The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

The Industry 4.0 and smart city solutions are impossible to be implemented without using IoT devices. There can be several problems in acquiring data from these IoT devices, problems that can lead to missing values. Without a complete set of data, the automation of processes is not possible or is not satisfying enough. The aim of this paper is to introduce a new algorithm that can be used to fill in the missing values of signals sent by IoT devices. In order to do that, we introduce Shepard local approximation operators in Riesz MV-algebras for one variable function and we structure the set of possible values of the IoT devices signals as Riesz MV-algebra. Based on these local approximation operators we define a new algorithm and we test it to prove that it can be used to fill in the missing values of signals sent by IoT devices.

In this article we continue the study started in [8] to use Riesz MValgebras for IoT devices signals processing. The Shepard local approximation operators introduced in [8] were defines such that to approximate single variable functions. In real industrial usage, the signals coming from IoT devices may be influenced by mode than a parameter, and thus we introduce generalized Shepard local approximation operators that can approximate multi-dimensional functions and some numerical experiments are considered.

The aim of the study is the tribological analysis of the crane drum brakes. A theoretical analysis of the wear processes for brake lining was performed and the coefficient of friction under tribological conditions was determined experimentally simulating the operating conditions for three types of brakes. The theoretical study of the wear was oriented towards of determining the lifetime of the brake lining. In the experimental determination of the coefficient of friction, the following parameters were taken into account: the contact pressure between the shoe and the drum; the initial speed of the brake drum; the humidity of the working environment; and the temperature of the drum-brake lining friction surfaces. After performing the experiments, a statistical analysis was conducted, that shows the amount the coefficient of friction is influenced by the previously mentioned parameters: the highest weight was humidity with a value of 35.58%, followed by temperature with a percentage of 23.95%, velocity with 4.54%, and lastly pressure with 4.19%. Furthermore, the equation that expresses the dependence between the coefficient of friction and the parameters is determined. We consider that the results obtained are important for brake manufacturers in order to improve braking efficiency and the safety of overhead cranes.

In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get the necessary optimality conditions, we use some regularization techniques, and this leads us to a problem of control for an inequality of the variational type. The optimal control problem consists, in our case, of minimizing a sequence of optimal control problems, where the control variable is given by a Neumann-type boundary condition. The state system is represented by a limit of a sequence, whose terms are obtained from the discretization, in time with finite difference and space with the finite element method of a regularized quasistatic contact problem with Coulomb friction. The purpose of this optimal control problem is that the traction force (the control variable) acting on one side of the boundary (the Neumann boundary condition) of the elastic body produces a displacement field (the state system solution) close enough to the imposed displacement field, and the traction force from the boundary remains small enough.

This study is concerned with the theory of Cosserat thermoelastic media, whose micro-particles possess microtemperatures. The mixed initial boundary value problem considered in this context is transformed in a temporally evolutionary equation on a Hilbert space. Using some results from the theory of semigroups, the existence and uniqueness of solution is proved. In the same manner, it approached the continuous dependence of the solution upon initial data and loads. From what we have studied, neither on the internet nor in the databases, we have not found qualitative issues addressed regarding the mixed problem in the context of the theory of thermoelasticity of Cosserat environments, in which the contribution of inner structure and microtemperatures are taken into account.