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The importance of contact and friction problems in different application areas is discussed. Methods and algorithms for numerical solutions using the finite element method are presented. Both elastic and elastic plastic materials are included as well as combination of contact and crack problems. The methods are applied to practical applications such as bolted joints, lugs and roller bearings.

The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem.

The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems.

With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data.

The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context.

In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

Some frictional contact problems are characterized by significant variations in the location and size of the contact area occurring in the process of deformation. When this feature is combined with strongly non‐linear, path‐dependent material behaviour, difficulties with convergence of the typically used iterative processes can be encountered. Demonstrates this by analysis of press‐fit connection, a typical problem in which both of those characteristics can be present. Offers an explanation as to the possible source of those difficulties. Suggests in support of this explanation, two simple modifications of the usual iterative schemes. In spite of their simplicity, they are found to be more robust than those usual schemes which are normally used in numerical analysis of similar problems.

The real challenge in the solution of contact problems is the lack of an optimal adaptive scheme. As the contact zone is a priori unknown, successive refinement and iterative method are necessary to obtain a high-accuracy solution. The purpose of this paper is to provide an optimal adaptive scheme based on second-generation finite element wavelets for the solution of non-linear variational inequality of the contact problem.

To generate an elementary multi-resolution mesh, the authors used hierarchical bases (HB) composed of Lagrange finite element interpolation functions. These HB functions are customized using second-generation wavelet techniques for a fast convergence rate. At each step of the algorithm, the active set method along with mesh adaptation is used for solving the constrained minimization problem of contact case. Wavelet coefficients-based error indicators are used, and computation is focused on mesh zones with a high error indication. The authors take advantage of the wavelet transform to develop a parameter-free adaptive scheme to generate an appropriate and optimal mesh.

Adaptive wavelet Galerkin scheme (AWGS), a newly developed method for multi-scale mesh adaptivity in this work, is a combination of the second-generation wavelet transform and finite element method and significantly improves the accuracy of the results without approximating an additional problem of error estimation equations. A comparative study is performed taking a solution on a highly refined mesh and results are generated using AWGS.

The proposed adaptive technique can be utilized in the simulation of mechanical and biomechanical structures where multiple bodies come into contact with each other. The algorithm of the method is easy to implement and found to be successful in producing a sufficiently accurate solution with relatively less number of mesh nodes.

Although many error estimation techniques have been developed over the past several years to solve contact problems adaptively, because of boundary non-linearity development, a reliable error estimator needs further investigation. The present study attempts to resolve this problem without having to recompute the entire solution on a new mesh.

A new algorithm to solve contact body problems is presented. The contact boundaries are divided into finite elements, and contact element matrices and vectors are computed using a modified variational principle. The contact conditions are incorporated into the total functional using the Lagrange multiplier method. This algorithm considers surface contacts rather than point contacts, and computes contact tractions directly. The Coulomb friction law is used as the friction condition. A transformation matrix based on static equilibrium is developed to solve extensive sliding problems. This algorithm is extended to the elasto‐plastic analysis and several example problems are presented to demonstrate the algorithm.

The purpose of this article is to describe a method for activating the contact‐contract‐action model, and to present findings based on its adaptation and integration into a formal library instruction course. Contact‐contract‐action, borrowed from social work practice, is used to promote strategic behavior change or “intervention” resulting from careful assessment of what the user needs (contact), what the user is willing to do to meet his or her information need (contract). After completing the contact and contract phases, the user engages in behavior to actually meet the need (action). Its theoretical bases are client self‐determination and problem solving.

The purpose of this paper is to present a new way to solve numerically a mechanical frictionless contact problem within a context of multiple sampling, frequently used to design robust structures.

This paper proposes to integrate a control-based approach, currently used in automation domain, for the solving of non-linear mechanical problem. More precisely, a fuzzy logic controller is designed to create a link between the normal gaps identified between the bodies and the normal contact pressures applied at the interface.

With this new strategy, the initial non-linear problem can be decomposed into a set of reduced linear problems solved using the finite element method. A projection built from the modal bases of each component in contact is considered to reduce computational time. Moreover, the proposed numerical applications highlight an interesting compromise between computation time and precision of contact data.

Currently, the proposed Fuzzy Logic Controller for Contact method has been developed for a frictionless contact problem in the case of 2D numerical applications. Therefore, as obtained results are very interesting, it will be possible to expand on these works in a future works for more complex problems including friction, 3D model and transient dynamic responses by adding other controllers.

In conclusion, this paper highlights the interest of studying a contact problem by considering automation approaches and defines the basis of future multidisciplinary works.

Contact problems are central to solid mechanics as contact is the principal method of applying loads to a deformable body and the point with resulting stress concentration is often the most critical point within the body. This paper presents a finite element model for the elastic contact between two cylinders at several positions. The effects of friction and surface roughness have been considered. The contact between two skew cylinders is also investigated. Results from finite element model show a good agreement with those of analytical solutions available in the literature. It was seen that the geometry of contacting bodies and orientation of applied load effect highly on contact stresses. Although the effect of surface roughness was seen to be more than that of friction, both of them can be assumed negligible in elastic contact problems.

The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.

In this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.

On the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.

The proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.