Such As Geometric Analysis Of The Nurbs Model And Algorithm

The traditional process of finite element analysis is implemented on the basis oftwo software platforms, CAD (geometric model) and CAE (analysis model)respectively. During this process, geometric CAD model is established through CADsystems, and the established design model is put into CAE software platform toproduce the analysis model. In this transformation, the geometric model undergoes arange of processing-and-generating analysis models, such as removal of details, modelsimplification, and dimensionality reduction, before taking the finite elements analysis.The designers expect that every analysis result can directly and intelligently reduce, orminimize, the modification and optimization of the guiding program with humanintervention。Whereas the current results of CAE analysis play a very limited role in themodification and optimization of these programs. So designers hope that the results ofCAE analysis can intelligently feedback to the design system and interfere the designsubsystem, so as to realize the feedback process of model transformation and analysisfrom CAE to CAD. This transformation from CAD to CAE fails to achieve the unity ofdesign model and analysis model.Given the above-mentioned problems in the mutual transformation from CAD toCAE, it is imperative to attain the unity of the design model and the analysis model, inorder to maintain the bidirectional mapping between CAD and CAE, and consequentlythe truly seamless integration between CAD and CAE. This paper proposes theisogeometric analysis which, based on the NURBS principles, constructs solid modelsvia NURBS’s powerful function of geometric modeling. Based on the basis functionsof NURBS (non-uniform rational B-spline), the isogeometric analysis expressesgeometry as certain linear combinations, and is used for precise description ofgeometric models. The node interpolation of NURBS and the ups and downs of basisfunctions’ orders are employed to generate finite element model and unit, while thenode interpolation will not alter the shape of geometry, thus abandoning the analysismodel of using mesh generator to create myopia in the traditional finite element. in other words, to construct geometric entities by NURBS can truly achieve the unity ofdesign model and analysis model.This paper mainly introduces the theory of knowledge NURBS and the basicprinciple of isogeometric analysis expressed by NURBS and its basic algorithm, andproposes the basic algorithm of NURBS-based modeling. The ternary parametersNURBS modeling technology proposed in this paper utilizes the algorithm ofcentroid parameters and the extraction of axis in the model to produce high-quality,and NURBS grids, which can be accurately expressed. Then the node interpolationand the ups and downs of basis functions’ orders allow for the division of grid and thegeneration of units, the model grids having uniform quality and the units beingcontinuants. VC++is used to develope software system,achieving the algorithms ofthe above isogeometric analysis and its NURBS implementation.