Keywords: nonlinear soil-structure interaction, domain decomposition, iterative coupling, interface relaxation, parallel algorithms, condensed tangent stiffness.

One of the generic classes of coupled systems in the field of civil engineering relates to modelling of soil-structure interaction problems, where due to the interaction between soil and structure subdomains at the interface, neither domain can be solved separately from the other without undue simplification, especially in the nonlinear range of response. Although coupled modelling of soil-structure interaction problems, may be achieved using a monolithic treatment, with the whole problem modelled as a single computational entity, a partitioned treatment, with different fields modelled as separate computational entities amongst which interaction effects are communicated offers major benefits in the context of nonlinear soil-structure interaction. Such benefits include i) allowing field-specific discretisation and solution procedures that have proven performance for each partitioned domain, ii) facilitating the reuse of existing nonlinear analysis software with all the resource savings that this brings, and iii) enabling parallel computations through problem partitioning [1,2].

Here, it is assumed that the soil-structure coupled system is divided into soil and structure subdomains, which are independently modelled. The interface interaction effects between the subdomains are then considered by applying the sequential and parallel Dirichlet-Neumann iterative coupling. The proposed solution scheme couples the response of the soil and structure subdomains by enforcing explicitly a compatibility and equilibrium condition at the interface. The treatment of separation and slip can be undertaken as a simple extension of the discussed approach through the use of interface elements that may be considered to be either part of one of the subdomains or part of the interface model. Different mathematical and computational characteristics of the coupling algorithms, including the governing convergence conditions, convergence rate and choice of algorithmic parameters have been investigated.

A new approach has been proposed for enhancing the performance of iterative coupling algorithms in coupled nonlinear analysis, which is based on use of the condensed interface tangent stiffness of the structure and soil model, depending on the variant coupling algorithms under consideration. Indeed, the proposed approach brings the numerical performance of the partitioned treatment close to the monolithic treatment, whilst maintaining the practical and computational benefits of the partitioned approach. The proposed methods will be generally applicable to the coupling of various computational procedures that are used in nonlinear soil-structure interaction analysis. In this context, these methods have the potential to provide an integrated interdisciplinary computational approach which combines the advanced features of both structural and geotechnical modelling for a variety of challenging problems in the field of nonlinear soil-structure interaction.

1

C.A. Fellippa, K.C. Park, C. Farhat, "Partitioned Analysis of Coupled Mechanical Systems", Computer methods in applied mechanics and engineering, 190, 3247-3270, 2001. doi:10.1016/S0045-7825(00)00391-1

2

C.H. Lai, "Diakoptics, Domain Decomposition and Parallel Computing", The Computer Journal, 37, 840-846, 1994. doi:10.1093/comjnl/37.10.840

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