Component Mode Synthesis for geometrically nonlinear structures

Component Mode Synthesis for geometrically nonlinear structures

Wenneker, F.

Tiso, P. (mentor)

Mechanical, Maritime and Materials Engineering

Precision and Microsystems Engineering

Engineering Mechanics

2013-11-11

In the field of computational physics and engineering, the introduction of computers opened a world of possibilities. The finite element method was developed in order to solve complex problems numerically. Over time, the method matured and structures in the field of engineering became more and more complex, resulting in large degree of freedom systems. Analyses on these systems can be a computationally heavy and expensive task, which led to the development of Component Mode Synthesis (CMS) techniques. These techniques generally consist of a combination of two other techniques: substructuring and Model Order Reduction (MOR). Substructuring is used to obtain the structural behaviour of large and/or complex structures by dividing them into several smaller and simpler substructures of which the structural behaviour is easier to determine. The global system is then obtained by assembly of the substructures. Using MOR, a full order model is approximated by a system of lower dimension by expressing the displacement field in terms of a set of reduced coordinates. In linear statics and dynamics problems, MOR is widely used. For nonlinear problems however, the same methods cannot be used. Two CMS techniques suitable for geometrically nonlinear structures are developed, based on the linear Craig-Bampton and Rubin methods. Both techniques use sets of component modes to approximate the displacement field. In this work, the methods are extended by adding additional component modes; modal derivatives. A modal derivative describes second-order nonlinear contributions of a vibration mode, when it is perturbed with the shape of another vibration mode. They can be systematically and cheaply computed once a reduction basis is formed for the linearised problem. The results will be presented and discussed.

Component Mode Synthesis
geometric nonlinearity
substructuring
modal derivatives
finite elements

http://resolver.tudelft.nl/uuid:eafb2041-904b-407a-b45c-55c5c7657ae7

Student theses

master thesis

(c) 2013 Wenneker, F.