Shape Optimization In Contact Problems Research Articles

Shape optimization for contact problems based on isogeometric analysis

We consider the shape optimization for mechanical connectors. To avoid the gap between the representation in CAD systems and the finite element simulation used by mathematical optimization, we choose an isogeometric approach for the solution of the contact problem within the optimization method. This leads to a shape optimization problem governed by an elastic contact problem. We handle the contact conditions using the mortar method and solve the resulting contact problem with a semismooth Newton method. The optimization problem is nonconvex and nonsmooth due to the contact conditions. To reduce the number of simulations, we use a derivative based optimization method. With the adjoint approach the design derivatives can be calculated efficiently. The resulting optimization problem is solved with a modified Bundle Trust Region algorithm.

Shape Optimization in Contact Problems with Coulomb Friction and a Solution-Dependent Friction Coefficient

The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb friction, where the coefficient of friction is assumed to depend on the unknown sol...

Shape optimization in contact problems of the theory of elasticity with incomplete external loading data

The contact interaction without friction of an absolutely rigid punch with an elastic half-space is considered. The external loads on the elastic medium are not fixed in advance, but a set containing all the admissible forms of applied forces is assumed to be specified. Using a guaranteed (minimax) approach, problems of optimizing the shape of the punch from the condition that its mass is a minimum are formulated. Inequality-type constraints, imposed on the total force and moments applied to the punch from the elastic-medium side, are assumed. Using Betti's reciprocal theorem and calculating the “worst” case for different types of constraints, the corresponding forces are determined and the optimum shape of the punch is obtained in analytical form.

Shape Optimization in Contact Problems with Coulomb Friction

The paper deals with a discretized problem of the shape optimization of elastic bodies in unilateral contact. The aim is to extend existing results to the case of contact problems following the Coulomb friction law. Mathematical modelling of the Coulomb friction problem leads to a quasi-variational inequality. It is shown that for small coefficients of friction the discretized problem with Coulomb friction has a unique solution and that this solution is Lipschitzian as a function of a control variable describing the shape of the elastic body. The shape optimization problem belongs to a class of so-called mathematical programs with equilibrium constraints (MPECs). The uniqueness of the equilibria for fixed controls enables us to apply the so-called implicit programming approach. Its main idea consists of minimizing a nonsmooth composite function generated by the objective and the (single-valued) control-state mapping. In this paper, the control-state mapping is much more complicated than in most MPECs solved in the literature so far, and the generalization of the relevant results is by no means straightforward. Numerical examples illustrate the efficiency and reliability of the suggested approach.

Shape optimization in contact problems with desired contact traction distribution on the specified contact surface

An efficatious technique is developed to deal with the shape optimization in conctact problems with desired contact traction on a specified contact surface. The error function with appropriate weighting coefficients for smoothing local and global contact traction distribution is proposed. Since the mapping from the space of design variables to the space of error function is usually not differentiable, a Genetic Algorithm is introduced without using the gradient calculations. The boundary element technique together with the transformation matrix method are employed for the contact traction analysis. To demonstrate the versatility and applicability of this approach, two examples with desired traction distributions of elliptical and rectangular types on the specified contact surface are solved respectively.

Shape optimization in contact problems with desired contact traction distribution on the specified contact surface

Shape optimization in contact problems with desired contact traction distribution on the specified contact surface

Signorini problem with Coulomb's law of friction. Shape optimization in contact problems

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Shape optimization in contact problems. Approximation and numerical realization

On etudie l'approximation du probleme de l'optimisation de domaine dans un probleme de contact d'un corps elastique supporte unilateralement par une base rigide. On presente deux essais numeriques

Shape optimization in contact problems based on penalization of the state inequality

The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.