Finite element formulations for nonlinear beam problems based on the absolute nodal coordinate formulation

Abstract

The spatial simulation of highly flexible bodies is becoming more effective and feasible thanks to the current state-of-the-art in the development of advanced formulations and computer processors. This makes it possible to solve problems comprising beam-like structures that undergo mechanical interactions in a flexible multibody system. A dynamic or static large deformation is a consequence of a number of sequences such as large overall motion, high-speed rotation, or mechanical elastic contact.

This dissertation focuses on the development and implementation of nonlinear finite element formulations based on the Absolute Nodal Coordinate Formulation (ANCF). The new formulations describe large overall motion accompanied by rotation and the subsequent large global or local deformations in a number of situations including the static and dynamic analyses of slender structures in application of the rotating structures and computational contact mechanics.

The general objective of this study is to provide a set of solution procedures to handle a wide range of highly nonlinear problems in the context of flexible multibody system dynamics using beam finite element in the framework of the ANCF. The particular objective of this dissertation is to introduce a pure finite element procedure to describe large deformation contact interaction between beam-like structures when the ANCF is the underlying beam finite element.