Preliminaries: Primal and dual assembly of dynamic models
Book chapter, 2020

There are several ways to formulate the dynamics of a substructure. The different domains in which the dynamics can be described will be reviewed since the manner in which substructures are characterized will later determine the substructuring methodology that can be applied. In addition to how the substructures are formulated, the way in which the coupling/decoupling problem is expressed will allow us in the subsequent chapters to develop different numerical and experimental techniques. Two conditions must be satisfied on the interface between substructures: a condition on the displacement field (compatibility) and on the interface stresses (force equilibrium). Those conditions can be accounted for following several different formulations, all mathematically equivalent, but each leading to different numerical methods, experimental approaches, and approximation techniques, as will be explained in the following chapters. In this chapter, we outline the basic concepts of the so-called three-field formulation, dual and primal assembly


Matthew S. Allen

University of Wisconsin Madison

Daniel J. Rixen

Technical University of Munich

Maarten van der Seijs

Vibes Technology

Paolo Tiso

Swiss Federal Institute of Technology in Zürich (ETH)

Thomas Abrahamsson

Chalmers, Mechanics and Maritime Sciences, Dynamics

Randall L. Mayes

Sandia National Laboratories

CISM International Centre for Mechanical Sciences, Courses and Lectures


Subject Categories

Applied Mechanics

Computational Mathematics

Fluid Mechanics and Acoustics



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