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Problemi termomeccanici di contatto - aspetti fisici e computazionali
No full textTesi di Dottorato in Meccanica delle Struttur
The shifted penalty method
No full textThe method presented here is a variation of the classical penalty one, suited to reduce penetration of the con- tacting surfaces. The slight but crucial modification concerns the introduction of a shift parameter that moves the min- imum point of the constrained potential toward the exact value, without any penalty increase. With respect to the clas- sical augmentation procedures, the solution improvement is embedded within the original penalty contribution. The problem is almost consistently linearized, and the shift is updated before each Newton’s iteration. However, adding few iterations, with respect to the original penalty method, a reduction of the penetration of several orders of magni- tude can be achieved. The numerical tests have shown very attractive characteristics and very stable solution paths. This permits to foresee a wide area of applications, not only in con- tact mechanics, but for any problem, like e.g. incompressible materials, where a penalty contribution is required
A formulation for frictionless contact problems using a weak form introduced by Nitsche
No full textIn this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of con- tact forces that are computed from the stresses in the contin- uum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of- freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces
A generalized formulation for contact between beams
Full text linkThe currently available formulations for contact between beams are based on the identification of the minimal distance points along the beam axes, followed by some tuning in case of non-circular beam cross-sections. Up to now a suitable implementation within the framework of the Finite Element Method is available both for the frictionless and for the frictional case. The procedure requires the explicit computation of the virtual work contribution due to the contacts. In such a context for solving the problem with implicit schemes, the formulation has also to be consistently linearized. With this respect both the frictionless and the frictional formulation present severe problems. To overcome all the cited problems a generalized formulation is proposed, which deals with contact between circular beams. It has to be remarked that the contact problem is treated first in a completely generic framework, and only in a second step the results are particularized to the FE formulation. For such purpose the centroids of the beams in the 3-D space are considered as parametric functions. The framework for the consistent linearization is developed in a very rigorous and systematic way, providing evidence of the symmetry of the operators. The procedure is quite cumbersome, hence here only the most heavy part, related to the computation of all the fundamental geometrical terms involved, is presented
Trends in Computational Contact Mechanics
No full textContact mechanics is a science that has a great impact on everyday life and is present in many different fields. These include civil, mechanical and environmental engin- eering, but also medicine since locomotion as well as functional joints do not work without friction. In one application friction is needed – like traction of car tyres – and in another application friction produces wear and costs – like in bearings. Thus it is of the utmost interest to have reliable and efficient methods and associated ana- lysis tools that can be applied to a vast range of contact problems.
Using the power of today’s computers many complex contact problems can be solved with numerical simulation tools. Despite the progress that has been reached with respect to the implementation of contact algorithms in commercial codes, vivid research is still going on in the area of contact mechanics. Thus, within the last years, computational contact mechanics has been a topic of intense research. The aim of the development is to devise robust solution schemes and new discretization techniques, which can be applied to different problem classes in engineering and science.
These are wide-ranging and include computational aspects of discretization tech- niques using finite and boundary element methods. Special solution algorithms for single- and multi-processor computing environments are of great interest for efficient solutions. Furthermore, multi-scale approaches have been applied suc- cessfully to contact problems and multi-field formulations were used for thermo- mechanical or electro-thermo-mechanical applications involving contact. Discrete element models include always contact and pose a challenge for the numerical treat- ment due to the high number of particles. Finally, problems like rolling wheels and tyres need special contact formulations and special algorithmic approaches.
Technical applications incorporate different interface problems. Examples are failure processes in heterogeneous materials, textile and laminated composites, in- teraction between road and tyres, hip implants or artificial knee joints as well as spraying of particles on surfaces and impact analysis of cars.
The present book summarizes work in the area of computational contact mechanics that was presented at the 1st International Conference on Computational Contact Mechanics in Lecce, Italy. The authors discuss different theoretical methodologies, algorithms for the solution of contact problems and apply these to different engineering problems
On the efficiency of new and old strategies for solving contact problems
No full textThe most recent progresses in the field of numerical treatment of contact problems permit to obtain high eficiency with a close correlation to the microscopical characteristics of the contact surfaces. In this paper a modification of standard strategies to satisfy contact constraintsispresented which yields a non-linear, srnaooth change of contact stiffness around the solution. Thus the adopted approach leads to an iterative method which does not depict numerical instabilities within the solution search process. This fact permits to achieve a better convergence rate with respect to standard methods
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