Substructured formulations of nonlinear structure problems - influence of the interface condition

Abstract

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is usally too expensive to be computed exactly in practice: an approximate version has to be sought, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

Non-invasive global–local coupling as a Schwarz domain decomposition method: acceleration and generalization

“…which was investigated in nonlinear relocalization techniques [14][15][16]38], but which is in general not possible in the non-invasive framework. Anyhow, in the case of a linear Global model, it is possible to derive a quasi-Newton approach.…”

“…In [12] the method was used in order to implement a nonlinear domain decomposition method [13][14][15][16] in a non-invasive manner with Code_aster. The extension of the approach to explicit dynamics was proposed in [17], improved in [18] and applied to the prediction of delamination under impact in [19].…”

A new impedance accounting for short‐ and long‐range effects in mixed substructured formulations of nonlinear problems

“…Let neigh( j ) be the set of the neighbors of subdomain j , we have or even Being an assembly among a few subdomains of sparse block‐diagonal matrices, this term is quite cheap to compute and does not require any extra‐computations, since local tangent stiffnesses are calculated anyway at each iteration of the solving process. The efficiency of the simple approximation has been studied in the context of nonlinear substructuring and condensation in some research works() and has given good results when tested on rather homogeneous structures of standard shape.…”

“…In the mechanical context, for instance, a common short‐scale approximation can be built by assembling interface stiffness of the neighbors. ()…”

“…[5][6][7][8][9] This article focuses on the nonlinear substructuring and condensation method, which has been investigated in previous studies. [10][11][12][13] The substructured formulation involves a choice of interface transmission conditions, which can be either primal, dual, or mixed, referring either to interface displacements, nodal interface reactions, or a linear combination of the 2 previous types, ie, Robin interface conditions. In this context, the mixed formulation has shown good efficiency, [13][14][15][16] mostly due to a sound choice of the parameter introduced in the linear combination of interface conditions.…”