On the use of Lagrange Multiplier State-Space Substructuring in dynamic substructuring analysis

Substructuring by Lagrange Multipliers

Improved Dynamic Substructuring on

For solving the eigenvalue problem of a structural system having a large number of degrees of freedom the authors introduced in 6] the improved condensation method using the Rayleigh functional of the exactly condensed nonlinear eigenvalue problem. In this paper we discuss the implementation of the method for substructured problems on a distributed memory MIMD Computer. Examples are presented w...

Convergence of a Substructuring Methodwith Lagrange Multipliers 1

Framework The main idea of our convergence analysis is summarized in the following lemma, which we will apply to F and M from (18) and (19). Lemma 1 Let U be a nite dimensional linear space with the inner product h ; i, k kU a norm on U , and the dual norm de ned by kukU 0 = sup~ u2U hu; ~ ui=k~ ukU . Let PV : U ! V be the h ; i orthogonal projection onto V , and F;M : U ! U symmetric linear op...

Analysis of Patch Substructuring Methods

Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties ...

On the Origins of Iterative Substructuring Methods

Substructuring methods were invented in the engineering community. A very early precursor is the so called " Moment Distribution Method " , or " Hardy Cross Method " named after its inventor [11]. Cross states in the introduction to his paper from 1930 his motivation for the method: The reactions in beams, bents, and arches which are immovably fixed at their ends have been extensively discussed...