مدلسازي نربز و توليد شبكه بر روي سطوح نربز

چكيده انگليسي :

Nurbs Modeling And Grid Generation On Nurbs Surfaces Sayed Ali Akbar Pourahmadi Babaki Sa pourahmadi@mc iut ac ir Date of Submission 2010 06 16 Department Of Mechanic Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Mahmud Ashrafi Zaadeh mahmud @cc iut ac ir Abstract Many physical and engineering problems require solving complex differential equations on a physical space For instance computational fluid dynamics and other simulation techniques can be mentioned which use numerical techniques to solve such problems The first step in using numerical techniques is the modeling of the physical space This is a formidable task for complex geometries and free shape objects In this thesis different techniques used in solid modeling are reviewed and the most advanced technique i e NURBS is presented in details NURBS is the industry de facto standard and is used in most CAD and CAM software Several techniques to generate NURBS curves surfaces and volumes have been studied and implemented in a matlab library of functions Then different techniques to arbitrarily distribute points on a NURBS curve are introduced In addition some algebraic and elliptic grid generation routines are developed to create high quality grids on NURBS surfaces The Nurbs format provides a common mathematical representation for both standard analytic shapes and free form curves and surfaces The derivatives of the physical coordinates with respect to the parametric coordinates can be evaluated directly High fidelity simulations using mesh based computational technologies such as computational fluid dynamics and computational structural mechanics are very important in providing valuable performance information of a design These simulations however require accurate geometry representation as well as high quality meshes about the design in order to obtain accurate data Unfortunately while three dimensional complex geometry is involved it is a challenge to maintain geometry fidelity while trying to obtain high quality meshes To resolve this problem we reviewed some of geometrics modelers specially Nurbs as a newest and efficient one This modeler is used in commercial systems include CAM and CAD as a standard due to its flexibility By means of Nurbs technique we can present curves surfaces and volumes and then we can extract some algorithms for generating Nurbs curve surfaces and volumes In the next step we should study appropriate distribution of nodes on the Nurbs curve which forms surface boundary of Nurbs In this part we gain some algorithm With these algorithms we can generate nodes on boundaries for grid generation Next using some algebraic methods capable us to generate initial grid on Nurbs surface Finally we will have a survey on elliptic method for grid generation For grid generation by means of elliptic method we need control functions for some states such as orthogonality smoothness concentration By using whole of algorithms with respect to aforementioned parts and referenced algorithms we write some codes in MATLAB which are capable modeling a many number of curves surfaces and volumes and generating grid on this modeled surfaces in some different states In this thesis the elliptic method for grid generation was selected In this method some control function should be considered The control functions usually are used for some cases such as orthogonality smoothness and concentration Finally a matlab code is prepared by using an aforementioned algorithm This code can model complicated surfaces and volumes and generate grid on them Keywords Nurbs Modeling Point Distribution On Nurbs Curves Structured Grid Generation Algebraic Grid Generation Arc Length Based Grid Generation Elliptic Grid Generation

پوراحمدي بابكي، علي اكبر

مدلسازي نربز و توليد شبكه بر روي سطوح نربز

توزيع نقطه روي منحني نربز , توليد شبكه بر اساس طول كمان , توليد شبكه به روش بيضوي