Vol 103 (3) ◽  
pp. 259-265 ◽  
Author(s):  
R. R. Allen ◽  
R. C. O’Massey
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Analytical Methods ◽  
Design Guidelines ◽  
Landing Gear ◽  
Nonlinear Mathematical Model ◽  
Nonlinear Characteristics ◽  
Aircraft Landing ◽  
Design Variables ◽  
Aircraft Landing Gear

An instability in the form of a self-excited, bounded longitudinal oscillation may occur in aircraft landing gear when one or more wheels lock due to excessive braking. The instability usually appears at ground speeds below 40 knots (20 m/s) and results from interaction between structural elasticity and the nonlinear characteristics of tire-runway friction. A nonlinear mathematical model is developed to study the dynamics of this divergence in a braked, dual tire landing gear. Analytical methods are presented to determine critical ground speeds in terms of runway friction characteristics and to predict the amplitude of steady-state oscillations. The effect of design variables on longitudinal stability is evaluated and design guidelines are presented which insure reduction of the severity of this divergent dynamic behavior.

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