Multiple scaling method for the calculation of threaded assemblies

Abstract The numerical computation of threaded structures usually leads to very large finite elements problems. We propose here a new method mixing FE small problems and a unidimensional elliptic problem to drastically reduce the computing costs. The method is based on the decomposition of the problem into two different problems stated over two different scales. The local one, involving only the detailed geometry of one thread is solved by standard finite element procedure, whereas the global one is unidimensional and allows parametric studies. The initial problem being very non-linear and involving several small parameters, the separation of the two sub-problems is postulated rather than deduced by asymptotic methods. Some results on the existence and uniqueness of the global solution are outlined before its discretization is detailed. Several significant situations are compared with direct FE computations of the initial problem for the linear case. Applications with elasto-plastic constitutive laws and unilateral sliding contact conditions on the threads are also dealt with.