Integration of Geometry and Finite Elements in the Analysis of Nonlinear Systems

Abstract eng:
In this paper, a method for the integration of computer aided design and analysis (I-CAD-A) is discussed. The method is based on using a finite element formulation that employs a kinematic description that is consistent with computational geometry methods. This allows for the development of an efficient interface between CAD systems and finite element (FE) and multibody system (MBS) software using simple linear coordinate transformation. The finite element absolute nodal coordinate formulation (ANCF) is used to successfully achieve this integration. ANCF structural finite elements, such as beams, plates, and shells, define shapes that are invariant under arbitrary rigid body displacements. It is shown in this paper that B-spline geometry can always be converted to ANCF geometry. The converse, however, is not true. ANCF provides the flexibility of selecting the basis functions, allowing for the development of finite elements with less number of degrees of freedom as compared to the B-spline counterparts. It is also demonstrated that the B-spline representation fails to capture certain type of discontinuities. To this end, C 0 discontinuities are classified as structural and non-structural discontinuities. Structural discontinuities do not allow for rigid body displacement between the finite elements, while non-structural discontinuities allow for such a rigid body displacement. Using ANCF finite elements, new FE/MBS meshes can be developed. These new FE meshes allow for describing mechanical joints that permit relative rigid body rotations using linear connectivity conditions. Furthermore, the new FE meshes have constant mass matrix and zero Coriolis and centrifugal forces despite the large relative rotation between the finite elements of the structure. Numerical results are presented in order to demonstrate the integration of CAD and FE/MBS analysis.

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