This paper is concerned with the modeling of power dissipation due to friction and its relation with wear estimation in wheel–rail contact. Wear is a complex multi-scale and multi-physical phenomenon appearing in rolling contact. Wear is generated by high contact stress and the work of friction forces. This phenomenon leads to the appearing of the worn material in the form of wear debris between contacting surfaces. In contact models, wear is usually described in terms of the wear depth function. This function modifies the gap between the contacting bodies as well as the shape of the surfaces of the wheel and rail in contact. In this paper, besides the wear depth function, the dissipated energy, rather than the contact stress, is taken into account to evaluate the wear impact on rail or wheel surfaces. The dissipated energy allows us to more precisely evaluate the wear debris amount as well as the depth of wear and its distribution along the contact interface. A two-dimensional rolling contact problem with frictional heat flow is considered. The elasto-plastic deformation of the rail is considered. This contact problem is governed by a coupled system of mechanical and thermal equations in terms of generalized stresses, displacement and temperature. The finite element method is used to discretize this problem. A discretized system of equations with nonpenetration and friction conditions is transformed and formulated as a nonlinear complementarity problem. The generalized Newton method is applied to numerically solve this mechanical subproblem. The Cholesky method is used to find the solution of the heat-conductive problem. The dissipated power is evaluated based on the resultant force and slip at a reference point. Numerical results including the distribution of slip velocity, power factor and wear rate are provided and discussed.

This work is concerned with the numerical procedure to solve two-dimensional wheel-rail contact problem between a rigid wheel and an elastic-plastic rail lying on a rigid foundation. The contact phenomenon includes Coulomb friction, frictional heat generation as well as the wear of the contacting surfaces. The wear depth function appears as an internal variable in the non-penetration condition updating the gap between the worn surfaces of the bodies. Moreover the dissipated energy due to friction is calculated to evaluate the loss of material and to determine the shape of the contacting surfaces during the wear evolution process. This contact problem is solved numerically using the finite element method as well as the operator splitting approach and semi-smooth Newton method. The distribution of contact surface stresses and temperatures as well as the evolution of the shape of the contact surfaces and the wear depth are reported and discussed. GRAPHICAL ABSTRACT

The paper deals with the adaptive optimal semi-active control of the slender vibrating structures subjected to the moving loads. The deflection of the structure is governed by Euler-Bernoulli beam equation approximated by the system of bilinear ordinary differential equations. The damping function of the structure support is chosen as the control function. The optimal control problem consists in finding such bang-bang control function to minimize the energy as well as the vibrations of the carrying structure. Although the switched optimal control is a very efficient tool in the reduction of structure vibrations it is very sensitive with respect to changes of the speed of the traveling load. This paper deals with the development of the adaptive descent type algorithm that enables the update of the optimal controls in real time based on the measured speed of the traveling load or structure’s state. The proposed algorithm uses reference optimal controls computed for the constant speeds and the set of functions describing the sensitivity of the system dynamics with respect to the measured parameters. Numerical computations are carried out for different speed scenarios of the moving load. The obtained numerical results indicate that the proposed adaptive controller can significantly outperform the reference optimal solutions.

The numerical method to solve multimaterial topology optimization problems for elastic bodies in unilateral contact with Tresca friction is developed in the paper. The displacement of the elastic body in contact is governed by elliptic equation with inequality boundary conditions. The body is assumed to consists from more than two distinct isotropic elastic materials. The materials distribution function is chosen as the design variable. Since high contact stress appears during the contact phenomenon the aim of the structural optimization problem is to find such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional rather than the perimeter functional. The first order necessary optimality condition is recalled and used to formulate the generalized gradient flow equations of Allen–Cahn type. The optimal topology is obtained as the steady state of the phase transition governed by the generalized Allen-Cahn equation. As the interface width parameter tends to zero the transition of the phase field model to the level set model is studied. The optimization problem is solved numerically using the operator splitting approach combined with the projection gradient method. Numerical examples confirming the applicability of the proposed method are provided and discussed.

The paper is concerned with the analysis and the numerical solution of the multimaterial topology optimization problems for bodies in unilateral contact. The contact phenomenon with Tresca friction is governed by the elliptic variational inequality. The structural optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional. The first order necessary optimality condition is formulated. The optimal topology is obtained as the steady state of the phase transition governed by the generalized Allen-Cahn equation. The optimization problem is solved numerically using the operator splitting approach combined with the projection gradient method. Numerical examples are provided and discussed.