The meccano method for finite element and isogeometric analysis

The Meccano Method for Finite Element and Isogeometric Analysis R. Montenegro (1)*, J.M. Cascón(2), E. Rodríguez(1), J.M. Escobar(1), M. Brovka(1), J.I. López(1), J. Ramírez(1) (1) University Institute for Intelligent Systems and Numerical Applications in Engineering, SIANI, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain, {rmontenegro,erodriguez,jmescobar}@siani.es, [email protected], [email protected], [email protected], http://www.dca.iusiani.ulpgc.es/proyecto2012-2014. (2) Department of Economics and History of Economics, Faculty of Economics and Management, Univ. of Salamanca, Spain, [email protected], http://campus.usal.es/~sinumcc. Abstract In this work we present the application of the meccano method [1] to solid modelling to be used in finite element and isogeometric analysis [2]. We will show the resolution of elliptic and parabolic PDE in three-dimensional complex domains. The discretization of the solid is obtained by constructing a volumetric parameterization of the solid. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a simultaneous mesh untangling and smoothing procedure. In the case of isogeometric analysis, the geometric approximation of the solid and the numerical solution have been accomplished by using T-splines that enables the local refinement. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited on the inner and the surface of the solid, and using the volumetric parameterization. Three-dimensional isogeometric analysis examples for complex solids are presented. In addition, we compare finite element and isogeometric solutions for several two-dimensional examples by using local adaptive strategies. References [1] R. Montenegro, J.M. Cascón, J.M. Escobar, E. Rodríguez, G. Montero, An automatic strategy for adaptive tetrahedral mesh generation, Applied Numerical Mathematics 59 (2009) 2203–2217. [2] J.M. Escobar, J.M. Cascón, E. Rodríguez, R. Montenegro, A new approach to solid modeling with trivariate T-splines based on mesh optimization, Comput. Methods Appl. Mech. Engrg. 200 (2011) 3210–3222.