Analysis and control of an electro-elastic contact problem

2021 ◽  
pp. 108128652110441
Author(s):  
Tao Chen ◽  
Rong Hu ◽  
Mircea Sofonea
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Strain Field ◽  
Variational Formulation ◽  
Continuous Dependence ◽  
Existence Result ◽  
Frictional Contact ◽  
Elastic Contact ◽  
Tresca’S Friction ◽  
And Control

We consider a mathematical model that describes the frictional contact of an electro-elastic body with a semi-insulator foundation. The process is static; the contact is bilateral and associated to Tresca’s friction law. We list the assumptions on the data and derive a variational formulation of the model, in the form of a system that couples two inclusions in which the unknowns are the strain field and the electric field. Then we prove the unique solvability of the system, as well as the continuous dependence of its solution with respect to the data. We use these results in the study of an associated optimal control problem, for which we prove an existence result. The proofs are based on arguments of monotonicity, compactness, convex analysis, and lower semicontinuity.

scholarly journals Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi

2020 ◽  
Vol 17 (2) ◽  
pp. 238-248
Author(s):  
Resmawan ◽  
M Eka ◽  
Nurwan ◽  
N Achmad
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Optimal Control ◽  
Drug Users ◽  
Minimum Principle ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Model Drug ◽  
And Control ◽  
The Mathematical Model

ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education   ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci       : Kontrol optimal; model matematika; pengguna narkoba; edukasi

Weak solvability of a piezoelectric contact problem

2009 ◽  
Vol 20 (2) ◽  
pp. 145-167 ◽  
Author(s):  
STANISŁAW MIGÓRSKI ◽  
ANNA OCHAL ◽  
MIRCEA SOFONEA
Keyword(s):  
Mathematical Model ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Constitutive Law ◽  
Potential Fields ◽  
Material Behaviour ◽  
Abstract Result ◽  
Electrically Conductive ◽  
Piezoelectric Body ◽  
Weak Solvability

We consider a mathematical model which describes the frictional contact between a piezoelectric body and a foundation. The material behaviour is modelled with a non-linear electro-elastic constitutive law, the contact is bilateral, the process is static and the foundation is assumed to be electrically conductive. Both the friction law and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system of two coupled hemi-variational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proof is based on an abstract result on operator inclusions in Banach spaces.

scholarly journals A CLASS OF QUASISTATIC CONTACT PROBLEMS FOR VISCOELASTIC MATERIALS WITH NONLOCAL COULOMB FRICTION AND TIME-DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 491-508 ◽  
Author(s):  
Si-sheng Yao ◽  
Nan-jing Huang
Keyword(s):  
Mathematical Model ◽  
Variational Inequality ◽  
Time Delay ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Contact Problems ◽  
Existence And Uniqueness Theorem ◽  
Differential Variational Inequality

In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.

scholarly journals Variational and Numerical Analysis for Frictional Contact Problem with Normal Compliance in Thermo-Electro-Viscoelasticity

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Mustapha Bouallala ◽  
El Hassan Essoufi ◽  
Mohamed Alaoui
Keyword(s):  
Contact Problem ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Approximate Solutions ◽  
Numerical Approach ◽  
Normal Compliance ◽  
Fully Discrete ◽  
Tresca’S Friction ◽  
Discrete Finite Element ◽  
Finite Element Schemes

In this paper, we consider a mathematical model of a contact problem in thermo-electro-viscoelasticity with the normal compliance conditions and Tresca’s friction law. We present a variational formulation of the problem, and we prove the existence and uniqueness of the weak solution. We also study the numerical approach using spatially semidiscrete and fully discrete finite element schemes with Euler’s backward scheme. Finally, we derive error estimates on the approximate solutions.

A PIEZOELECTRIC CONTACT PROBLEM WITH SLIP DEPENDENT COEFFICIENT OF FRICTION

2004 ◽  
Vol 9 (3) ◽  
pp. 229-242 ◽  
Author(s):  
M. Sofonea
Keyword(s):  
Mathematical Model ◽  
Weak Solution ◽  
Contact Problem ◽  
Coefficient Of Friction ◽  
Dry Friction ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Coupled System ◽  
Piezoelectric Body ◽  
The Coefficient Of Friction

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an obstacle. The constitutive relation of the material is assumed to be electroelastic and involves a nonlinear elasticity operator. The contact is modelled with a version of Coulomb's law of dry friction in which the coefficient of friction depends on the slip. We derive a variational formulation for the model which is in form of a coupled system involving as unknowns the displacement field and the electric potential. Then we provide the existence of a weak solution to the model and, under a smallness assumption, we provide its uniqueness. The proof is based on a result obtained in [14] in the study of elliptic quasi‐variational inequalities.

