scholarly journals A vibrating thermoelastic plate in a contact with an obstacle

2015 ◽  
Vol 63 (1) ◽  
pp. 39-52
Author(s):  
Igor Bock ◽  
Jiří Jarušek
Keyword(s):  
Weak Solution ◽  
Variational Inequality ◽  
Parabolic Equation ◽  
Heat Source ◽  
Time Derivative ◽  
Thermal Strain ◽  
Dynamic Contact ◽  
Dynamic Contact Problem ◽  
Penalization Method ◽  
Thermoelastic Plate

Abstract We deal with a dynamic contact problem for a thermoelastic plate vibrating against a rigid obstacle. Dynamics is described by a hyperbolic variational inequality for deflections. The plate is subjected to a perpendicular force and to a heat source. The parabolic equation for the thermal strain resultant contains the time derivative of the deflection. We formulate a weak solution of the system and verify its existence using the penalization method.

Dynamic contact of a thermoelastic Mindlin–Timoshenko beam with a rigid obstacle

2017 ◽  
Vol 23 (3) ◽  
pp. 411-419
Author(s):  
Igor Bock
Keyword(s):  
Timoshenko Beam ◽  
Vector Measure ◽  
Time Derivative ◽  
Thermal Strain ◽  
Dynamic Contact ◽  
Penalization Method ◽  
Unilateral Problem ◽  
Complementarity Conditions ◽  
Rigid Obstacle ◽  
Angle Of Rotation

We concentrate on the dynamics of a thermoelastic Mindlin–Timoshenko beam striking a rigid obstacle. We state classical formulations involving complementarity conditions. Weak formulations are in the form of systems consisting of a hyperbolic variational inequality for a deflection, a hyperbolic and a parabolic equation for an angle of rotation and a thermal strain, respectively. The penalization method is applied to solve the unilateral problem. The time derivative of the function representing the deflection of the beam’s middle line is not continuous due to the hitting the obstacle. The acceleration term has the form of a vector measure.

scholarly journals Numerical solution of the dynamic contact problem of elasto-plastic bodies

2018 ◽  
pp. 1-31
Author(s):  
Mikhail Pavlovich Galanin ◽  
Nikolay Nikolaevich Proshunin ◽  
Aleksandr Sergeevich Rodin
Keyword(s):  
Contact Problem ◽  
Numerical Solution ◽  
Dynamic Contact ◽  
Dynamic Contact Problem

A TRANSIENT DYNAMIC CONTACT PROBLEM IN THREE DIMENSIONS

1994 ◽  
Vol 05 (02) ◽  
pp. 215-217
Author(s):  
T.Y. Fan ◽  
H.G. Hahn ◽  
A. Voigt
Keyword(s):  
Contact Problem ◽  
Contact Stress ◽  
Dynamic Stress ◽  
Three Dimensional ◽  
Dynamic Contact ◽  
Three Dimensions ◽  
Dynamic Contact Problem ◽  
Transient Dynamic ◽  
Elliptic Region ◽  
Contact Displacement

In this study a three-dimensional transient dynamic contact problem is solved, and a theorem relating the contact stress and displacement over an elliptic region is proved. Numerical results for the contact displacement-time variation clearly demonstrate the effect of inertia induced by the dynamic stress.

Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition

2021 ◽  
pp. 1-35
Author(s):  
Galina Bizhanova
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Parabolic Equation ◽  
Small Parameter ◽  
Unique Solvability ◽  
Time Derivative ◽  
Holder Space ◽  
Hölder Space ◽  
Space Solution ◽  
Unperturbed Problem

There is studied the Hölder space solution u ε of the problem for parabolic equation with the time derivative ε ∂ t u ε | Σ in the boundary condition, where ε > 0 is a small parameter. The unique solvability of the perturbed problem and estimates of it’s solution are obtained. The convergence of u ε as ε → 0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

COEFFICIENT INVERSE PROBLEMS FOR THE PARABOLIC EQUATION WITH GENERAL WEAK DEGENERATION

2021 ◽  
Vol 9 (1) ◽  
pp. 91-106
Author(s):  
N. Huzyk ◽  
O. Brodyak
Keyword(s):  
Parabolic Equation ◽  
Inverse Problems ◽  
Existence And Uniqueness ◽  
Space Variable ◽  
Time Derivative ◽  
Classical Solutions ◽  
Linear Polynomial ◽  
Coefficient Inverse Problems ◽  
Degenerate Parabolic ◽  
Increasing Function

It is investigated the inverse problems for the degenerate parabolic equation. The mi- nor coeffcient of this equation is a linear polynomial with respect to space variable with two unknown time-dependent functions. The degeneration of the equation is caused by the monotone increasing function at the time derivative. It is established conditions of existence and uniqueness of the classical solutions to the named problems in the case of weak degeneration.

scholarly journals The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Huashui Zhan
Keyword(s):  
Weak Solution ◽  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Variable Exponents ◽  
Boundary Value Condition ◽  
Anisotropic Parabolic Equation

Consider an anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x,t)vxipi(x)-2vxi)xi+f(v,x,t), where bi(x,t)∈C1(QT¯), pi(x)∈C1(Ω¯), pi(x)>1, bi(x,t)≥0, f(v,x,t)≥0. If {bi(x,t)} is degenerate on Γ2⊂∂Ω, then the second boundary value condition is imposed on the remaining part ∂Ω∖Γ2. The uniqueness of weak solution can be proved without the boundary value condition on Γ2.

Numerical Study of a Small Droplet Movement in a Microchannel under Heat Source

2019 ◽  
Vol 894 ◽  
pp. 104-111
Author(s):  
Thanh Long Le ◽  
Jyh Chen Chen ◽  
Huy Bich Nguyen
Keyword(s):  
Contact Angle ◽  
Heat Source ◽  
Water Droplet ◽  
Stokes Equations ◽  
Numerical Study ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Initial Position ◽  
Immiscible Fluids ◽  
Two Phase

In this study, the numerical computation is used to investigate the transient movement of a water droplet in a microchannel. For tracking the evolution of the free interface between two immiscible fluids, we employed the finite element method with the two-phase level set technique to solve the Navier-Stokes equations coupled with the energy equation. Both the upper wall and the bottom wall of the microchannel are set to be an ambient temperature. 40mW heat source is placed at the distance of 1 mm from the initial position of a water droplet. When the heat source is turned on, a pair of asymmetric thermocapillary convection vortices is formed inside the droplet and the thermocapillary on the receding side is smaller than that on the advancing side. The temperature gradient inside the droplet increases quickly at the initial times and then decreases versus time. Therefore, the actuation velocity of the water droplet first increases significantly, and then decreases continuously. The dynamic contact angle is strongly affected by the oil flow motion and the net thermocapillary momentum inside the droplet. The advancing contact angle is always larger than the receding contact angle during actuation process.

Sign in / Sign up

Export Citation Format

Share Document