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SUMMARYA simple and e ective algorithm for the modular construction of non-matched interfaces is presented for the partitioned solution of large-scale structural problems. The formulation is based on a recently developed four-ÿeld variational principle, which introduces a connection frame between the interfaced partitions. A key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisÿed a priori. The method is demonstrated with several 2D and 3D example problems.

We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variation-ally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.

This paper describes a novel version of the method of Lagrange multipliers for an improved modeling of multi-point constraints that emanate from contact-impact problems, partitioned structural analysis using parallel computers, and structural inverse problems. It is shown that the classical method of Lagrange multipliers can lead to a non-unique set of constraint conditions for the modeling of interfaces involving more than two or multi-point substructural interface nodes. The proposed version of the method of Lagrange multipliers leads not only to unique construction of constraints but also encounters no singularity in modeling an arbitrary number of multi-point constraints. An important utilization of the present method is in the regularized modeling of interfaces whose rigidities are radically different from one to another. The present approach is demonstrated via several examples for its simplicity in modeling constraints, ease of implementation and computational advantages.