The meccano method for isogeometric solid modeling and applications

[EN]We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure...

The meccano method for simultaneous volume parametrization and mesh generation of complex solids

[EN]The meccano method is a novel and promising mesh generation method for simultaneously creating adaptive tetrahedral meshes and volume parametrizations of a complex solid. We highlight the fact that the method requires minimum user intervention and has a low computational cost. The method builds a 3-D triangulation of the solid as a deformation of an appropriate tetrahedral mesh of the meccano. The new mesh generator combines an automatic parametrization of surface triangulations, a local refinement algorithm for 3-D nested triangulations and a simultaneous untangling and smoothing procedure. At present, the procedure is fully automatic for a genus-zero solid. In this case, the meccano can be a single cube. The efficiency of the proposed technique is shown with several applications...

A new approach to solid modeling with trivariate

[EN]We present a new method to construct a trivariate T-spline representation of complex genuszero solids for the application of isogeometric analysis. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid...

Comparison of the meccano method with standard mesh generation techniques

[EN]The meccano method is a novel and promising mesh generation technique for simultaneously creating adaptive tetrahedral meshes and volume parameterizations of a complex solid. The method combines several former procedures: a mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. In this paper we present the main advantages of our method against other standard mesh generation techniques. We show that our method constructs meshes that can be locally refined by using the Kossaczky bisection rule and maintaining a high mesh quality. Finally, we generate volume T-mesh for isogeometric analysis, based on the volume parameterization obtained by the method…

The meccano method for isogeometric solid modeling

[EN]We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. The proposed technique only demands the surface of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and a simple parametric domain. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying the meccano method. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points situated both on the inner and on the surface of the solid...

Mesh Generation and Isogeometric Analysis

[EN]We present advances of the meccano method [1,2] for tetrahedral mesh generation and volumetric parameterization of solids. The method combines several former procedures: a mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. The key of the method lies in defining a one-to-one volumetric transformation between the parametric and physical domains. Results with adaptive finite elements will be shown for several engineering problems. In addition, the application of the method to T-spline modelling and isogeometric analysis [3,4] of complex geometries will be introduced…

Tetrahedral mesh optimization combining boundary and inner node relocation and adaptive local refinement

[EN]This work introduces a new technique for tetrahedral mesh optimization. The procedure relocates boundary and inner nodes without changing the mesh topology. In order to maintain the boundary approximation while boundary nodes are moved, a local refinement of tetrahedra with faces on the solid boundary is necessary in some cases. New nodes are projected on the boundary by using a surface parameterization. In this work, the proposed method is applied to tetrahedral meshes of genus-zero solids that are generated by the meccano method. In this case, the solid boundary is automatically decomposed into six surface patches which are parameterized into the six faces of a cube with the Floater parameterization...