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 Re: [Geopdes-users] Second derivatives of nurbs basis functions From: Rafael Vazquez - 2012-11-26 09:39:55 ```Dear Lee, there is a new PhD student in Pavia that has just started the implementation of second order derivatives in GeoPDEs, with an example of a fourth order problem. As soon as the code is ready and tested we will release it, but It will take some time. If you want to do it yourself, it should not be difficult. In 2D, the second derivatives are already computed for a spline space with a NURBS geometry. For NURBS, you should add the computation of the second derivatives in the parametric domain in the functions bsp_2_nrb_*. The derivatives in the physical domain are computed as in the case of splines. And please, feel free to give me any comment or suggestion about version 2. Feedback from the users is very welcome. Regards, Rafa Il 25/11/2012 15:52, 李新康 ha scritto: > Dear Rafael Vazquez, > These days I am thinking on how to compute the second derivative of nurbs basis functions. I notice in GeoPDEs 1.0(I still use GeoPDEs version 1.0 because I think it is less difficult to understand than version 2), there are functions 'sp_bspline_2d_param' and 'sp_bspline_2d_phys' that can compute the second derivative of nurbs basis functions in parametric domain and physics domain respectively by making the option 'hessian' true, however, there's no function compute the second derivative of nurbs functions. > There are some mechanics problems need the second derivative of nurbs basis functions, such as Kichhoff plate problem. I find it is too difficult for me to add a function myself, so I ask for your help. Could you add a function in GeoPDEs that can get the hessian matrix of Gauss quadrature points in physical domain in structure 'sp', something like sp_nurbs_2d_phys(sp,msh,'gradient',ture,'hessian,true') and then we can get 'sp.shape_function_hessians' in structure 'sp'? > I am very appreciate for your help. > Thank you very much! > > > Yous sincerely, > Lee > ```
 [Geopdes-users] Second derivatives of nurbs basis functions From: 李新康 - 2012-11-25 14:52:48 ```Dear Rafael Vazquez, These days I am thinking on how to compute the second derivative of nurbs basis functions. I notice in GeoPDEs 1.0(I still use GeoPDEs version 1.0 because I think it is less difficult to understand than version 2), there are functions 'sp_bspline_2d_param' and 'sp_bspline_2d_phys' that can compute the second derivative of nurbs basis functions in parametric domain and physics domain respectively by making the option 'hessian' true, however, there's no function compute the second derivative of nurbs functions. There are some mechanics problems need the second derivative of nurbs basis functions, such as Kichhoff plate problem. I find it is too difficult for me to add a function myself, so I ask for your help. Could you add a function in GeoPDEs that can get the hessian matrix of Gauss quadrature points in physical domain in structure 'sp', something like sp_nurbs_2d_phys(sp,msh,'gradient',ture,'hessian,true') and then we can get 'sp.shape_function_hessians' in structure 'sp'? I am very appreciate for your help. Thank you very much! Yous sincerely, Lee ```
 [Geopdes-users] A new GeoPDEs package for T-splines From: Rafael Vazquez - 2012-11-05 11:31:51 ```Dear GeoPDEs users, I am happy to announce the release of a new GeoPDEs package that supports T-splines. This new package offers the possibility to import a T-spline geometry designed with the Autodesk T-spline plug-in for Rhino3D, and saved in the new file format available in the plug-in, which is based on Bezier extraction. As usual, the package can be downloaded from the GeoPDEs webpage: http://geopdes.sourceforge.net The new package includes some simple examples, to show how the two main data structures of GeoPDEs, msh and space, can be computed from Bezier extraction. Other features of GeoPDEs, such as exporting the results to VTK format or computing the error in L2 and H1 norm, have been also adapted to Bezier extraction. For now the T-spline capability of GeoPDEs is restricted to planar surfaces, and all the examples are written for the scalar Laplacian. If you are interested in developing (and sharing) further extensions of the package, feel free to contact me for help. I attach below an e-mail from Mike Scott with more information about the Autodesk T-spline plug-in for Rhino3d, and a link to the beta-version. Regards, Rafael Vazquez Dear IGA Researchers, In an effort to make T-spline-based IGA technology more accessible to the academic community we have attached a link to the new beta-version of the IGA-capable Autodesk T-spline plugin for Rhino3d. Included are free 32 and 64-bit installers for the plugin as well as a write-up of the new IGA-related commands and an introduction to the underlying technology. We have also included a directory of geometries which have appeared in past T-spline/IGA papers and which you can use to explore the functionality of the plugin. http://www.ices.utexas.edu/~mscott/tsiga_plugin.zip Note that all Autodesk products are free to academic researchers. This means that as the plugin moves from beta to release it will remain free. Rhino however is not free but has very reasonable academic pricing. The next release of the T-spline plugin for Rhino will be happening in the next few weeks so check tsplines.com in the coming weeks to get the official release. I hope this proves helpful in your own IGA-related research and we look forward to your feedback as we continue to improve and expand these capabilities. Best Regards, Mike Scott, Tom Hughes, Tom Sederberg, and Matt Sederberg Michael A. Scott Assistant Professor Civil and Environmental Engineering Brigham Young University 370 Clyde Building Provo, UT 84602 U.S.A office: (801) 422-6324 cell: (512) 538-8224 michael.scott@... http://users.ices.utexas.edu/~mscott ```

Showing 3 results of 3