Modélisation simplifiée d'assemblages par éléments équivalents

Abstract : Nowadays, numerical simulation has become a mandatory tool to design and optimise industrial parts. Even though the progress made in terms of computational resources have been tremendous, simulations are getting increasingly complex and thus ever more "memory and CPU greedy". All these issues have to be considered in the field of assembly. Indeed, modelling each assembly point with a non negligible number of nodes and elements would make the CPU cost explode because running a simulation of assemblies containing a high number of assembly points (e.g. plane, car, bridge, etc.) fully modelled would lead to solve many local non-linear problems such as contact problems, large deformations, plastic and damage behaviour, etc. A new way to carry out such simulations - while keeping at the same time reasonable CPU and memory needs - is then required. The idea is to create an equivalent element which would therefore be used in replacement of each assembly point and thus provide simplification in the treatment of each simulation. Although this element simplifies the model, it has to model as closely as possible all the non-linear mechanical behaviour and the geometrical properties of the initial assembly point. Several representation are presented including a virtual representation built with the default finite elements when two plates are simply put in contact. The aim of this equivalent element is to model one part of a structure containing an assembly point by a simplified part (e.g. beam element, spring, etc.) integrating a maximum of information about the nature of this part (mechanical properties, geometry, etc.) with respect to the local and global elastic plastic behaviour of the structure. An equivalent damage evolution law to model the rupture of the assembly point is also developped within the virtual representation. First of all, a complete model to help define properly the equivalent element must be introduced. This model depends on the materials (with a specific elastic plastic behaviour) and the geometry considered. The thermo-mechanical past due to the assembly point insertion is considered. The equivalent element's behaviour is then identified using F/d or C/d curves from the complete model through an optimisation step whose goal is to minimise a cost function representing the least square error between the complete and equivalent F/d an C/a curves. Eventually, an additional simplification of the assembly point - faster but less precise - has been elaborated using the connectors concept. A condensation of the virtual element to construct this connector is done through the use of all the results coming from former virtual representation's simulations. All these representations are validated on multipoint assemblies cases by comparing numerical and experimental results.
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Submitted on : Wednesday, December 30, 2009 - 10:59:48 AM
Last modification on : Monday, November 12, 2018 - 11:01:53 AM
Long-term archiving on : Thursday, June 17, 2010 - 10:12:40 PM

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  • HAL Id : tel-00443533, version 1

Citation

Maxime Berot. Modélisation simplifiée d'assemblages par éléments équivalents. Mécanique [physics.med-ph]. École Nationale Supérieure des Mines de Paris, 2009. Français. ⟨tel-00443533⟩

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