Research On Rational Absolute Nodal Coordinate Formulation Finite Element And Its Relationship With The NURBS Surface

Scientific researchers had developed numerous computational geometrictechnologies in the past decades. These geometric descriptions mostly can improvethe integration between the CAD and CAA (I-CAD-A). The most useful geometricdescriptions in the engineering design is the Non-Uniform Rational B-Spline(NURBS). However, due to the distinction between the geometric descriptionmethods in CAA software and CAD software, it is inconvenient for the interactiveengineering design and analysis. This dissertation is an extended study of the new I-CAD-A method, the integration between ANCF and NURBS.This dissertation represents and proved the linear transformation matrix betweenthe ANCF finite surface element and the i×j (i+j <6, i,j3,i,j∈N~＋)Bezier tensionproduct surface based on the established transformation matrix between the ANCFcable element and the Bezier curve. The transformation matrix describes the linearrelationship between the ANCF nodal coordinates and the control points of Beziersurface. This transformation matrix can be used in the conversion between ANCFsurface element and all i×j (i+j <6, i,j3,i,j∈N~＋)Bezier tension product surface.It is a general transformation matrix. The general transformation matrix and itsinverse matrix can convert the geometric configuration described in CAD to the CAAwithout any distortion and can convert the distorted geometric configuration in CAAsoftware due to internal or external force back to the CAD software.Because the B-spline tension product surface can be regarded as a piecewiseBezier tension product surfaces, this dissertation represents the transformation matrixbetween the ANCF finite surface element and the i×j (i+j <6, i,j3,i,j∈N~＋)B-splinetension product surface based on the established linear transformation matrix betweenthe ANCF and the Bezier surfaces. This transformation matrix is not in a recursiveform but in a more visible numerical form. After that, this dissertation established theRANCF finite surface element. The RANCF finite surface element maintains theRational Bezier surface definition structure and one can control the configuration ofRANCF geometry by moving the RANCF nodal coordinates. The establishment ofRANCF extends the capability of ANCF on geometric description, which improvesthe integration between ANCF and NURBS.At last, because the NURBS tension product surface can be regarded as apiecewise rational Bezier tension product surfaces, PRANCF finite surface elementcan be obtained based on the established RANCF finite surface element. Thisdissertation gives the explanation of the relationship between NURBS and PRANCFsurfaces. One can obtain the PRANCF finite surface element through RANCF surfacematching.