Maximizing Distance of the Golf Drive: An Optimal Control Study

1975 ◽  
Vol 97 (4) ◽  
pp. 362-367 ◽  
Author(s):  
M. A. Lampsa
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Variational Formulation ◽  
Necessary Conditions ◽  
Model Parameter ◽  
Steepest Ascent ◽  
Parameter Values ◽  
Control Study

Optimal control theory is used to search for the optimal control torques necessary to maximize distance of the golf drive. In the method, a mathematical model of a generalized golf swing is first developed. Film of the author’s swing serves to verify the model and to supply parameter values, constraints, and actual torques. The variational formulation of optimal control theory is utilized to establish necessary conditions for optimal control, in which constraint violations are discouraged by inclusion of penalty functions. Finally, the method of steepest ascent is used to compute optimal control torques. Also, comparison of optimal and actual torques is made, and the sensitivity of the results to small changes in model parameter values is investigated.

Quasi-Static Linear Thermo-Viscoelastic Process with Irregular Viscous Dissipation

2017 ◽  
Vol 9 (4) ◽  
pp. 924-943
Author(s):  
Farid Messelmi ◽  
Abdelbaki Merouani ◽  
Hicham Abdelaziz
Keyword(s):  
Mathematical Model ◽  
Function Space ◽  
Weak Solutions ◽  
Equilibrium Equation ◽  
Variational Formulation ◽  
Existence Result ◽  
Energy Equation ◽  
Dissipative Function ◽  
Internal Forces ◽  
Linear Body

AbstractWe consider a mathematical model which describes the quasi-static evolution of a thermo-viscoelastic linear body with taking into account the effects of internal forces which generate a non linear viscous dissipative function. We derive a variational formulation of the system of equilibrium equation and energy equation. An existence result of weak solutions was obtained in an appropriate function space.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach

2021 ◽  
Vol 145 ◽  
pp. 110789
Author(s):  
Parthasakha Das ◽  
Samhita Das ◽  
Pritha Das ◽  
Fathalla A. Rihan ◽  
Muhammet Uzuntarla ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Combinatorial Therapy ◽  
Model Based ◽  
Cancer Remission

scholarly journals Prevalence, awareness, treatment, and control of dyslipidemia among diabetes mellitus patients and predictors of optimal dyslipidemia control: results from the Korea National Health and Nutrition Examination Survey

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Seung Jae Kim ◽  
Oh. Deog Kwon ◽  
Kyung-Soo Kim
Keyword(s):  
Diabetes Mellitus ◽  
Optimal Control ◽  
National Health ◽  
Age Groups ◽  
Density Lipoprotein ◽  
Nutrition Examination Survey ◽  
Cross Sectional ◽  
Health And Nutrition ◽  
Factors Influencing ◽  
And Control

Abstract Background This study aimed to investigate the prevalence, awareness, treatment, and control rates of dyslipidemia and identify the predictors of optimal control (low-density lipoprotein cholesterol < 100 mg/dL) among patients with diabetes mellitus (DM). Methods A cross-sectional study was conducted using the representative Korea National Health and Nutrition Examination Survey (2014–2018). Overall, 4311 patients with DM, aged ≥19 years, and without cardiovascular diseases were selected, and the prevalence, awareness, treatment, and control rates of dyslipidemia were calculated. Univariate and multivariate logistic regression analyses were conducted to evaluate the factors influencing the optimal control of dyslipidemia. Results Dyslipidemia was prevalent in 83.3% of patients with DM, but the awareness and treatment rates were 36.5 and 26.9%, respectively. The control rate among all patients with dyslipidemia was 18.8%, whereas it was 61.1% among those being treated. Prevalence and awareness rates were also significantly higher in women than in men. Dyslipidemia was most prevalent in those aged 19–39 years, but the rates of awareness, treatment, and control among all patients with dyslipidemia in this age group were significantly lower than those in other age groups. The predictors of optimal control were age ≥ 40 years [range 40–49 years: adjusted odds ratio (aOR) 3.73, 95% confidence interval (CI) 1.43–9.72; 50–59 years: aOR 6.25, 95% CI 2.50–15.65; 60–69 years: aOR 6.96, 95% CI 2.77–17.44; 70–79 years: aOR 9.21, 95% CI 3.58–23.74; and ≥ 80 years: aOR 4.43, 95% CI 1.60–12.27]; urban living (aOR 1.44, 95% CI 1.15–1.80); higher body mass index (aOR 1.27, 95% CI 1.13–1.42); lower glycated hemoglobin levels (aOR 0.71, 95% CI 0.67–0.76); hypertension (aOR 1.53, 95% CI 1.22–1.92); poorer self-rated health status (aOR 0.72, 95% CI 0.62–0.84); and receiving regular health check-ups (aOR 1.58, 95% CI 1.25–2.00). Conclusions Most patients with DM were diagnosed with dyslipidemia, but many were unaware of or untreated for their condition. Therefore, their control rate was suboptimal. Thus, by understanding factors influencing optimal control of dyslipidemia, physicians should make more effort to encourage patients to undergo treatment and thus, adequately control their dyslipidemia.

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