Browsing by Subject "Contact"

Now showing 1 - 5 of 5

Open Access
Functionalization of carbon nanotubes
(2005) Dağ, Sefa
Open Access
Hierarchical NURBS in frictionless contact
(Elsevier, 2016) Temizer, İ.; Hesch, C.
This work investigates mortar-based frictionless contact in the context of NURBS discretizations that are subjected to local hierarchical refinement. The investigations emphasize three sets of choices which lead to different contact algorithms that have distinct advantages and disadvantages. First, on the optimization side, both exterior and interior point methods are applied, thus spanning inexact constraint enforcement algorithms of the penalty or barrier type as well as exact ones of the primal-dual type. Second, on the discretization side, the hierarchical basis set of the mortar variables is inherited either directly from the discretization of the slave surface or after an intermediate normalization step to satisfy the partition of unity. Third, in interaction with both optimization and discretization, the kinematic mortar variable is recovered from the actual normal gap through the full or lumped solution of a linear system of equations. The implications of different choices are highlighted through benchmark problems which monitor the solution quality at the global level through the structural force evolution and at the local level through the contact pressure distribution. © 2015 Elsevier B.V.
Open Access
An interior point method for isogeometric contact
(Elsevier, 2014) Temizer, I.; Abdalla, M. M.; Gürdal, Z.
The interior point method is applied to frictionless contact mechanics problems and is shown to be a viable alternative to the augmented Lagrangian approach. The method is derived from a mixed formulation which induces a contact discretization scheme in the spirit of the mortar method and naturally delivers slack variables that help constrain the solution to the feasible region. The derivation of the algorithm as well as its robustness benefits from the contact interface description that is induced by NURBS-based isogeometric volume discretizations. Various interior point algorithms are discussed, including a primal-dual approach that satisfies the unilateral contact constraints exactly, in addition to two primal approaches that retain an arbitrary barrier parameter. The developed algorithms can easily be pursued starting from an augmented Lagrangian implementation. Numerical investigations on benchmark problems demonstrate the efficiency and the robustness of the framework, but also highlight current limitations that suggest paths for future research. Overall, the results indicate that the interior point method can challenge the augmented Lagrangian method in contact mechanics, even displaying potential for higher efficiency and robustness. © 2014 Elsevier B.V.
Open Access
A mixed formulation of mortar-based contact with friction
(Elsevier, 2013) Temizer, I.
A classical three-field mixed variational formulation of frictionless contact is extended to the frictional regime. The construction of the variational framework with respect to a curvilinear coordinate system naturally induces projected mortar counterparts of tangential kinetic and kinematic quantities while automatically satisfying incremental objectivity of the associated discrete penalty-regularized mortar constraints. Mixed contact variables that contribute to the boundary value problem are then obtained through unconstrained, lumped or constrained recovery approaches, complemented by Uzawa augmentations. Patch tests and surface locking studies are presented together with local and global quality monitors of the contact interactions in two- and three-dimensional settings at the infinitesimal and finite deformation regimes. © 2012 Elsevier B.V.
Open Access
A mixed formulation of mortar-based frictionless contact
(2012) Temizer, I.
A class of mortar-based frictionless contact formulations is derived based on a classical three-field mixed variational framework. Within a penalty regularization complemented by Uzawa augmentations, discrete mortar constraints are naturally induced by the variational setting. Major aspects of earlier mortar approaches are obtained through constrained, lumped or unconstrained recovery procedures for the mixed kinematic and kinetic mortar quantities from their projected counterparts. Two- and three-dimensional examples at the infinitesimal and finite deformation regimes highlight the local and global quality of the contact interactions. © 2012 Elsevier B.V.