Integrated mechanically based CAE system using B-Spline finite elements

Abstract In a product development cycle interaction between design and analysis should be very intensive. However, currently existing Computer Aided Engineering systems substantially limit such interaction, since design and analysis are realized in them as two isolated modules. These limitations can be distinguished on two levels: the conceptual and the technical. On the conceptual level a gap exists according to the functionality of each module: the design module is based on purely geometric operations, while the analysis module is based on physical phenomena. On the technical level an environmental gap exists that is characterized by differences in mathematical representation and computational methods. This is partially dictated by the functionality of each module. As a result of these limitations, each iteration between design and analysis and vice versa requires remodeling of the object and conversion of its mathematical representation. In order to overcome these problems, a mechanical B-Spline finite element model is proposed in this work to be used for both geometric design and mechanical analysis. With this approach the target object is modeled as a physical entity from the very beginning of the geometric design stage. Furthermore, both modules utilize the same computational environment—B-Spline finite element, and the same representational environment—B-Spline representation. Therefore, design and analysis are tightly integrated into a completely unified system, and corresponding analysis operations can be performed simultaneously with the geometric design. Technically, this eliminates remodeling and conversion operations between the design and analysis stages of the product development cycle. Conceptually, this allows engineers to substantially shorten the product development cycle time, test many more design variants, tune the final product more finely according to its functionality and reduce the total product development cost. A few examples verifying feasibility and demonstrating performance of the proposed system are presented in the paper. These are developing sculptured surface objects based upon an elastic linear plate model and developing sculptured solid objects based upon an elastic linear solid model.

[1]  Andrew P. Witkin,et al.  Spacetime constraints , 1988, SIGGRAPH.

[2]  D. Thalmann,et al.  Deformable surfaces using physically based particle , 1995 .

[3]  Arie Jacobi,et al.  Minimization, constraints and composite Bézier curves , 1994, Comput. Aided Geom. Des..

[4]  Anath Fischer,et al.  New B‐Spline Finite Element approach for geometrical design and mechanical analysis , 1998 .

[5]  D. Deitz.  One-stop design and analysis , 1997 .

[6]  T. Y. Yang,et al.  A new 48 d.o.f. quadrilateral shell element with variable-order polynomial and rational B-spline geometries with rigid body modes , 1984 .

[7]  S. C. Fan,et al.  A Nine-Node Spline Element Folk Free Vibration Analysis of General Plates , 1993 .

[8]  Simon Wang,et al.  A UNIFIED TIMOSHENKO BEAM B‐SPLINE RAYLEIGH–RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES , 1997 .

[9]  Alex Pentland,et al.  Good vibrations: modal dynamics for graphics and animation , 1989, SIGGRAPH.

[10]  B. Barsky,et al.  An Introduction to Splines for Use in Computer Graphics and Geometric Modeling , 1987 .

[11]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[12]  Hong Qin,et al.  Dynamic NURBS with geometric constraints for interactive sculpting , 1994, TOGS.

[13]  David Baraff,et al.  Analytical methods for dynamic simulation of non-penetrating rigid bodies , 1989, SIGGRAPH.

[14]  David C. Gossard,et al.  Multidimensional curve fitting to unorganized data points by nonlinear minimization , 1995, Comput. Aided Des..

[15]  Demetri Terzopoulos,et al.  Modeling inelastic deformation: viscolelasticity, plasticity, fracture , 1988, SIGGRAPH.

[16]  Avinash C. Kak,et al.  Deforming virtual objects interactively in accordance with an elastic model , 1996, Comput. Aided Des..

[17]  A. M. Davies.  A numerical investigation of errors arising in applying the galerkin method of the solution of nonlinear partial differential equations , 1977 .

[18]  George Celniker,et al.  Deformable curve and surface finite-elements for free-form shape design , 1991, SIGGRAPH.

[19]  Dimitris N. Metaxas,et al.  Dynamic deformation of solid primitives with constraints , 1992, SIGGRAPH.

[20]  David E. Breen,et al.  Predicting the drape of woven cloth using interacting particles , 1994, SIGGRAPH.

[21]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[22]  Ricki Blau,et al.  Approximate and probabilistic algorithms for shading and rendering structured particle systems , 1985, SIGGRAPH.

[23]  Andrew P. Witkin,et al.  Free-form shape design using triangulated surfaces , 1994, SIGGRAPH.

[24]  Parris K. Egbert,et al.  Vector Fields: an Interactive Tool for Animation, Modeling and Simulation with Physically Based 3D Particle Systems and Soft Objects , 1994, Comput. Graph. Forum.

[25]  Elaine Cohen,et al.  Physical modeling with B-spline surfaces for interactive design and animation , 1990, I3D '90.

[26]  Andrew P. Witkin,et al.  Variational surface modeling , 1992, SIGGRAPH.

[27]  Ronen Barzel,et al.  A modeling system based on dynamic constraints , 1988, SIGGRAPH.