دانلود رایگان مقاله تحلیل المان مرزی ایزوهندسی برای مساله مقاومت موج با T اسپلاین

Abstract

In this paper we couple collocated Boundary Element Methods (BEM) with unstructured analysis-suitable T-spline surfaces for solving a linear Boundary Integral Equation (BIE) arising in the context of a ship-hydrodynamic problem, namely the so-called Neumann–Kelvin problem, following the formulation by Brard (1972) and Baar and Price (1988). The local-refinement capabilities of the adopted T-spline bases, which are used for representing both the geometry of the hull and approximating the solution of the associated BIE, in accordance with the Isogeometric concept proposed by Hughes et al. (2005), lead to a solver that achieves the same error level for many fewer degrees of freedom as compared with the corresponding NURBS-based Isogeometric-BEM solver recently developed in Belibassakis et al. (2013). In this connection, this paper makes a step towards integrating modern CAD representations for ship-hulls with hydrodynamic solvers of improved accuracy and efficiency, which is a prerequisite for building efficient ship-hull optimizers

6. Conclusions

In this work, we have demonstrated the advantages of T-splines technology in the context of the ship wave resistance calculation. The higher smoothness of the bases for a single T-spline surface along with the ability for local refinement allowed us to achieve enhanced convergence rates with considerably fewer degrees of freedom when compared to our prior NURBS approach. For the prolate spheroid example, the T-spline based local refinement process requires considerably fewer degrees of freedom compared to the corresponding NURBS-based global refinement process (e.g., for an error of 5.5 × 10−4 the required degrees of freedom are approximately 600 for T-spline vs. 1600 for the corresponding NURBS representation, i.e., a reduction of 62.5%; see Fig. 6). The exact same picture is drawn from our second example, i.e., the ship hull. This significant enhancement permits our T-spline based IGA-BEM solver to be embedded with significantly lower cost in any optimization process for designing ship hulls with minimum wave resistance; see, e.g. [37]. Future work will focus on this direction as well as on the extension of the methodology to treat effects of nonlinearities in the wave resistance problem.