Adaptive multi-analysis strategy for contact problems with friction

Abstract

The objective of the work presented here is to develop an efficient strategy for the parametric analysis of bolted joints designed for aerospace applications. These joints are used in elastic structural assemblies with local nonlinearities (such as unilateral contact with friction) under quasi-static loading. Our approach is based on a decomposition of an assembly into substructures (representing the parts) and interfaces (representing the connections). The problem within each substructure is solved by the finite element method, while an iterative scheme based on the LATIN method (Ladeveze in Nonlinear computational structural mechanics—new approaches and non-incremental methods of calculation, 1999) is used for the global resolution. The proposed strategy consists in calculating response surfaces (Rajashekhar and Ellingwood in Struct Saf 12:205–220, 1993) such that each point of a surface is associated with a design configuration. Each design configuration corresponds to a set of values of all the variable parameters (friction coefficients, prestresses) which are introduced into the mechanical analysis. Here, instead of carrying out a full calculation for each point of the surface, we propose to use the capabilities of the LATIN method and reutilize the solution of one problem (for one set of parameters) in order to solve similar problems (for the other sets of parameters) (Boucard and Champaney in Int J Numer Methods Eng 57:1259–1281, 2003). The strategy is adaptive in the sense that it takes into account the results of the previous calculations. The method presented can be used for several types of nonlinear problems requiring multiple analyses: for example, it has already been used for structural identification (Allix and Vidal in Comput Methods Appl Mech Eng 191:2727–2758, 2001).