A thermodynamically consistent non-linear mathematical model for thermoviscoelastic plates/shells with finite deformation and finite strain based on classical continuum mechanics

2020 ◽  
Vol 126 ◽  
pp. 103565
Author(s):  
K.S. Surana ◽  
S.S.C. Mathi
Keyword(s):  
Mathematical Model ◽  
Continuum Mechanics ◽  
Finite Deformation ◽  
Finite Strain ◽  
Non Linear

Imprecision of Laboratory Determinations and Diagnostic Accuracy: Theoretical Considerations

1974 ◽  
Vol 13 (03) ◽  
pp. 151-158 ◽  
Author(s):  
D. A. B. Lindbebo ◽  
Fr. R. Watson
Keyword(s):  
Mathematical Model ◽  
Diagnostic Accuracy ◽  
Diagnostic Process ◽  
Clinical Laboratories ◽  
Non Linear ◽  
Theoretical Considerations ◽  
Made In

Recent studies suggest the determinations of clinical laboratories must be made more precise than at present. This paper presents a means of examining benefits of improvement in precision. To do this we use a mathematical model of the effect upon the diagnostic process of imprecision in measurements and the influence upon these two of Importance of Diagnosis and Prevalence of Disease. The interaction of these effects is grossly non-linear. There is therefore no proper intuitive answer to questions involving these matters. The effects can always, however, be calculated.Including a great many assumptions the modeling suggests that improvements in precision of any determination ought probably to be made in hospital rather than screening laboratories, unless Importance of Diagnosis is extremely high.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals MODELING AND PRODUCTIVITY PREDICTION OF THE COMPANIES-INTERNAL CROWDSOURCING-BASED IDEATION

2021 ◽  
Vol 1 ◽  
pp. 2147-2156
Author(s):  
Pavel Livotov
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Research Question ◽  
Performance Function ◽  
Non Linear ◽  
Series Of Experiments ◽  
Productivity Prediction ◽  
A Company

AbstractThe internal crowdsourcing-based ideation within a company can be defined as an involvement of its staff, specialists, managers, and other employees, to propose solution ideas for a pre-defined problem. This paper addresses a question, how many participants of the company-internal ideation process are required to nearly reach the ideation limit for the problems with a finite number of workable solutions. To answer the research question, the author proposes a set of metrics and a non-linear ideation performance function with a positive decreasing slope and ideation limit for the closed-ended problems. Three series of experiments helped to explore relationships between the metric attributes and resulted in a mathematical model which allows companies to predict the productivity metrics of their crowdsourcing ideation activities such as quantity of different ideas and ideation limit as a function of the number of contributors, their average personal creativity and ideation efficiency of a contributors’ group.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

scholarly journals Optimal Allocation of the Irrigation Water Through a Non Linear Mathematical Model

2008 ◽  
Vol 3 (3) ◽  
pp. 191 ◽  
Author(s):  
P. Rubino ◽  
M. Catalano ◽  
R. Rana ◽  
A. Caliandro
Keyword(s):  
Mathematical Model ◽  
Irrigation Water ◽  
Optimal Allocation ◽  
Non Linear

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

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