دانلود رایگان مقاله تکمیل حجم ترکیبی با عناصر بزیر مرتبه بالاتر

Abstract

This paper proposes a methodology to create a hybrid volumetric representation from a 2-manifold without boundaries represented with untrimmed B-spline surfaces. The product consists of trivariate tensor product B-splines near the boundary and unstructured higher-order Bézier tetrahedral elements in the interior of the object with C0 smoothness across their interfaces. The B-spline elements are constructed by offsetting the input surface into its interior. Then, an intermediate interface consisting of Bézier triangles is built to match the inner boundary of the B-spline representation. The rest of the space, bounded by the intermediate interface, is then filled with unstructured Bézier tetrahedral elements. Our approach to constructing stiffness and mass matrices takes into account the dependencies of interior Bézier tetrahedral elements on exterior B-spline elements along their interface, so that C0 smoothness is automatically maintained when performing computer graphics simulations, representing material properties, or performing isogeometric analysis. We apply our methodology on a variety of 3-D objects and demonstrate a fast convergence rate with our 2-D studies.

6. Conclusion

In this paper we present a framework to create a hybrid volumetric representation as a generalization of Martin et al. (2012a). The product consists of trivariate B-spline elements on the exterior and unstructured higher-order Bézier tetrahedral elements in the interior of the object. The B-spline representation can be constructed by offsetting the boundary inward in a variety of ways. The rest of the space is then filled with Bézier tetrahedral elements whose boundaries match an intermediate surface consisting of Bézier triangles extracted from the inner surface of the B-spline representation. Our approach maintains a C0 continuity across the common boundary between exterior and interior mesh by including the interface constraints in the construction of stiffness and mass matrices. The resulting hybrid volumetric representation is feasible for representing complex materials and properties and isogeometric analysis simulations. It is a geometry completion and overcomes the problems of gaps and overlaps in Martin et al. (2012a). It is more general than Sevilla et al. (2008) and Sevilla et al. (2011) in that it provides for simulations with smoothly adjacent hexahedra near the boundary. Our test cases demonstrate that it improves the convergence rate and has a more stable behavior during simulations (Fig. 2).