Integration of Computer Aided Design and Analysis Using the Absolute Nodal Coordinate Formulation

Abstract

The goal of this study is to develop a new procedure for the integration of computer aided design and analysis (ICADA) using absolute nodal coordinate formulation (ANCF). Bezier, B-spline and NURBS are widely used as geometric description in CAD system. A new computer procedure is introduced for the integration of geometric description and the ANCF finite element analysis. The procedure is based on developing a linear transformation that can be used to transform systematically the Bezier and B-spline representation to an ANCF finite element mesh preserving the same geometry. To describe complex geometric shapes such as rational Bezier and NURBS curves that can not be described using non-rational finite element methods, a new rational absolute nodal coordinate formulation (RANCF) is used. RANCF finite elements will preserve the important properties of ANCF finite elements that allow for straight forward implementation of general nonlinear constitutive equations in the case of beam, plate and shell structures. RANCF finite elements will correctly describe arbitrary rigid body displacement and will lead to constant mass matrix by assuming that the weights that enter into the formulation of the rational functions remain constant. As a consequence, the Coriolis and centrifugal forces will be identically equal to zero in this new formulation. Using the transformation developed in this paper, the equations of motion of a finite element mesh that represents exactly the geometry used in CAD system can be developed. Such a linear transformation will facilitate the ICADA. A large strain theory is used to formulate the nonlinear elastic forces. Numerical examples are presented in order to demonstrate the use of the computer implementation of the method.