A suitable computational strategy for the parametric analysis of problems with multiple contact.

*(English)*Zbl 1062.74607Summary: The aim of the present work is to develop an application of the LArge Time INcrement (LATIN) approach for the parametric analysis of static problems with multiple contacts. The methodology adopted was originally introduced to solve viscoplastic and large-transformation problems. Here, the applications concern elastic, quasi-static structural assemblies with local non-linearities such as unilateral contact with friction. Our approach is based on a decomposition of the assembly into substructures and interfaces. The interfaces play the vital role of enabling the local non-linearities, such as contact and friction, to be modelled easily and accurately. The problem on each substructure is solved by the finite element method and an iterative scheme based on the LATIN method is used for the global resolution. More specifically, the objective is to calculate a large number of design configurations. Each design configuration corresponds to a set of values of all the variable parameters (friction coefficients, prestress) which are introduced into the mechanical analysis. A full computation is needed for each set of parameters. Here we propose, as an alternative to carrying out these full computations, to use the capability of the LATIN method to re-use the solution to a given problem (for one set of parameters) in order to solve similar problems (for the other sets of parameters).

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74M15 | Contact in solid mechanics |

74M10 | Friction in solid mechanics |

##### Keywords:

parametric uncertainties; contact; friction; non-incremental method; substructuring method; multi-resolution
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\textit{P. A. Boucard} and \textit{L. Champaney}, Int. J. Numer. Methods Eng. 57, No. 9, 1259--1281 (2003; Zbl 1062.74607)

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