## New Finite Element Mesh for Efficient Modeling of Spatial Flexible Link Articulated Systems

thesis

posted on 05.11.2016 by Ashraf M. Hamed#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

This work introduces new FE/MBS meshes that employ linear connectivity conditions and allow for arbitrarily large rigid body displacements between the finite elements. A linear formulation of rotational joints is systematically obtained using the absolute nodal coordinate formulation finite elements. The algebraic joint constraint equations are introduced at a preprocessing stage to efficiently eliminate dependent coordinates. The proposed joints allow for joint deformation modes, and therefore, this joint formulation can be considered a generalization of the pin joint formulation used in rigid MBS analysis. The proposed joint deformation modes allow for the calculations of the joint strains which can be discontinuous as the result of the finite relative rotation. Because ANCF finite elements lead to a constant mass matrix, an identity generalized mass matrix can be obtained for the FE mesh despite the fact that the finite elements of the mesh are not rigidly connected. The new linear flexible chain meshes are used for the modeling of different MBS models including flexible belt chains and a typical flexible link tracked vehicle. The constant inertia and the linear connectivity conditions lead to significant reduction in the dimensions and the number of non-zero entries of matrices that are used at the position, velocity, and acceleration analysis steps. This dissertation also examines the limitations of using B-spline representation as an analysis tool by comparing its geometry with the ANCF geometry. It is shown that while both B-spline and ANCF geometries can be used to model non-structural discontinuities, there are fundamental differences between B-spline and ANCF geometries. First, while B-spline geometry can always be converted to ANCF geometry, the converse is not true; that is, ANCF geometry cannot always be converted to B-spline geometry. Second, the rigid structure of the B-spline recurrence formula restricts the order of the basis functions used in the polynomial interpolation. This leads to models with significantly larger number of degrees of freedom as compared to those obtained using ANCF. Third, in addition to the known fact that B-spline does not allow for straightforward modeling of T-junctions, B-spline representation cannot be used in a straightforward manner to model structural discontinuities.