Contact Problem

The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automatic-differentiation-based notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Copyright © 2010 John Wiley & Sons, Ltd.

The Children's Social Behavior Questionnaire (CSBQ) contains items referring to behavior problems seen in children with milder variants of PDD. Data of large samples of children diagnosed as having high-functioning autism, PDDNOS, ADHD, and other child-psychiatric disorders were gathered. Besides the CSBQ, parents completed the Autism Behavior Checklist (ABC) and the Child Behavior Checklist (CBCL). The data provided the basis for scale construction of the CSBQ, a comparison of the CSBQ scales with other instruments and a comparison of groups on scores on the CSBQ. The 5 scales obtained referred to Acting-out behaviors, Social Contact problems, Social Insight problems, Anxious/Rigid behaviors and Stereotypical behaviors. Results show that the CSBQ has good psychometric qualities with respect to both reliability and validity. A comparison of the different groups showed that significant group differences were found on all scales. In general, the autism group received the highest scores, followed by the PDDNOS group and the ADHD group. Exceptions were on the Acting-out scale, where the ADHD group scored highest and on the Social Insight scale, where no significant difference was found between the PDDNOS group and the ADHD group. Implications of the results and suggestions for further research are dicussed.

In this paper, a numerical method to solve the non-linear contact problem between a tyre and the road in the time domain is presented. The response of the tyre is calculated by a convolu- tion between the contact forces and the tyre's Green's functions. Influence functions for the points in the contact zone are calculated from the tyre model, and

Dynamic obstacle and Signorini problems are discretized by continuous and discontinuous finite elements in space and time. The resulting discrete problems are attributed to a standard implicit time-stepping scheme through relaxation of impact phenomena and suitable numerical integration. The method can cope with dynamic contact problems, which is shown by an analysis of a model problem. Moreover, numerical examples demonstrate that it is actually able to approximate the solution of dynamic contact problems, which are not fully covered by the theory. Copyright © 2008 John Wiley & Sons, Ltd.

A 3-D domain decomposition method for fully coupled electrothermomechanical contact problems is presented. The formulation is based on the cell method. Contacting domains are linked together by introducing a new reference frame (i.e., the mortar surface). Field discontinuities across contact interfaces are simulated by suitable constitutive operators. It is shown that the same coupling strategy can be adopted for the electrical, thermal, and mechanical contact problems. Compatibility constraints are imposed by means of dual Lagrange multipliers defined on the mortar surface. Coupled nonlinear algebraic equations are finally cast into a saddle-point problem, which is resolved by combining the Schur complement method with the Newton-Raphson method. The proposed mortar approach is validated with a commercial 3-D finite-element method multiphysics software package.

This paper deals with simultaneous topology and shape optimization of elastic contact problems. The structural optimization problem for an elastic contact problem is formulated. Shape as well as topological derivatives formulae of the cost functional are provided using material derivative and asymptotic expansion methods, respectively. These derivatives are employed to formulate necessary optimality condition for simultaneous shape and topology optimization and to calculate a descent direction in numerical algorithm. Level set based numerical algorithm for the solution of this optimization problem is proposed. Numerical examples are provided and discussed.

This article advocates a new methodology for the finite element solution of contact problems involving bodies that may undergo finite motions and deformations. The analysis is based on a decomposition of the two-body contact problem into two simultaneous sub-problems, and results naturally in geometrically unbiased discretization of the contacting surfaces. A proposed two-dimensional contact element is specifically designed to unconditionally allow for exact transmission of constant normal traction through interacting surfaces.

We use parametric cubic spline functions to develop a numerical method for computing approximations to the solution of a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. We show that the present method gives approximations which are better than those produced by other collocation, finite-difference, and spline methods. A numerical example is given to illustrate the applicability and efficiency of the new method.