Wyniki wyszukiwania - BazTech

1

Numerical modelling of a dynamic contact problem with normal damped response and unilateral constraint

Barboteu M., Ouafik Y., Sofonea M.

Journal of Theoretical and Applied Mechanics

|

2018

|

Vol. 56 nr 2

483--496

EN

We consider a mathematical model which describes the dynamic evolution of a viscoelastic body in frictional contact with an obstacle. The contact is modelled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb’s law of dry friction. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we use a penalty method to approximate the constraint. Then, we provide numerical simulations in the study of a two-dimensional example and compare the penalty model with the original one.

2

Analysis of selected contact algorithms types in terms of their parameters selection

Panowicz R.

Journal of KONES

|

2013

|

Vol. 20, No. 1

263--268

EN

The analysis of many engineering problems involves not only deformation of the considered system, but occurrence of the interaction between the individual separate elements of the system as well. The occurrence of friction is the most common phenomenon occurring during this interaction. In the case of intense friction, the heat released in this process is also important. In computer methods of mechanics, the process of interaction between bodies is carried out using special algorithms. The most frequently applied are: the penalty method, the barrier method, direct elimination of constraints, the Lagrange multiplier method, the perturbed Lagrangian method, the augmented Lagrangian method, Nitsche method. Owing to its easy implementation process, an approach based on a penalty function is often applied. In this approach, the contact between the bodies can be identified with the presence of the spring between the elements of the bodies in the contact. The stiffness of the spring depends on: material bulk modulus, face area, volume or shell diagonal and a numerically selected scale factor. The article will present the results of analyses that will allow fast and easy selection of its value. In the analyses there were presented the results considering the basic types of contacts: node to surface, surface to surface and surface to surface mortar.

3

Control in obstacle three-layered plate problem

Lovisek J.

Journal of Theoretical and Applied Mechanics

|

2002

|

Vol. 40 nr 3

611-647

EN

The problem to find an optimal thickness of a three-layered plate (ignoring shears in the middle plate) in a set of bounded Lipschitz continuous functions is considered. The variable thickness of the exterior layer of the plate is to be optimized to reach the minimal weight under some constraints for maximal stresses. The cost functionals represent: 1) weight of the three-layered plate, 2) positive distribution (a non-negative Radon measure). The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible functions. The existence of the optimal thickness is proved and some convergence analysis for an approximate penalized optimal control problem is presented. We prove the existence of a solution to the weight minimization problem or minimization the work of interaction forces on the basis of a general theorem on the control of variational inequalities.

PL

W pracy zajęto się problemem doboru optymalnej grubości trójwarstwowej płyty (z pominięciem naprężeń stycznych w warstwie środkowej) w zbierze ograniczonych, ciągłych funkcji Lipschitza. Zmienna grubość warstwy zewnętrznej jest optymalizowana poprzez minimalizację ciężaru przy pewnych ograniczeniach narzuconych na maksymalne naprężenia. zastosowane funkcjonały kosztu reprezentują: 1) ciężar trójwarstwowej płyty, 2) dodatni rozkład (nieujemna miara Radona). Zagadnienie stanu opisano nierównością wariacyjną oraz uwzględniono wpływ zmiennych konstrukcyjnych na współczynniki i zbiór dopuszczalnych funkcji. Udowodniono istnienie optymalnej grubości warstwy i przedstawiono analizę zbieżności przybliżonego problemu optymalizacji metodą funkcji kary. Wykazano istnienie rozwiązania przy minimalizacji ciężaru płyty i minimalizacji pracy sił oddziaływania pomiędzy płytą a podporą na podstawie ogólnego twierdzenia o doborze parametrów w układach opisanych nierównościami wariacyjnymi.

4

Discrete relaxed method for semilinear parabolic optimal control problem

Chryssoverghi I., Coletsos J., Kokkinis B.

Control and Cybernetics

|

1999

|

Vol. 28, no 2

157-176

EN

We consider an optimal control problem for systems governed by semilinear parabolic partial differential equations with control and state constraints, without any convexity assumptions. A discrete optimization method is proposed to solve this problem in its relaxed form which combines a penalized Armijo type method with a finite element discretization and constructs sequences of discrete Gamkrelidze relaxed controls. Under appropriate assumptions, we prove that accumulation points of these sequences satisfy the relaxed Pontryagin necessary conditions for optimality. Moreover, we show that the Gamkrelidze controls thus generated can be replaced by simulating piecewise constant classical controls.