Research On Rational Absolute Nodal Coordinate Formulation Finite Element And The Relationship With The Nurbs Curve

Today, the computer aided design (CAD) and computer aided analysis (CAA) ofengineering are typically performed in two separate software environments. Theincompatibility makes it difficult or even impossible to preserve the same referencegeometry created in CAD systems when the finite element analysis is performed.The description used in the finite element absolute nodal coordinate formulation(ANCF) is consistent with the descriptions used in computational geometry andCAD. In propose to express circle and conics we must use its rational form. Thispaper focuses on the method of conversion from the NURBS curve to RANCF cableelement to integrate CAD and CAA so we can reduce the time cost in transformationfrom CAD parametrical geometry to CAA model and improve the efficiency ofanalysis.Based on the method that conversing a Bezier curve to ANCF finite element,use the property of the rational Bezier curve at the end points, the RANCF finiteelement is founded. The relationship between the nodal coordinates in thehomogeneous space and the ones in the Euclid space. Use the concept ofhomogeneous coordinate, the transformation from a lower-order rational Beziercurve to the RANCF finite element is explored. In this paper, the relationship isfounded which between the weights of RANCF finite element and the rational Beziercurve. These conditions are equal to the algorithm of the degree elevation of therational Bezier curve. The effect of weight coefficients on the RANCF finite elementis also been discussed, which is the difference between RANCF and ANCF finiteelement.Using the knot insert algorithm, we can transform a NURBS curve to a set ofrational Bezier curves, then we can converse a NURBS curve to some RANCF finiteelement. The research on how the continuity effect the finite element analysis is alsobe done in this paper. The B-spline representations can change the number of theknots without increase the order of the curve; get higher degree of the continuity at apoint on a curve or a surface by using the concept of the knot multiplicity. Thisconcept can be also used with the ANCF finite elements. For the cubic B-splinerepresentation, C3continuity will blend two segments together by automatically. Themethod of conversing a set of RANCF finite element to a NURBS curve is alsogiven. The progress can demonstrate that the NURBS and RANCF finite element iscompatible.The motion equations are given in this paper. Circle is been chosen andconversed to RANCF finite element. At last, reaction of the cantilever which is effected by the impact force; the rotation of the pendulum with the shape of circleare been taken as a example to demonstrate the theory in this paper and to show theaccuracy and the convergence.