1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

Four decades after the development of the first dynamic substructuring techniques, there is a necessity to classify the different methods in a general framework that outlines the relations between them. In this paper, a certain vision on substructuring methods is proposed, by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept. Thereafter, based on the dual and primal assembly of substructures, a general framework for the classification of the methods is presented. This framework allows us to indicate how the various classes of methods, proposed along the years, can be derived from a clear mathematical description of substructured problems. Current bottlenecks in experimental dynamic substructuring, as well as solutions found in literature, will also be briefly discussed.

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General Framework for Dynamic Substructuring: History, Review and Classification of Techniques

https://hal.archives-ouvertes.fr/hal-01537661/document

A hybrid method of component mode synthesis

https://hal.archives-ouvertes.fr/hal-01357931/document

Nonlinear normal modes, Part I: A useful framework for the structural dynamicist

1 Formulation of the equations of motion 2 Element energy functions 3 Introduction to the finite element displacement method 4 In-plane vibration of plates 5 Vibration of solids 6 Flexural vibration of plates 7 Vibration of stiffened plates and folded plate structures 8 Vibration of shells 9 Vibration of laminated plates and shells 10 Hierarchical finite element method 11 Analysis of free vibration 12 Forced response 13 Forced response II 14 Computer analysis technique

Introduction to finite element vibration analysis

A method for treating a complex structure as an assemblage of distinct regions, or substructures, is presented. Using basic mass and stiffness matrices for the substructures, together with conditions of geometrical compatibility along substructure boundaries, the method employs two forms of generalized coordinates. Boundary generalized coordinates give displacements and rotations of points along substructure boundaries and are related to the displacement modes of the substructures known as "constraint modes." All constraint modes are generated by matrix operations from substructure input data. Substructure normal-mode generalized coordinates are related to free vibration modes of the substructures relative to completely restrained boundaries. The definition of substructure modes and the requirement of compatibility along substructure boundaries lead to coordinate transformation matrices that are employed in obtaining system mass and stiffness matrices from the mass and stiffness matrices of the substructures. Provision is made, through a RayleighRitz procedure, for reducing the total number of degrees of freedom of a structure while retaining accurate description of its dynamic behavior. Substructure boundaries may have any degree of redundancy. An example is presented giving a free vibration analysis of a structure having a highly indeterminate substructure boundary.

/pdf/coupling-of-substructures-for-dynamic-analyses-nzj32t1oao.pdf

M. C. C. Bampton

Papers

Coupling of substructures for dynamic analyses.